Reading & Writing Process
Students will use a variety of recursive reading and writing processes.
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Khan Academy CCSS Lesson Links
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Subtract polynomials (intro) - Example: Evaluate (4x²-3) - (3x³-3x+2).
https://www.khanacademy.org/e/subtract-polynomials
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Multiply monomials by polynomials: area model - Use area to understand how to multiply monomials by polynomials.
https://www.khanacademy.org/e/multiply-monomials-by-polynomials-intuition
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Add & subtract polynomials - Example: Subtract -2x²+4x-1 from 6x²+3x-9.
https://www.khanacademy.org/e/add---subtract-polynomials-challenge
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Multiply monomials by polynomials - Use the distributive property to express the product of a monomial and a polynomial as a single polynomial.
https://www.khanacademy.org/e/finding-the-product-of-a-monomial-and-a-polynomial
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Multiply monomials - More challenging multiplying monomial problems like find the area or find missing values to make an equation true.
https://www.khanacademy.org/e/multiply-monomials-challenge
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Multiply binomials by polynomials - Use the distributive property to express the product of a binomial and a polynomial as a single polynomial.
https://www.khanacademy.org/e/multiplying_polynomials
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Add polynomials (intro) - Example: Add (2x²-3) and (7x³-4x+1).
https://www.khanacademy.org/e/adding_and_subtracting_polynomials
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Multiply binomials - Multiply binomials of the form (ax + b).
https://www.khanacademy.org/e/multiply-binomials-coefficient
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Add & subtract polynomials: two variables - Example: Subtract aâ´+4a²b²-2bâ´ from -3aâ´+5a^2b²+2bâ´.
https://www.khanacademy.org/e/add---subtract-polynomials--two-variables-challenge
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Special products of binomials intro - Find perfect squares of the forms (x+a)² and (x-a)², and differences of squares of the form (x+a)(x-a).
https://www.khanacademy.org/e/multiplying_expressions_1
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Multiply binomials intro - Use the distributive property to express the product of two binomials as a single polynomial.
https://www.khanacademy.org/e/multiplying_expressions_0.5
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Multiply monomials by polynomials challenge - Example: Find the values of the variables to make the following equation true -11(y²-cy+2) = dy²+33y-f.
https://www.khanacademy.org/e/multiply-monomials-by-polynomials-challenge
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Add & subtract polynomials: two variables (intro) - Example: Subtract (x²+2xy-y) and (3x+5xy+2y²).
https://www.khanacademy.org/e/adding-and-subtracting-polynomials-2
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Add & subtract polynomials: find the error - Choose which step an error was made in adding or subtracting polynomials.
https://www.khanacademy.org/e/add---subtract-polynomials--find-the-error
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Special products of binomials - Find special products (perfect squares and difference of squares) of "advanced" binomials: binomials with leading coefficients other than 1; binomials with higher degrees; and binomials with two variables.
https://www.khanacademy.org/e/finding-special-products
Standard APR.1
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Multiply monomials intro - Express the product of two monomial expressions as a single monomial
https://www.khanacademy.org/e/finding-the-product-of-two-monomials
Standard APR.2
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Use the Polynomial Remainder Theorem - Use the PRT (Polynomial Remainder Theorem) to determine the factors of polynomials and their remainders when divided by linear expressions.
https://www.khanacademy.org/e/remainder-theorem-of-polynomials
Standard APR.3
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Find zeros of polynomials - Use various methods in order to find all the zeros of polynomial expressions or functions.
https://www.khanacademy.org/e/find-the-zeros-of-polynomials
Standard APR.3
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard APR.3
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Positive & negative intervals of polynomials - Given a polynomial, determine the intervals in which it is positive or negative.
https://www.khanacademy.org/e/positive-and-negative-intervals-of-polynomials
Standard APR.4
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Prove polynomial identities - Determine whether given polynomial identities are true, and whether given proofs of such identities are valid.
https://www.khanacademy.org/e/polynomial-identities
Standard APR.5
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Expand binomials - Use the binomial theorem in order to expand integer powers of binomial expressions.
https://www.khanacademy.org/e/binomial-theorem
Standard APR.6
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Simplify rational expressions (advanced) - Factor the numerator and the denominator of a rational expression using advanced methods, and cancel out common terms.
https://www.khanacademy.org/e/simplifying_rational_expressions_3
Standard APR.6
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Divide polynomials with remainders: monomial divisors - Rewrite expressions of the form a(x)/b(x), where a is a polynomial b is a monomial, in the form q(x)+r(x)/b(x), where q and r are polynomials and the degree of r is less than the degree of b.
https://www.khanacademy.org/e/divide-polynomials-by-monomials
Standard APR.6
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Divide polynomials with remainders - Rewrite expressions of the form a(x)/b(x), where a and b are polynomials, in the form q(x)+r(x)/b(x), where q and r are polynomials and the degree of r is less than the degree of b.
https://www.khanacademy.org/e/dividing-polynomials-with-remainders
Standard APR.6
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Divide polynomials with remainders: binomial divisors - Rewrite expressions of the form a(x)/b(x), where a is a polynomial b is a linear binomial, in the form q(x)+r(x)/b(x), where q and r are polynomials and the degree of r is less than the degree of b.
https://www.khanacademy.org/e/divide-polynomials-by-binomials
Standard APR.6
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Simplify rational expressions: common monomial factors - Factor the numerator and the denominator of a rational expression and cancel out common monomial factors.
https://www.khanacademy.org/e/simplifying_rational_expressions_1
Standard APR.6
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Simplify rational expressions: common binomial factors - Factor the numerator and the denominator of a rational expression and cancel out common binomial terms.
https://www.khanacademy.org/e/simplifying_rational_expressions_2
Standard APR.7
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Add & subtract rational expressions: unlike denominators - Add and subtract rational expressions with relatively prime denominators by manipulating them to have the same denominators.
https://www.khanacademy.org/e/adding_and_subtracting_rational_expressions_2
Standard APR.7
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Multiply & divide rational expressions - Example: Multiply and simplify (a²-4)/(a²-1) X (a+1)/(a+2).
https://www.khanacademy.org/e/multiplying_and_dividing_rational_expressions_2
Standard APR.7
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Add & subtract rational expressions - Example: Subtract and simplify (a-2)/(a+2) - (a-3)/(a²+4a+4).
https://www.khanacademy.org/e/adding_and_subtracting_rational_expressions_5
Standard APR.7
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Nested fractions - Simplify rational expressions that contain rational expressions within their numerators or denominators.
https://www.khanacademy.org/e/nested-fractions
Standard APR.7
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Multiply & divide rational expressions (advanced) - Example: Multiply and simplify (3x²y)/(2ab) X (14a²b)/(18xy²).
https://www.khanacademy.org/e/multiplying_and_dividing_rational_expressions_3
Standard APR.7
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Add & subtract rational expressions: factored denominators - Example: Add and simplify x/(2x+1)(x-7) + 2x²/(2x-3)(x-7).
https://www.khanacademy.org/e/adding_and_subtracting_rational_expressions_3
Standard APR.7
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Add & subtract rational expressions: like denominators - Example: Add and simplify 6/(2x²-7) + (-3x-8)/(2x²-7).
https://www.khanacademy.org/e/adding_and_subtracting_rational_expressions
Standard APR.7
Common Core Area - Arithmetic with Polynomials and Rational Expressions
Skill - Multiply & divide rational expressions (basic) - Example: Multiply and simplify (6x³/5)*(2/3x).
https://www.khanacademy.org/e/multiplying_and_dividing_rational_expressions_1
Standard CED.1
Common Core Area - Creating Equations
Skill - Equations & inequalities word problems - Construct an equation or an inequality that model a given context. Modeling expressions can be quadratic, rational, or exponential.
https://www.khanacademy.org/e/modeling-with-one-variable-equations-and-inequalities
Standard CED.1
Common Core Area - Creating Equations
Skill - Multiple units word problems - Solve word problems that contain multiple quantities that are measured in different units.
https://www.khanacademy.org/e/units
Standard CED.2
Common Core Area - Creating Equations
Skill - Systems of equations word problems - Solve word problems by modeling them into a system of equations and solving it.
https://www.khanacademy.org/e/understanding-systems-of-equations-word-problems
Standard CED.2
Common Core Area - Creating Equations
Skill - Graphing linear functions word problems - Graph the line that represents a real-world relationship that is given verbally.
https://www.khanacademy.org/e/graphing-linear-functions-word-problems
Standard CED.2
Common Core Area - Creating Equations
Skill - Age word problems - Solve age word problems with a system of equations.
https://www.khanacademy.org/e/age_word_problems
Standard CED.2
Common Core Area - Creating Equations
Skill - Linear models word problems - Solve general word problems about real-world relationships that can be modeled by linear equations or functions.
https://www.khanacademy.org/e/constructing-and-interpreting-linear-functions
Standard CED.2
Common Core Area - Creating Equations
Skill - Construct exponential models - Given a verbal description of the rate of change of a real world situation, find the exponential function that models it.
https://www.khanacademy.org/e/construct-exponential-models-according-to-rate-of-change
Standard CED.2
Common Core Area - Creating Equations
Skill - Systems of equations word problems capstone - Solve word problems that involve systems of equations, where there can either be a single solution, no solution, or infinite solutions.
https://www.khanacademy.org/e/systems-of-equations-word-problems-capstone
Standard CED.2
Common Core Area - Creating Equations
Skill - Modeling with sinusoidal functions - Given the description of a real-world relationship, find the sinusoidal function that models it.
https://www.khanacademy.org/e/modeling-with-periodic-functions
Standard CED.2
Common Core Area - Creating Equations
Skill - Writing linear functions word problems - Find a linear function that represents a real-world relationship that is given verbally.
https://www.khanacademy.org/e/constructing-linear-functions-word-problems
Standard CED.3
Common Core Area - Creating Equations
Skill - Solutions of systems of inequalities - Check whether an ordered pair is a solution of a system of two-variable linear inequalities.
https://www.khanacademy.org/e/checking-solutions-to-systems-of-inequalities
Standard CED.3
Common Core Area - Creating Equations
Skill - Solutions of inequalities: graphical - Given the graph of a two-variable linear inequality, check whether a given pair of values is a solution of the inequality.
https://www.khanacademy.org/e/graphically-check-solutions-to-inequalities
Standard CED.3
Common Core Area - Creating Equations
Skill - Systems of equations word problems capstone - Solve word problems that involve systems of equations, where there can either be a single solution, no solution, or infinite solutions.
https://www.khanacademy.org/e/systems-of-equations-word-problems-capstone
Standard CED.3
Common Core Area - Creating Equations
Skill - Systems of inequalities word problems - Solve word problems that involve systems of linear inequalities.
https://www.khanacademy.org/e/modeling-systems-of-linear-inequalities
Standard CED.3
Common Core Area - Creating Equations
Skill - Constraint solutions of two-variable inequalities - Find the range of values of one variable that corresponds to a given value of the other variable in a linear inequality.
https://www.khanacademy.org/e/graphing_inequalities
Standard CED.3
Common Core Area - Creating Equations
Skill - Solutions of inequalities: algebraic - Given a two-variable linear inequality, check whether a given pair of values is a solution of the inequality.
https://www.khanacademy.org/e/checking-solutions-to-two-var-inequalities
Standard CED.3
Common Core Area - Creating Equations
Skill - Two-variable inequalities word problems - Solve word problems that involve linear inequalities in two variables.
https://www.khanacademy.org/e/modeling-constraints
Standard CED.3
Common Core Area - Creating Equations
Skill - Constraint solutions of systems of inequalities - Find the range of values of one variable that corresponds to a given value of the other variable in a system of two-variable linear inequalities.
https://www.khanacademy.org/e/graphing_systems_of_inequalities
Standard CED.3
Common Core Area - Creating Equations
Skill - Systems of equations word problems - Solve word problems by modeling them into a system of equations and solving it.
https://www.khanacademy.org/e/understanding-systems-of-equations-word-problems
Standard CED.3
Common Core Area - Creating Equations
Skill - Age word problems - Solve age word problems with a system of equations.
https://www.khanacademy.org/e/age_word_problems
Standard CED.4
Common Core Area - Creating Equations
Skill - Manipulate formulas - Solve multi-variable formulas for a specific variable in order to solve some word problems.
https://www.khanacademy.org/e/manipulating-formulas
Standard REI.1
Common Core Area - Reasoning with Equations and Inequalities
Skill - Coming Soon -
Standard REI.2
Common Core Area - Reasoning with Equations and Inequalities
Skill - Solve square-root equations - Solve square-root equations by first arranging them and then taking the square of both sides.
https://www.khanacademy.org/e/solve-square-root-equations-advanced
Standard REI.2
Common Core Area - Reasoning with Equations and Inequalities
Skill - Extraneous solutions of radical equations - Practice some problems that involve thinking about the conditions for obtaining extraneous solutions while solving radical equations.
https://www.khanacademy.org/e/extraneous-solutions-to-radical-equations
Standard REI.2
Common Core Area - Reasoning with Equations and Inequalities
Skill - Equations with one rational expression - Solve equations that have one rational expression whose numerator and denominator are linear expressions.
https://www.khanacademy.org/e/linear_equations_4
Standard REI.2
Common Core Area - Reasoning with Equations and Inequalities
Skill - Solve square-root equations (basic) - Solve square-root equations by taking the square of both sides.
https://www.khanacademy.org/e/solve-square-root-equations-basic
Standard REI.2
Common Core Area - Reasoning with Equations and Inequalities
Skill - Equations with two rational expressions - Solve advanced rational equations with multiple expressions.
https://www.khanacademy.org/e/rational-equations-3
Standard REI.2
Common Core Area - Reasoning with Equations and Inequalities
Skill - Equations with one rational expression (advanced) - Solve equations that have one rational expression whose numerator and denominator are polynomial expressions.
https://www.khanacademy.org/e/solving_rational_equations_2
Standard REI.3
Common Core Area - Reasoning with Equations and Inequalities
Skill - Compound inequalities - Solve compound linear inequalities. For example, solve 5z+7<27 OR -3z≤18.
https://www.khanacademy.org/e/compound_inequalities
Standard REI.3
Common Core Area - Reasoning with Equations and Inequalities
Skill - Linear equations with unknown coefficients - Solve a linear equation where the coefficients are represented by letters.
https://www.khanacademy.org/e/solving_for_a_variable
Standard REI.3
Common Core Area - Reasoning with Equations and Inequalities
Skill - Multi-step linear inequalities - Solve linear inequalities that take multiple steps to solve.
https://www.khanacademy.org/e/linear_inequalities
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratic word problems (standard form) - Solve real-world word problems that involve quadratic models. In this exercise, that models are given in standard form.
https://www.khanacademy.org/e/key-features-quadratics
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Solve quadratic equations: complex solutions - Solve quadratic equations using the quadratic formula. Some of the equations have real solutions while others have complex solutions.
https://www.khanacademy.org/e/quadratic-formula-with-complex-solutions
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratics by taking square roots - Solve quadratic equations of the form (x+a)²-b=0. These can be solved using square roots. For example, solve (x-5)²-4=0.
https://www.khanacademy.org/e/solving_quadratics_by_taking_the_square_root
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Number of solutions of quadratic equations - Analyze quadratic equations in order to determine how many different real number solutions they have.
https://www.khanacademy.org/e/determine-the-number-of-solutions-of-a-quadratic-equation
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Completing the square (intro) - Practice the method of completing the square with quadratic expressions.
https://www.khanacademy.org/e/completing_the_square_in_quadratic_expressions
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratics by taking square roots: strategy - Analyze the process of solving a quadratic equation by taking the square root.
https://www.khanacademy.org/e/understanding-the-equation-solving-process
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratics by factoring - Solve quadratic equations of the form ax^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring_2
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratics by factoring (intro) - Solve quadratic equations of the form x^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Completing the square (intermediate) - Solve quadratic equations of the form x^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_1
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Completing the square - Solve quadratic equations of the form ax^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_2
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratic formula - Solve quadratic equations using the quadratic formula. For example, solve -9x+10x²+8=14.
https://www.khanacademy.org/e/quadratic_equation
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Solve equations using structure - Solve advanced equations by strategically using quadratic factorization methods.
https://www.khanacademy.org/e/solving-quadratics-by-using-structure
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratic formula - Solve quadratic equations using the quadratic formula. For example, solve -9x+10x²+8=14.
https://www.khanacademy.org/e/quadratic_equation
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratic word problems (standard form) - Solve real-world word problems that involve quadratic models. In this exercise, that models are given in standard form.
https://www.khanacademy.org/e/key-features-quadratics
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Solve quadratic equations: complex solutions - Solve quadratic equations using the quadratic formula. Some of the equations have real solutions while others have complex solutions.
https://www.khanacademy.org/e/quadratic-formula-with-complex-solutions
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratics by taking square roots - Solve quadratic equations of the form (x+a)²-b=0. These can be solved using square roots. For example, solve (x-5)²-4=0.
https://www.khanacademy.org/e/solving_quadratics_by_taking_the_square_root
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Number of solutions of quadratic equations - Analyze quadratic equations in order to determine how many different real number solutions they have.
https://www.khanacademy.org/e/determine-the-number-of-solutions-of-a-quadratic-equation
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Completing the square (intro) - Practice the method of completing the square with quadratic expressions.
https://www.khanacademy.org/e/completing_the_square_in_quadratic_expressions
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratics by taking square roots: strategy - Analyze the process of solving a quadratic equation by taking the square root.
https://www.khanacademy.org/e/understanding-the-equation-solving-process
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratics by factoring - Solve quadratic equations of the form ax^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring_2
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratics by factoring (intro) - Solve quadratic equations of the form x^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Completing the square (intermediate) - Solve quadratic equations of the form x^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_1
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Completing the square - Solve quadratic equations of the form ax^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_2
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratic formula - Solve quadratic equations using the quadratic formula. For example, solve -9x+10x²+8=14.
https://www.khanacademy.org/e/quadratic_equation
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratic word problems (standard form) - Solve real-world word problems that involve quadratic models. In this exercise, that models are given in standard form.
https://www.khanacademy.org/e/key-features-quadratics
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Solve equations using structure - Solve advanced equations by strategically using quadratic factorization methods.
https://www.khanacademy.org/e/solving-quadratics-by-using-structure
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Completing the square - Solve quadratic equations of the form ax^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_2
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Completing the square (intermediate) - Solve quadratic equations of the form x^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_1
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratics by factoring (intro) - Solve quadratic equations of the form x^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratics by factoring - Solve quadratic equations of the form ax^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring_2
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratics by taking square roots: strategy - Analyze the process of solving a quadratic equation by taking the square root.
https://www.khanacademy.org/e/understanding-the-equation-solving-process
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Completing the square (intro) - Practice the method of completing the square with quadratic expressions.
https://www.khanacademy.org/e/completing_the_square_in_quadratic_expressions
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Number of solutions of quadratic equations - Analyze quadratic equations in order to determine how many different real number solutions they have.
https://www.khanacademy.org/e/determine-the-number-of-solutions-of-a-quadratic-equation
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Quadratics by taking square roots - Solve quadratic equations of the form (x+a)²-b=0. These can be solved using square roots. For example, solve (x-5)²-4=0.
https://www.khanacademy.org/e/solving_quadratics_by_taking_the_square_root
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Solve quadratic equations: complex solutions - Solve quadratic equations using the quadratic formula. Some of the equations have real solutions while others have complex solutions.
https://www.khanacademy.org/e/quadratic-formula-with-complex-solutions
Standard REI.4
Common Core Area - Reasoning with Equations and Inequalities
Skill - Solve equations using structure - Solve advanced equations by strategically using quadratic factorization methods.
https://www.khanacademy.org/e/solving-quadratics-by-using-structure
Standard REI.5
Common Core Area - Reasoning with Equations and Inequalities
Skill - Equivalent systems of equations - Determine whether a couple of given systems of equations are equivalent or not to a third given system.
https://www.khanacademy.org/e/understanding-solution-methods-to-systems-of-equations
Standard REI.6
Common Core Area - Reasoning with Equations and Inequalities
Skill - Systems of equations with elimination - Solve systems of equation with one-step elimination (e.g., x-values or y-values cancel each other out).
https://www.khanacademy.org/e/systems_of_equations_with_elimination_0.5
Standard REI.6
Common Core Area - Reasoning with Equations and Inequalities
Skill - Systems of equations with elimination challenge - Solve systems of equation with multi-step elimination (e.g., a manipulation is needed in order for x-values or y-values to cancel each other out).
https://www.khanacademy.org/e/systems_of_equations_with_elimination
Standard REI.6
Common Core Area - Reasoning with Equations and Inequalities
Skill - Systems of equations word problems capstone - Solve word problems that involve systems of equations, where there can either be a single solution, no solution, or infinite solutions.
https://www.khanacademy.org/e/systems-of-equations-word-problems-capstone
Standard REI.6
Common Core Area - Reasoning with Equations and Inequalities
Skill - Systems of equations with graphing - Graph a system of equations in slope-intercept or standard form, and find their solution using the graphs.
https://www.khanacademy.org/e/graphing_systems_of_equations
Standard REI.6
Common Core Area - Reasoning with Equations and Inequalities
Skill - Solutions of systems of equations - Verify whether a given pair of values is a solution to a system of equations.
https://www.khanacademy.org/e/verifying-solutions-to-systems-of-equations
Standard REI.6
Common Core Area - Reasoning with Equations and Inequalities
Skill - Age word problems - Solve age word problems with a system of equations.
https://www.khanacademy.org/e/age_word_problems
Standard REI.6
Common Core Area - Reasoning with Equations and Inequalities
Skill - Systems of equations word problems - Solve word problems by modeling them into a system of equations and solving it.
https://www.khanacademy.org/e/understanding-systems-of-equations-word-problems
Standard REI.6
Common Core Area - Reasoning with Equations and Inequalities
Skill - Linear systems of equations capstone - Solve systems of equations with any number of solutions using any solution method.
https://www.khanacademy.org/e/systems_of_equations
Standard REI.6
Common Core Area - Reasoning with Equations and Inequalities
Skill - Systems of equations with substitution - Solve systems of equations where one of the equations is solved for one of the variables.
https://www.khanacademy.org/e/systems_of_equations_with_substitution
Standard REI.7
Common Core Area - Reasoning with Equations and Inequalities
Skill - Coming Soon -
Standard REI.8
Common Core Area - Reasoning with Equations and Inequalities
Skill - Represent linear systems with matrices - Determine the matrix that represents a given system of linear equations.
https://www.khanacademy.org/e/represent-systems-with-matrices
Standard REI.8
Common Core Area - Reasoning with Equations and Inequalities
Skill - Represent linear systems with matrix equations - Represent systems of two linear equations with matrix equations by determining A and b in the matrix equation A*x=b.
https://www.khanacademy.org/e/writing-systems-of-equations-as-matrix-equations
Standard REI.8
Common Core Area - Reasoning with Equations and Inequalities
Skill - Matrix row operations - Determine the matrix that is the result of performing a specific row operation on a given matrix.
https://www.khanacademy.org/e/perform-elementary-matrix-row-operations
Standard REI.9
Common Core Area - Reasoning with Equations and Inequalities
Skill - Determine invertible matrices - Given a 2x2 matrix, determine whether it has an inverse.
https://www.khanacademy.org/e/determine-invertibile-2x2-matrices
Standard REI.9
Common Core Area - Reasoning with Equations and Inequalities
Skill - Find the inverse of a 2x2 matrix - Find the inverse matrix of a given 2x2 matrix.
https://www.khanacademy.org/e/matrix_inverse_2x2
Standard REI.9
Common Core Area - Reasoning with Equations and Inequalities
Skill - Determine inverse matrices - Given a pair of matrices, determine whether they are inverses of each other.
https://www.khanacademy.org/e/determine-inverse-matrices
Standard REI.10
Common Core Area - Reasoning with Equations and Inequalities
Skill - Solutions to 2-variable equations - Determine which ordered pairs are solutions to equations.
https://www.khanacademy.org/e/plugging_in_values
Standard REI.10
Common Core Area - Reasoning with Equations and Inequalities
Skill - Number of solutions to a system of equations graphically - Determine the number of solutions of a given system of equations by considering its graph.
https://www.khanacademy.org/e/graphical-solutions-to-systems
Standard REI.10
Common Core Area - Reasoning with Equations and Inequalities
Skill - Slope-intercept intro - Practice your basic understanding of slope-intercept form for linear equations.
https://www.khanacademy.org/e/slope-from-an-equation-in-slope-intercept-form
Standard REI.10
Common Core Area - Reasoning with Equations and Inequalities
Skill - Complete solutions to 2-variable equations - Given the x or y value of a 2-variable equation solution, find the value for the other variable in the solution.
https://www.khanacademy.org/e/graphing-solutions-to-two-variable-linear-equations
Standard REI.10
Common Core Area - Reasoning with Equations and Inequalities
Skill - Number of solutions to a system of equations algebraically - Determine the number of solutions of a given system of equations by considering its algebraic solution process.
https://www.khanacademy.org/e/constructing-consistent-and-inconsistent-system
Standard REI.10
Common Core Area - Reasoning with Equations and Inequalities
Skill - Intercepts from a graph - Look at the graph of an equation to find x-intercepts and y-intercepts
https://www.khanacademy.org/e/linear-function-intercepts
Standard REI.11
Common Core Area - Reasoning with Equations and Inequalities
Skill - Systems of equations with graphing - Graph a system of equations in slope-intercept or standard form, and find their solution using the graphs.
https://www.khanacademy.org/e/graphing_systems_of_equations
Standard REI.11
Common Core Area - Reasoning with Equations and Inequalities
Skill - Interpret equations graphically - Practice the connection between the graphical representation of equations and their algebraic solutions.
https://www.khanacademy.org/e/systems-of-nonlinear-equations
Standard REI.11
Common Core Area - Reasoning with Equations and Inequalities
Skill - Solutions of systems of equations - Verify whether a given pair of values is a solution to a system of equations.
https://www.khanacademy.org/e/verifying-solutions-to-systems-of-equations
Standard REI.11
Common Core Area - Reasoning with Equations and Inequalities
Skill - Number of solutions to a system of equations graphically - Determine the number of solutions of a given system of equations by considering its graph.
https://www.khanacademy.org/e/graphical-solutions-to-systems
Standard REI.11
Common Core Area - Reasoning with Equations and Inequalities
Skill - Solve equations graphically - Solve advanced and complicated equations using the power of graphs.
https://www.khanacademy.org/e/intersecting-functions
Standard REI.11
Common Core Area - Reasoning with Equations and Inequalities
Skill - Number of solutions to a system of equations algebraically - Determine the number of solutions of a given system of equations by considering its algebraic solution process.
https://www.khanacademy.org/e/constructing-consistent-and-inconsistent-system
Standard REI.12
Common Core Area - Reasoning with Equations and Inequalities
Skill - Two-variable inequalities from their graphs - Fit an algebraic two-variable inequality to its appropriate graph.
https://www.khanacademy.org/e/graphs_of_inequalities
Standard REI.12
Common Core Area - Reasoning with Equations and Inequalities
Skill - Systems of inequalities graphs - Find the graph that represents the solution to a system of inequalities.
https://www.khanacademy.org/e/graphing_systems_of_inequalities_2
Standard REI.12
Common Core Area - Reasoning with Equations and Inequalities
Skill - Graphs of inequalities - Graph two-variable linear inequalities.
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models: changing units - Given a function that models an exponential situation, rewrite the function in order to find its change for a different time unit.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-for-a-different-unit
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models: changing units - Given a function that models an exponential situation, rewrite the function in order to find its change for a different time unit.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-for-a-different-unit
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: common factor - Practice finding the greatest common factors of polynomials and factoring them out of the polynomials.
https://www.khanacademy.org/e/factoring-polynomials
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Analyzing structure with linear inequalities - Given some information about a real-world context, analyze expressions containing unknown variables that model that context.
https://www.khanacademy.org/e/compare-expressions-with-unknown-variables-word-problems
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Multiply monomials - More challenging multiplying monomial problems like find the area or find missing values to make an equation true.
https://www.khanacademy.org/e/multiply-monomials-challenge
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models: with manipulation - Given a function that models an exponential situation, rewrite the function in order to analyze its rate of change.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-with-manipulation
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: common factor - Practice finding the greatest common factors of polynomials and factoring them out of the polynomials.
https://www.khanacademy.org/e/factoring-polynomials
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Analyzing structure with linear inequalities - Given some information about a real-world context, analyze expressions containing unknown variables that model that context.
https://www.khanacademy.org/e/compare-expressions-with-unknown-variables-word-problems
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Multiply monomials - More challenging multiplying monomial problems like find the area or find missing values to make an equation true.
https://www.khanacademy.org/e/multiply-monomials-challenge
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models: with manipulation - Given a function that models an exponential situation, rewrite the function in order to analyze its rate of change.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-with-manipulation
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: common factor - Practice finding the greatest common factors of polynomials and factoring them out of the polynomials.
https://www.khanacademy.org/e/factoring-polynomials
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models: changing units - Given a function that models an exponential situation, rewrite the function in order to find its change for a different time unit.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-for-a-different-unit
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Analyzing structure with linear inequalities - Given some information about a real-world context, analyze expressions containing unknown variables that model that context.
https://www.khanacademy.org/e/compare-expressions-with-unknown-variables-word-problems
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Multiply monomials - More challenging multiplying monomial problems like find the area or find missing values to make an equation true.
https://www.khanacademy.org/e/multiply-monomials-challenge
Standard SSE.1
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models: with manipulation - Given a function that models an exponential situation, rewrite the function in order to analyze its rate of change.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-with-manipulation
Standard SSE.2
Common Core Area - Seeing Structure in Expressions
Skill - Factor monomials - Factor monomials as products of smaller monomials.
https://www.khanacademy.org/e/factoring-monomials
Standard SSE.2
Common Core Area - Seeing Structure in Expressions
Skill - Factoring polynomials challenge - Review your skills for using the structure of expressions with some challenge problems.
https://www.khanacademy.org/e/advanced-structure-in-expressions
Standard SSE.2
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: special product forms - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using special product factorization methods.
https://www.khanacademy.org/e/factoring_difference_of_squares_3
Standard SSE.2
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: common factor - Practice finding the greatest common factors of polynomials and factoring them out of the polynomials.
https://www.khanacademy.org/e/factoring-polynomials
Standard SSE.2
Common Core Area - Seeing Structure in Expressions
Skill - Perfect squares - Factor quadratic expressions of the general perfect square forms: (ax)²+2abx+b² or (ax)²-2abx+b². The factored expressions have the general forms (ax+b)² or (ax-b)².
https://www.khanacademy.org/e/factoring-perfect-squares
Standard SSE.2
Common Core Area - Seeing Structure in Expressions
Skill - Solve equations using structure - Solve advanced equations by strategically using quadratic factorization methods.
https://www.khanacademy.org/e/solving-quadratics-by-using-structure
Standard SSE.2
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: quadratic methods (challenge) - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using quadratic factorization methods.
https://www.khanacademy.org/e/factoring_polynomials_with_two_variables
Standard SSE.2
Common Core Area - Seeing Structure in Expressions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard SSE.2
Common Core Area - Seeing Structure in Expressions
Skill - Find zeros of polynomials - Use various methods in order to find all the zeros of polynomial expressions or functions.
https://www.khanacademy.org/e/find-the-zeros-of-polynomials
Standard SSE.2
Common Core Area - Seeing Structure in Expressions
Skill - Difference of squares - Factor quadratic expressions of the general difference of squares form: (ax)^2-b^2. The factored expressions have the general form (ax+b)(ax-b).
https://www.khanacademy.org/e/factoring_difference_of_squares_2
Standard SSE.2
Common Core Area - Seeing Structure in Expressions
Skill - Evaluate expressions using structure - Given some information about several unknown variables, evaluate an expression containing those variables.
https://www.khanacademy.org/e/expressions_with_unknown_variables
Standard SSE.2
Common Core Area - Seeing Structure in Expressions
Skill - Difference of squares intro - Factor quadratic expressions into the special products of the general form (x+a)(x-a).
https://www.khanacademy.org/e/factoring_difference_of_squares_1
Standard SSE.2
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: quadratic methods - Factor polynomials that can be factored as the product of a monomial and a quadratic expression, then further factor the quadratic expression.
https://www.khanacademy.org/e/factoring_polynomials_2
Standard SSE.2
Common Core Area - Seeing Structure in Expressions
Skill - Manipulate expressions using structure - Rewrite an expression containing two unknown variables by using a given equation that contains those variables.
https://www.khanacademy.org/e/structure-in-expressions-1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Convert linear equations to standard form - Convert linear equations in various forms into standard form.
https://www.khanacademy.org/e/converting_between_slope_intercept_and_standard_form
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Linear systems of equations capstone - Solve systems of equations with any number of solutions using any solution method.
https://www.khanacademy.org/e/systems_of_equations
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Rewrite exponential expressions - Rewrite a given exponential expression in a specific desired form.
https://www.khanacademy.org/e/rewrite-exponential-expressions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models: with manipulation - Given a function that models an exponential situation, rewrite the function in order to analyze its rate of change.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-with-manipulation
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Quadratic word problems (standard form) - Solve real-world word problems that involve quadratic models. In this exercise, that models are given in standard form.
https://www.khanacademy.org/e/key-features-quadratics
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Equivalent forms of exponential expressions - Determine whether pairs of exponential expressions are equivalent.
https://www.khanacademy.org/e/equivalent-forms-of-expressions-with-variable-exponents
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret time in exponential models - Given a function that models an exponential situation, find the time interval over which the quantity changes by a given factor.
https://www.khanacademy.org/e/rewriting-and-interpreting-exponential-functions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Difference of squares intro - Factor quadratic expressions into the special products of the general form (x+a)(x-a).
https://www.khanacademy.org/e/factoring_difference_of_squares_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Slope from equation - Find the slopes of lines whose equations are given in various forms. For example, find the slope of 2x+3y=5.
https://www.khanacademy.org/e/slope-from-an-equation-in-standard-form
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Graph parabolas in all forms - Graph quadratic functions given in any form.
https://www.khanacademy.org/e/graphing_parabolas_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Quadratics by factoring (intro) - Solve quadratic equations of the form x^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Features of quadratic functions: strategy - Identify the form of a quadratic function that immediately reveals a given feature of that function. Features in question are the y-intercept of the graph, the zeroes ("roots") of the function, and the vertex of the parabola.
https://www.khanacademy.org/e/identifying-and-using-quadratic-forms
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Completing the square (intermediate) - Solve quadratic equations of the form x^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor quadratics by grouping - Factor quadratics of the form ax²+bx+c.
https://www.khanacademy.org/e/factoring_polynomials_by_grouping_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Features of quadratic functions - Find the zeroes ("roots") of quadratic functions and the vertex of their parabolas. Functions are given in standard, vertex, and factored form.
https://www.khanacademy.org/e/rewriting-expressions-to-reveal-information
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Graph quadratics in standard form - Graph quadratic functions given in the standard form ax²+bx+c. For example, graph y=5x²-20x+15.
https://www.khanacademy.org/e/graphing_parabolas_0.5
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: special product forms - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using special product factorization methods.
https://www.khanacademy.org/e/factoring_difference_of_squares_3
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Perfect squares - Factor quadratic expressions of the general perfect square forms: (ax)²+2abx+b² or (ax)²-2abx+b². The factored expressions have the general forms (ax+b)² or (ax-b)².
https://www.khanacademy.org/e/factoring-perfect-squares
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models - Given a function that models an exponential situation, find the factor by which the quantity changes per unit time interval.
https://www.khanacademy.org/e/modeling-with-exponential-functions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: quadratic methods (challenge) - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using quadratic factorization methods.
https://www.khanacademy.org/e/factoring_polynomials_with_two_variables
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Analyzing structure with linear inequalities - Given some information about a real-world context, analyze expressions containing unknown variables that model that context.
https://www.khanacademy.org/e/compare-expressions-with-unknown-variables-word-problems
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factoring quadratics intro - Factor quadratics of the form x²+bx+c.
https://www.khanacademy.org/e/factoring_polynomials_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Completing the square - Solve quadratic equations of the form ax^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models: changing units - Given a function that models an exponential situation, rewrite the function in order to find its change for a different time unit.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-for-a-different-unit
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Solve equations using structure - Solve advanced equations by strategically using quadratic factorization methods.
https://www.khanacademy.org/e/solving-quadratics-by-using-structure
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Quadratics by factoring - Solve quadratic equations of the form ax^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: common factor - Practice finding the greatest common factors of polynomials and factoring them out of the polynomials.
https://www.khanacademy.org/e/factoring-polynomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Perfect squares - Factor quadratic expressions of the general perfect square forms: (ax)²+2abx+b² or (ax)²-2abx+b². The factored expressions have the general forms (ax+b)² or (ax-b)².
https://www.khanacademy.org/e/factoring-perfect-squares
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Graph parabolas in all forms - Graph quadratic functions given in any form.
https://www.khanacademy.org/e/graphing_parabolas_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Slope from equation - Find the slopes of lines whose equations are given in various forms. For example, find the slope of 2x+3y=5.
https://www.khanacademy.org/e/slope-from-an-equation-in-standard-form
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Difference of squares intro - Factor quadratic expressions into the special products of the general form (x+a)(x-a).
https://www.khanacademy.org/e/factoring_difference_of_squares_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Equivalent forms of exponential expressions - Determine whether pairs of exponential expressions are equivalent.
https://www.khanacademy.org/e/equivalent-forms-of-expressions-with-variable-exponents
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Quadratic word problems (standard form) - Solve real-world word problems that involve quadratic models. In this exercise, that models are given in standard form.
https://www.khanacademy.org/e/key-features-quadratics
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models: with manipulation - Given a function that models an exponential situation, rewrite the function in order to analyze its rate of change.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-with-manipulation
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Rewrite exponential expressions - Rewrite a given exponential expression in a specific desired form.
https://www.khanacademy.org/e/rewrite-exponential-expressions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Linear systems of equations capstone - Solve systems of equations with any number of solutions using any solution method.
https://www.khanacademy.org/e/systems_of_equations
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Convert linear equations to standard form - Convert linear equations in various forms into standard form.
https://www.khanacademy.org/e/converting_between_slope_intercept_and_standard_form
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor quadratics by grouping - Factor quadratics of the form ax²+bx+c.
https://www.khanacademy.org/e/factoring_polynomials_by_grouping_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Features of quadratic functions - Find the zeroes ("roots") of quadratic functions and the vertex of their parabolas. Functions are given in standard, vertex, and factored form.
https://www.khanacademy.org/e/rewriting-expressions-to-reveal-information
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Graph quadratics in standard form - Graph quadratic functions given in the standard form ax²+bx+c. For example, graph y=5x²-20x+15.
https://www.khanacademy.org/e/graphing_parabolas_0.5
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: special product forms - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using special product factorization methods.
https://www.khanacademy.org/e/factoring_difference_of_squares_3
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Completing the square (intro) - Practice the method of completing the square with quadratic expressions.
https://www.khanacademy.org/e/completing_the_square_in_quadratic_expressions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models - Given a function that models an exponential situation, find the factor by which the quantity changes per unit time interval.
https://www.khanacademy.org/e/modeling-with-exponential-functions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret time in exponential models - Given a function that models an exponential situation, find the time interval over which the quantity changes by a given factor.
https://www.khanacademy.org/e/rewriting-and-interpreting-exponential-functions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: quadratic methods (challenge) - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using quadratic factorization methods.
https://www.khanacademy.org/e/factoring_polynomials_with_two_variables
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Analyzing structure with linear inequalities - Given some information about a real-world context, analyze expressions containing unknown variables that model that context.
https://www.khanacademy.org/e/compare-expressions-with-unknown-variables-word-problems
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factoring quadratics intro - Factor quadratics of the form x²+bx+c.
https://www.khanacademy.org/e/factoring_polynomials_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Completing the square - Solve quadratic equations of the form ax^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models: changing units - Given a function that models an exponential situation, rewrite the function in order to find its change for a different time unit.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-for-a-different-unit
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Solve equations using structure - Solve advanced equations by strategically using quadratic factorization methods.
https://www.khanacademy.org/e/solving-quadratics-by-using-structure
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: common factor - Practice finding the greatest common factors of polynomials and factoring them out of the polynomials.
https://www.khanacademy.org/e/factoring-polynomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: quadratic methods - Factor polynomials that can be factored as the product of a monomial and a quadratic expression, then further factor the quadratic expression.
https://www.khanacademy.org/e/factoring_polynomials_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor monomials - Factor monomials as products of smaller monomials.
https://www.khanacademy.org/e/factoring-monomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Find zeros of polynomials - Use various methods in order to find all the zeros of polynomial expressions or functions.
https://www.khanacademy.org/e/find-the-zeros-of-polynomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Compare features of functions - Compare various features between two functions, each represented in a different way.
https://www.khanacademy.org/e/comparing-features-of-functions-2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models: with manipulation - Given a function that models an exponential situation, rewrite the function in order to analyze its rate of change.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-with-manipulation
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models - Given a function that models an exponential situation, find the factor by which the quantity changes per unit time interval.
https://www.khanacademy.org/e/modeling-with-exponential-functions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Perfect squares - Factor quadratic expressions of the general perfect square forms: (ax)²+2abx+b² or (ax)²-2abx+b². The factored expressions have the general forms (ax+b)² or (ax-b)².
https://www.khanacademy.org/e/factoring-perfect-squares
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: special product forms - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using special product factorization methods.
https://www.khanacademy.org/e/factoring_difference_of_squares_3
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Graph quadratics in standard form - Graph quadratic functions given in the standard form ax²+bx+c. For example, graph y=5x²-20x+15.
https://www.khanacademy.org/e/graphing_parabolas_0.5
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Features of quadratic functions - Find the zeroes ("roots") of quadratic functions and the vertex of their parabolas. Functions are given in standard, vertex, and factored form.
https://www.khanacademy.org/e/rewriting-expressions-to-reveal-information
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor quadratics by grouping - Factor quadratics of the form ax²+bx+c.
https://www.khanacademy.org/e/factoring_polynomials_by_grouping_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Convert linear equations to standard form - Convert linear equations in various forms into standard form.
https://www.khanacademy.org/e/converting_between_slope_intercept_and_standard_form
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Linear systems of equations capstone - Solve systems of equations with any number of solutions using any solution method.
https://www.khanacademy.org/e/systems_of_equations
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Rewrite exponential expressions - Rewrite a given exponential expression in a specific desired form.
https://www.khanacademy.org/e/rewrite-exponential-expressions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret time in exponential models - Given a function that models an exponential situation, find the time interval over which the quantity changes by a given factor.
https://www.khanacademy.org/e/rewriting-and-interpreting-exponential-functions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Quadratic word problems (standard form) - Solve real-world word problems that involve quadratic models. In this exercise, that models are given in standard form.
https://www.khanacademy.org/e/key-features-quadratics
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Equivalent forms of exponential expressions - Determine whether pairs of exponential expressions are equivalent.
https://www.khanacademy.org/e/equivalent-forms-of-expressions-with-variable-exponents
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Difference of squares intro - Factor quadratic expressions into the special products of the general form (x+a)(x-a).
https://www.khanacademy.org/e/factoring_difference_of_squares_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Slope from equation - Find the slopes of lines whose equations are given in various forms. For example, find the slope of 2x+3y=5.
https://www.khanacademy.org/e/slope-from-an-equation-in-standard-form
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Graph parabolas in all forms - Graph quadratic functions given in any form.
https://www.khanacademy.org/e/graphing_parabolas_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Quadratics by factoring (intro) - Solve quadratic equations of the form x^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Features of quadratic functions: strategy - Identify the form of a quadratic function that immediately reveals a given feature of that function. Features in question are the y-intercept of the graph, the zeroes ("roots") of the function, and the vertex of the parabola.
https://www.khanacademy.org/e/identifying-and-using-quadratic-forms
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Completing the square (intermediate) - Solve quadratic equations of the form x^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor monomials - Factor monomials as products of smaller monomials.
https://www.khanacademy.org/e/factoring-monomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: quadratic methods - Factor polynomials that can be factored as the product of a monomial and a quadratic expression, then further factor the quadratic expression.
https://www.khanacademy.org/e/factoring_polynomials_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Quadratics by factoring (intro) - Solve quadratic equations of the form x^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Features of quadratic functions: strategy - Identify the form of a quadratic function that immediately reveals a given feature of that function. Features in question are the y-intercept of the graph, the zeroes ("roots") of the function, and the vertex of the parabola.
https://www.khanacademy.org/e/identifying-and-using-quadratic-forms
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Completing the square (intermediate) - Solve quadratic equations of the form x^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Completing the square (intro) - Practice the method of completing the square with quadratic expressions.
https://www.khanacademy.org/e/completing_the_square_in_quadratic_expressions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Compare features of functions - Compare various features between two functions, each represented in a different way.
https://www.khanacademy.org/e/comparing-features-of-functions-2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Quadratics by factoring - Solve quadratic equations of the form ax^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Find zeros of polynomials - Use various methods in order to find all the zeros of polynomial expressions or functions.
https://www.khanacademy.org/e/find-the-zeros-of-polynomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor monomials - Factor monomials as products of smaller monomials.
https://www.khanacademy.org/e/factoring-monomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: quadratic methods - Factor polynomials that can be factored as the product of a monomial and a quadratic expression, then further factor the quadratic expression.
https://www.khanacademy.org/e/factoring_polynomials_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: common factor - Practice finding the greatest common factors of polynomials and factoring them out of the polynomials.
https://www.khanacademy.org/e/factoring-polynomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Solve equations using structure - Solve advanced equations by strategically using quadratic factorization methods.
https://www.khanacademy.org/e/solving-quadratics-by-using-structure
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models: changing units - Given a function that models an exponential situation, rewrite the function in order to find its change for a different time unit.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-for-a-different-unit
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Completing the square - Solve quadratic equations of the form ax^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factoring quadratics intro - Factor quadratics of the form x²+bx+c.
https://www.khanacademy.org/e/factoring_polynomials_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Analyzing structure with linear inequalities - Given some information about a real-world context, analyze expressions containing unknown variables that model that context.
https://www.khanacademy.org/e/compare-expressions-with-unknown-variables-word-problems
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: quadratic methods (challenge) - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using quadratic factorization methods.
https://www.khanacademy.org/e/factoring_polynomials_with_two_variables
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Slope from equation - Find the slopes of lines whose equations are given in various forms. For example, find the slope of 2x+3y=5.
https://www.khanacademy.org/e/slope-from-an-equation-in-standard-form
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Features of quadratic functions - Find the zeroes ("roots") of quadratic functions and the vertex of their parabolas. Functions are given in standard, vertex, and factored form.
https://www.khanacademy.org/e/rewriting-expressions-to-reveal-information
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor quadratics by grouping - Factor quadratics of the form ax²+bx+c.
https://www.khanacademy.org/e/factoring_polynomials_by_grouping_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Convert linear equations to standard form - Convert linear equations in various forms into standard form.
https://www.khanacademy.org/e/converting_between_slope_intercept_and_standard_form
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Linear systems of equations capstone - Solve systems of equations with any number of solutions using any solution method.
https://www.khanacademy.org/e/systems_of_equations
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Rewrite exponential expressions - Rewrite a given exponential expression in a specific desired form.
https://www.khanacademy.org/e/rewrite-exponential-expressions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models: with manipulation - Given a function that models an exponential situation, rewrite the function in order to analyze its rate of change.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-with-manipulation
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Quadratic word problems (standard form) - Solve real-world word problems that involve quadratic models. In this exercise, that models are given in standard form.
https://www.khanacademy.org/e/key-features-quadratics
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Equivalent forms of exponential expressions - Determine whether pairs of exponential expressions are equivalent.
https://www.khanacademy.org/e/equivalent-forms-of-expressions-with-variable-exponents
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Difference of squares intro - Factor quadratic expressions into the special products of the general form (x+a)(x-a).
https://www.khanacademy.org/e/factoring_difference_of_squares_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Compare features of functions - Compare various features between two functions, each represented in a different way.
https://www.khanacademy.org/e/comparing-features-of-functions-2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Graph parabolas in all forms - Graph quadratic functions given in any form.
https://www.khanacademy.org/e/graphing_parabolas_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Quadratics by factoring (intro) - Solve quadratic equations of the form x^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Features of quadratic functions: strategy - Identify the form of a quadratic function that immediately reveals a given feature of that function. Features in question are the y-intercept of the graph, the zeroes ("roots") of the function, and the vertex of the parabola.
https://www.khanacademy.org/e/identifying-and-using-quadratic-forms
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Completing the square (intermediate) - Solve quadratic equations of the form x^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Completing the square (intro) - Practice the method of completing the square with quadratic expressions.
https://www.khanacademy.org/e/completing_the_square_in_quadratic_expressions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Compare features of functions - Compare various features between two functions, each represented in a different way.
https://www.khanacademy.org/e/comparing-features-of-functions-2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Quadratics by factoring - Solve quadratic equations of the form ax^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Find zeros of polynomials - Use various methods in order to find all the zeros of polynomial expressions or functions.
https://www.khanacademy.org/e/find-the-zeros-of-polynomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Analyzing structure with linear inequalities - Given some information about a real-world context, analyze expressions containing unknown variables that model that context.
https://www.khanacademy.org/e/compare-expressions-with-unknown-variables-word-problems
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Find zeros of polynomials - Use various methods in order to find all the zeros of polynomial expressions or functions.
https://www.khanacademy.org/e/find-the-zeros-of-polynomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor monomials - Factor monomials as products of smaller monomials.
https://www.khanacademy.org/e/factoring-monomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: quadratic methods - Factor polynomials that can be factored as the product of a monomial and a quadratic expression, then further factor the quadratic expression.
https://www.khanacademy.org/e/factoring_polynomials_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: common factor - Practice finding the greatest common factors of polynomials and factoring them out of the polynomials.
https://www.khanacademy.org/e/factoring-polynomials
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Solve equations using structure - Solve advanced equations by strategically using quadratic factorization methods.
https://www.khanacademy.org/e/solving-quadratics-by-using-structure
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models: changing units - Given a function that models an exponential situation, rewrite the function in order to find its change for a different time unit.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-for-a-different-unit
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Completing the square - Solve quadratic equations of the form ax^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factoring quadratics intro - Factor quadratics of the form x²+bx+c.
https://www.khanacademy.org/e/factoring_polynomials_1
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: quadratic methods (challenge) - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using quadratic factorization methods.
https://www.khanacademy.org/e/factoring_polynomials_with_two_variables
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret time in exponential models - Given a function that models an exponential situation, find the time interval over which the quantity changes by a given factor.
https://www.khanacademy.org/e/rewriting-and-interpreting-exponential-functions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Interpret change in exponential models - Given a function that models an exponential situation, find the factor by which the quantity changes per unit time interval.
https://www.khanacademy.org/e/modeling-with-exponential-functions
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Perfect squares - Factor quadratic expressions of the general perfect square forms: (ax)²+2abx+b² or (ax)²-2abx+b². The factored expressions have the general forms (ax+b)² or (ax-b)².
https://www.khanacademy.org/e/factoring-perfect-squares
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Factor polynomials: special product forms - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using special product factorization methods.
https://www.khanacademy.org/e/factoring_difference_of_squares_3
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Graph quadratics in standard form - Graph quadratic functions given in the standard form ax²+bx+c. For example, graph y=5x²-20x+15.
https://www.khanacademy.org/e/graphing_parabolas_0.5
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Quadratics by factoring - Solve quadratic equations of the form ax^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring_2
Standard SSE.3
Common Core Area - Seeing Structure in Expressions
Skill - Completing the square (intro) - Practice the method of completing the square with quadratic expressions.
https://www.khanacademy.org/e/completing_the_square_in_quadratic_expressions
Standard SSE.4
Common Core Area - Seeing Structure in Expressions
Skill - Finite geometric series in sigma notation - Practice writing finite geometric series like 3 + 6 + 12 + 24 in sigma notation.
https://www.khanacademy.org/e/writing-finite-geometric-series-in-sigma-notation
Standard SSE.4
Common Core Area - Seeing Structure in Expressions
Skill - Finite geometric series - Evaluate finite geometric series given in sigma notation, recursively, or explicitly.
https://www.khanacademy.org/e/geometric-series--1
Standard SSE.4
Common Core Area - Seeing Structure in Expressions
Skill - Finite geometric series word problems - Understanding and solving problems with the formula for a finite geometric series
Standard BF.1
Common Core Area - Building Functions
Skill - Construct exponential models - Given a verbal description of the rate of change of a real world situation, find the exponential function that models it.
https://www.khanacademy.org/e/construct-exponential-models-according-to-rate-of-change
Standard BF.1
Common Core Area - Building Functions
Skill - Model with composite functions - Given two basic functions that model a real-world situation, compose them in order to model a more complex situation.
https://www.khanacademy.org/e/modeling-with-composite-functions
Standard BF.1
Common Core Area - Building Functions
Skill - Writing linear functions word problems - Find a linear function that represents a real-world relationship that is given verbally.
https://www.khanacademy.org/e/constructing-linear-functions-word-problems
Standard BF.1
Common Core Area - Building Functions
Skill - Model with function combination - Given two basic functions that model a real-world situation, combine them using the appropriate arithmetic operation in order to model a more complex situation.
https://www.khanacademy.org/e/combining-functions-with-arithmetic-operations
Standard BF.1
Common Core Area - Building Functions
Skill - Modeling with sinusoidal functions - Given the description of a real-world relationship, find the sinusoidal function that models it.
https://www.khanacademy.org/e/modeling-with-periodic-functions
Standard BF.1
Common Core Area - Building Functions
Skill - Linear models word problems - Solve general word problems about real-world relationships that can be modeled by linear equations or functions.
https://www.khanacademy.org/e/constructing-and-interpreting-linear-functions
Standard BF.1
Common Core Area - Building Functions
Skill - Sequences word problems - Given a verbal description of a real-world relationship, determine the sequence that models that relationship.
https://www.khanacademy.org/e/recursive_explicit
Standard BF.1
Common Core Area - Building Functions
Skill - Construct exponential models - Given a verbal description of the rate of change of a real world situation, find the exponential function that models it.
https://www.khanacademy.org/e/construct-exponential-models-according-to-rate-of-change
Standard BF.1
Common Core Area - Building Functions
Skill - Model with composite functions - Given two basic functions that model a real-world situation, compose them in order to model a more complex situation.
https://www.khanacademy.org/e/modeling-with-composite-functions
Standard BF.1
Common Core Area - Building Functions
Skill - Writing linear functions word problems - Find a linear function that represents a real-world relationship that is given verbally.
https://www.khanacademy.org/e/constructing-linear-functions-word-problems
Standard BF.1
Common Core Area - Building Functions
Skill - Model with function combination - Given two basic functions that model a real-world situation, combine them using the appropriate arithmetic operation in order to model a more complex situation.
https://www.khanacademy.org/e/combining-functions-with-arithmetic-operations
Standard BF.1
Common Core Area - Building Functions
Skill - Writing linear functions word problems - Find a linear function that represents a real-world relationship that is given verbally.
https://www.khanacademy.org/e/constructing-linear-functions-word-problems
Standard BF.1
Common Core Area - Building Functions
Skill - Modeling with sinusoidal functions - Given the description of a real-world relationship, find the sinusoidal function that models it.
https://www.khanacademy.org/e/modeling-with-periodic-functions
Standard BF.1
Common Core Area - Building Functions
Skill - Linear models word problems - Solve general word problems about real-world relationships that can be modeled by linear equations or functions.
https://www.khanacademy.org/e/constructing-and-interpreting-linear-functions
Standard BF.1
Common Core Area - Building Functions
Skill - Sequences word problems - Given a verbal description of a real-world relationship, determine the sequence that models that relationship.
https://www.khanacademy.org/e/recursive_explicit
Standard BF.1
Common Core Area - Building Functions
Skill - Construct exponential models - Given a verbal description of the rate of change of a real world situation, find the exponential function that models it.
https://www.khanacademy.org/e/construct-exponential-models-according-to-rate-of-change
Standard BF.1
Common Core Area - Building Functions
Skill - Model with composite functions - Given two basic functions that model a real-world situation, compose them in order to model a more complex situation.
https://www.khanacademy.org/e/modeling-with-composite-functions
Standard BF.1
Common Core Area - Building Functions
Skill - Linear models word problems - Solve general word problems about real-world relationships that can be modeled by linear equations or functions.
https://www.khanacademy.org/e/constructing-and-interpreting-linear-functions
Standard BF.1
Common Core Area - Building Functions
Skill - Sequences word problems - Given a verbal description of a real-world relationship, determine the sequence that models that relationship.
https://www.khanacademy.org/e/recursive_explicit
Standard BF.1
Common Core Area - Building Functions
Skill - Model with function combination - Given two basic functions that model a real-world situation, combine them using the appropriate arithmetic operation in order to model a more complex situation.
https://www.khanacademy.org/e/combining-functions-with-arithmetic-operations
Standard BF.1
Common Core Area - Building Functions
Skill - Modeling with sinusoidal functions - Given the description of a real-world relationship, find the sinusoidal function that models it.
https://www.khanacademy.org/e/modeling-with-periodic-functions
Standard BF.1
Common Core Area - Building Functions
Skill - Linear models word problems - Solve general word problems about real-world relationships that can be modeled by linear equations or functions.
https://www.khanacademy.org/e/constructing-and-interpreting-linear-functions
Standard BF.1
Common Core Area - Building Functions
Skill - Sequences word problems - Given a verbal description of a real-world relationship, determine the sequence that models that relationship.
https://www.khanacademy.org/e/recursive_explicit
Standard BF.1
Common Core Area - Building Functions
Skill - Construct exponential models - Given a verbal description of the rate of change of a real world situation, find the exponential function that models it.
https://www.khanacademy.org/e/construct-exponential-models-according-to-rate-of-change
Standard BF.1
Common Core Area - Building Functions
Skill - Model with composite functions - Given two basic functions that model a real-world situation, compose them in order to model a more complex situation.
https://www.khanacademy.org/e/modeling-with-composite-functions
Standard BF.1
Common Core Area - Building Functions
Skill - Writing linear functions word problems - Find a linear function that represents a real-world relationship that is given verbally.
https://www.khanacademy.org/e/constructing-linear-functions-word-problems
Standard BF.1
Common Core Area - Building Functions
Skill - Model with function combination - Given two basic functions that model a real-world situation, combine them using the appropriate arithmetic operation in order to model a more complex situation.
https://www.khanacademy.org/e/combining-functions-with-arithmetic-operations
Standard BF.1
Common Core Area - Building Functions
Skill - Modeling with sinusoidal functions - Given the description of a real-world relationship, find the sinusoidal function that models it.
https://www.khanacademy.org/e/modeling-with-periodic-functions
Standard BF.2
Common Core Area - Building Functions
Skill - Converting recursive & explicit forms of arithmetic sequences - Given the explicit formula of an arithmetic sequence, find its recursive formula, and vice versa.
https://www.khanacademy.org/e/explicit-and-recursive-formulas-of-arithmetic-sequences
Standard BF.2
Common Core Area - Building Functions
Skill - Explicit formulas for geometric sequences - Solve problems such as: The first four terms in a geometric sequence are 1/3, 1, 3, and 9. Find an explicit formula for the sequence.
https://www.khanacademy.org/e/sequences-as-functions
Standard BF.2
Common Core Area - Building Functions
Skill - Explicit formulas for arithmetic sequences - Solve problems such as: The first four terms in an arithmetic sequence are 12, 5, -2, and -9. Find an explicit formula for the sequence.
https://www.khanacademy.org/e/explicit-formulas-for-arithmetic-sequences
Standard BF.2
Common Core Area - Building Functions
Skill - Converting recursive & explicit forms of geometric sequences - Given the explicit formula of a geometric sequence, find its recursive formula, and vice versa.
https://www.khanacademy.org/e/explicit-and-recursive-formulas-of-geometric-sequences
Standard BF.2
Common Core Area - Building Functions
Skill - Sequences word problems - Given a verbal description of a real-world relationship, determine the sequence that models that relationship.
https://www.khanacademy.org/e/recursive_explicit
Standard BF.2
Common Core Area - Building Functions
Skill - Recursive formulas for geometric sequences - Find the recursive formula of a geometric sequence given the first few terms or given an explicit formula.
https://www.khanacademy.org/e/recursive-formulas-for-geometric-sequences
Standard BF.2
Common Core Area - Building Functions
Skill - Recursive formulas for arithmetic sequences - Find the recursive formula of an arithmetic sequence given the first few terms.
https://www.khanacademy.org/e/recursive-formulas-for-arithmetic-sequences
Standard BF.3
Common Core Area - Building Functions
Skill - Even & odd functions - Given the graph of a function, determine if it's even, odd, or neither.
https://www.khanacademy.org/e/even_and_odd_functions
Standard BF.3
Common Core Area - Building Functions
Skill - Shift functions - Shift functions horizontally and vertically, and practice the relationship between the graphical and the algebraic representations of those shifts.
https://www.khanacademy.org/e/shift-functions
Standard BF.3
Common Core Area - Building Functions
Skill - Construct sinusoidal functions - Given a few features of a sinusoidal function, find its formula.
https://www.khanacademy.org/e/construct-sinusoidal-functions
Standard BF.3
Common Core Area - Building Functions
Skill - Radical functions & their graphs - Given the formula of a square-root or a cube-root function, find the appropriate graph.
https://www.khanacademy.org/e/graphs-of-radical-functions
Standard BF.3
Common Core Area - Building Functions
Skill - Graphs of logarithmic functions - Graph logarithmic functions and find the appropriate graph given the function.
https://www.khanacademy.org/e/graphs-of-exponentials-and-logarithms
Standard BF.3
Common Core Area - Building Functions
Skill - Graph sinusoidal functions - Given the formula of a sinusoidal function of the form a*f(bx)+d, draw its graph.
https://www.khanacademy.org/e/graphs_of_sine_and_cosine
Standard BF.3
Common Core Area - Building Functions
Skill - Even & odd polynomials - Given the formula of a polynomial function, determine whether that function is even, odd, or neither.
https://www.khanacademy.org/e/determine-if-a-polynomial-is-even-or-odd
Standard BF.3
Common Core Area - Building Functions
Skill - Graphs of exponential functions - Graph exponential functions and find the appropriate graph given the function.
https://www.khanacademy.org/e/graphs-of-exponential-functions
Standard BF.3
Common Core Area - Building Functions
Skill - Transforming functions - Given the graphs of functions f and g where g is a transformation of f, determine the formula of g in terms of f.
https://www.khanacademy.org/e/shifting_and_reflecting_functions
Standard BF.4
Common Core Area - Building Functions
Skill - Determine if a function is invertible - Given the table of values of a function, determine whether it is invertible or not.
https://www.khanacademy.org/e/inverse-domain-range
Standard BF.4
Common Core Area - Building Functions
Skill - Evaluate inverse functions - Practice evaluating the inverse function of a function that is given either as a formula, or as a graph, or as a table of values.
https://www.khanacademy.org/e/understanding-inverse-functions
Standard BF.4
Common Core Area - Building Functions
Skill - Verify inverse functions - Given the formulas of two functions, compose the functions and determine whether they are inverses of each other.
https://www.khanacademy.org/e/inverses_of_functions
Standard BF.4
Common Core Area - Building Functions
Skill - Restrict domains of functions to make them invertible - Given the graph of a function, find ways to restrict its domain in order to make it invertible.
https://www.khanacademy.org/e/restrict-the-domains-of-functions
Standard BF.4
Common Core Area - Building Functions
Skill - Find inverse functions - Practice finding the formula of the inverse function of a given polynomial, radical, or rational function.
https://www.khanacademy.org/e/algebraically-finding-inverses
Standard BF.4
Common Core Area - Building Functions
Skill - Verify inverse functions - Given the formulas of two functions, compose the functions and determine whether they are inverses of each other.
https://www.khanacademy.org/e/inverses_of_functions
Standard BF.4
Common Core Area - Building Functions
Skill - Determine if a function is invertible - Given the table of values of a function, determine whether it is invertible or not.
https://www.khanacademy.org/e/inverse-domain-range
Standard BF.4
Common Core Area - Building Functions
Skill - Find inverse functions - Practice finding the formula of the inverse function of a given polynomial, radical, or rational function.
https://www.khanacademy.org/e/algebraically-finding-inverses
Standard BF.4
Common Core Area - Building Functions
Skill - Restrict domains of functions to make them invertible - Given the graph of a function, find ways to restrict its domain in order to make it invertible.
https://www.khanacademy.org/e/restrict-the-domains-of-functions
Standard BF.4
Common Core Area - Building Functions
Skill - Verify inverse functions - Given the formulas of two functions, compose the functions and determine whether they are inverses of each other.
https://www.khanacademy.org/e/inverses_of_functions
Standard BF.4
Common Core Area - Building Functions
Skill - Restrict domains of functions to make them invertible - Given the graph of a function, find ways to restrict its domain in order to make it invertible.
https://www.khanacademy.org/e/restrict-the-domains-of-functions
Standard BF.4
Common Core Area - Building Functions
Skill - Verify inverse functions - Given the formulas of two functions, compose the functions and determine whether they are inverses of each other.
https://www.khanacademy.org/e/inverses_of_functions
Standard BF.4
Common Core Area - Building Functions
Skill - Find inverse functions - Practice finding the formula of the inverse function of a given polynomial, radical, or rational function.
https://www.khanacademy.org/e/algebraically-finding-inverses
Standard BF.4
Common Core Area - Building Functions
Skill - Determine if a function is invertible - Given the table of values of a function, determine whether it is invertible or not.
https://www.khanacademy.org/e/inverse-domain-range
Standard BF.4
Common Core Area - Building Functions
Skill - Evaluate inverse functions - Practice evaluating the inverse function of a function that is given either as a formula, or as a graph, or as a table of values.
https://www.khanacademy.org/e/understanding-inverse-functions
Standard BF.4
Common Core Area - Building Functions
Skill - Verify inverse functions - Given the formulas of two functions, compose the functions and determine whether they are inverses of each other.
https://www.khanacademy.org/e/inverses_of_functions
Standard BF.4
Common Core Area - Building Functions
Skill - Restrict domains of functions to make them invertible - Given the graph of a function, find ways to restrict its domain in order to make it invertible.
https://www.khanacademy.org/e/restrict-the-domains-of-functions
Standard BF.4
Common Core Area - Building Functions
Skill - Find inverse functions - Practice finding the formula of the inverse function of a given polynomial, radical, or rational function.
https://www.khanacademy.org/e/algebraically-finding-inverses
Standard BF.4
Common Core Area - Building Functions
Skill - Determine if a function is invertible - Given the table of values of a function, determine whether it is invertible or not.
https://www.khanacademy.org/e/inverse-domain-range
Standard BF.4
Common Core Area - Building Functions
Skill - Evaluate inverse functions - Practice evaluating the inverse function of a function that is given either as a formula, or as a graph, or as a table of values.
https://www.khanacademy.org/e/understanding-inverse-functions
Standard BF.4
Common Core Area - Building Functions
Skill - Restrict domains of functions to make them invertible - Given the graph of a function, find ways to restrict its domain in order to make it invertible.
https://www.khanacademy.org/e/restrict-the-domains-of-functions
Standard BF.4
Common Core Area - Building Functions
Skill - Find inverse functions - Practice finding the formula of the inverse function of a given polynomial, radical, or rational function.
https://www.khanacademy.org/e/algebraically-finding-inverses
Standard BF.4
Common Core Area - Building Functions
Skill - Determine if a function is invertible - Given the table of values of a function, determine whether it is invertible or not.
https://www.khanacademy.org/e/inverse-domain-range
Standard BF.4
Common Core Area - Building Functions
Skill - Evaluate inverse functions - Practice evaluating the inverse function of a function that is given either as a formula, or as a graph, or as a table of values.
https://www.khanacademy.org/e/understanding-inverse-functions
Standard BF.4
Common Core Area - Building Functions
Skill - Evaluate inverse functions - Practice evaluating the inverse function of a function that is given either as a formula, or as a graph, or as a table of values.
https://www.khanacademy.org/e/understanding-inverse-functions
Standard BF.5
Common Core Area - Building Functions
Skill - Relationship between exponentials & logarithms - Solve various problems that focus on the relationship between a^x=b and log_a(b)=x.
https://www.khanacademy.org/e/understanding-logs-as-inverse-exponentials
Standard BF.5
Common Core Area - Building Functions
Skill - Evaluate logarithms - Evaluate basic logarithmic expressions by using the fact that a^x=b is equivalent to log_a(b)=x.
https://www.khanacademy.org/e/logarithms_1
Standard BF.5
Common Core Area - Building Functions
Skill - Evaluate logarithms (advanced) - Evaluate advanced logarithmic expressions by using the fact that a^x=b is equivalent to log_a(b)=x.
Standard IF.1
Common Core Area - Interpreting Functions
Skill - Function inputs & outputs: graph - Find all the inputs that correspond to a given function output, using the function's graph.
https://www.khanacademy.org/e/match-inputs-to-outputs-from-a-graph
Standard IF.1
Common Core Area - Interpreting Functions
Skill - Function inputs & outputs: equation - Find all the inputs that correspond to a given function output, using the function's formula.
https://www.khanacademy.org/e/functions_matching_inputs_outputs
Standard IF.1
Common Core Area - Interpreting Functions
Skill - Function rules from equations - Create functions that match one variable to the other in a two-variable equation.
https://www.khanacademy.org/e/functions-from-equations
Standard IF.1
Common Core Area - Interpreting Functions
Skill - Recognize functions from tables - Determine whether a table of values of a relationship represents a function.
https://www.khanacademy.org/e/recognizing_functions
Standard IF.1
Common Core Area - Interpreting Functions
Skill - Domain of advanced functions - Determine the domain of functions whose expressions are a combination of different types of assignment rules.
https://www.khanacademy.org/e/domain_of_a_function
Standard IF.1
Common Core Area - Interpreting Functions
Skill - Recognize functions from graphs - Determine whether a given graph represents a function.
https://www.khanacademy.org/e/recog-func-2
Standard IF.1
Common Core Area - Interpreting Functions
Skill - Domain of advanced piecewise functions - Determine the domain of piecewise functions whose assignment rules have different expression types.
https://www.khanacademy.org/e/determine-the-domain-of-advanced-piecewise-functions
Standard IF.1
Common Core Area - Interpreting Functions
Skill - Range of quadratic functions - Given the equation of a quadratic function, determine its range.
https://www.khanacademy.org/e/range_of_a_function
Standard IF.1
Common Core Area - Interpreting Functions
Skill - Evaluate functions from their graph - Evaluate functions for specific inputs given the graph of the function.
https://www.khanacademy.org/e/evaluate-functions-from-their-graph
Standard IF.1
Common Core Area - Interpreting Functions
Skill - Evaluate function expressions - Evaluate expressions that contain function notation, given the functions' graphs.
https://www.khanacademy.org/e/functions_2
Standard IF.2
Common Core Area - Interpreting Functions
Skill - Evaluate sequences in recursive form - Find the first few terms of sequences that are defined recursively.
https://www.khanacademy.org/e/evaluating-sequences-in-recursive-form
Standard IF.2
Common Core Area - Interpreting Functions
Skill - Function inputs & outputs: equation - Find all the inputs that correspond to a given function output, using the function's formula.
https://www.khanacademy.org/e/functions_matching_inputs_outputs
Standard IF.2
Common Core Area - Interpreting Functions
Skill - Evaluate step functions - Given the graph of a step function, find the function's outputs for given specific inputs.
https://www.khanacademy.org/e/evaluate-step-functions-from-their-graph
Standard IF.2
Common Core Area - Interpreting Functions
Skill - Use arithmetic sequence formulas - Given the formula of an arithmetic sequence, either in explicit form or in recursive form, find a specific term in the sequence.
https://www.khanacademy.org/e/arithmetic_sequences_2
Standard IF.2
Common Core Area - Interpreting Functions
Skill - Function notation word problems - Interpret expressions with function notation in terms of the context that the function models.
https://www.khanacademy.org/e/function-notation-in-context
Standard IF.2
Common Core Area - Interpreting Functions
Skill - Evaluate functions from their graph - Evaluate functions for specific inputs given the graph of the function.
https://www.khanacademy.org/e/evaluate-functions-from-their-graph
Standard IF.2
Common Core Area - Interpreting Functions
Skill - Evaluate piecewise functions - Given the formula of a piecewise function, evaluate it for a specific input.
https://www.khanacademy.org/e/evaluating-piecewise-functions
Standard IF.2
Common Core Area - Interpreting Functions
Skill - Use geometric sequence formulas - Given the formula of a geometric sequence, either in explicit form or in recursive form, find a specific term in the sequence.
https://www.khanacademy.org/e/geometric_sequences_2
Standard IF.2
Common Core Area - Interpreting Functions
Skill - Function inputs & outputs: graph - Find all the inputs that correspond to a given function output, using the function's graph.
https://www.khanacademy.org/e/match-inputs-to-outputs-from-a-graph
Standard IF.2
Common Core Area - Interpreting Functions
Skill - Evaluate function expressions - Evaluate expressions that contain function notation, given the functions' graphs.
https://www.khanacademy.org/e/functions_2
Standard IF.2
Common Core Area - Interpreting Functions
Skill - Evaluate functions - Evaluate functions for specific inputs given the formula of the function.
https://www.khanacademy.org/e/functions_1
Standard IF.3
Common Core Area - Interpreting Functions
Skill - Extend geometric sequences - Given the first few terms in a geometric sequence, find the next term in the sequence.
https://www.khanacademy.org/e/geometric_sequences_1
Standard IF.3
Common Core Area - Interpreting Functions
Skill - Extend geometric sequences: negatives & fractions - Find the next term in a geometric sequence. The problems in this quiz involve relatively difficult calculations.
https://www.khanacademy.org/e/extend-geometric-sequences-negatives-fractions
Standard IF.3
Common Core Area - Interpreting Functions
Skill - Use arithmetic sequence formulas - Given the formula of an arithmetic sequence, either in explicit form or in recursive form, find a specific term in the sequence.
https://www.khanacademy.org/e/arithmetic_sequences_2
Standard IF.3
Common Core Area - Interpreting Functions
Skill - Use geometric sequence formulas - Given the formula of a geometric sequence, either in explicit form or in recursive form, find a specific term in the sequence.
https://www.khanacademy.org/e/geometric_sequences_2
Standard IF.3
Common Core Area - Interpreting Functions
Skill - Extend arithmetic sequences - Given the first few terms in an arithmetic sequence, find the next term in the sequence.
https://www.khanacademy.org/e/arithmetic_sequences_1
Standard IF.4
Common Core Area - Interpreting Functions
Skill - Linear models word problems - Solve general word problems about real-world relationships that can be modeled by linear equations or functions.
https://www.khanacademy.org/e/constructing-and-interpreting-linear-functions
Standard IF.4
Common Core Area - Interpreting Functions
Skill - Graph interpretation word problems - Match features of graphs of modeling functions to their real-world meaning.
https://www.khanacademy.org/e/interpret-features-func-2
Standard IF.4
Common Core Area - Interpreting Functions
Skill - End behavior of algebraic models - Given the graph that models a real world context, answer a question about the end behavior of the graph.
https://www.khanacademy.org/e/recog-features-func-2
Standard IF.4
Common Core Area - Interpreting Functions
Skill - Linear equations word problems: graphs - Solve word problems about real world relationships that are given in graphs.
https://www.khanacademy.org/e/interpreting-linear-graphs
Standard IF.4
Common Core Area - Interpreting Functions
Skill - Quadratic word problems (standard form) - Solve real-world word problems that involve quadratic models. In this exercise, that models are given in standard form.
https://www.khanacademy.org/e/key-features-quadratics
Standard IF.4
Common Core Area - Interpreting Functions
Skill - Comparing linear functions word problem - Compare features of two real-world relationships that can be modeled by linear functions, where the functions are represented in different ways.
https://www.khanacademy.org/e/comparing-features-of-functions-1
Standard IF.4
Common Core Area - Interpreting Functions
Skill - Periodicity of algebraic models - Given the graph that models a real world context, answer a question about the periodicity of the graph.
https://www.khanacademy.org/e/interpret-the-periodicity-of-modeling-functions
Standard IF.4
Common Core Area - Interpreting Functions
Skill - Linear equations word problems: tables - Solve word problems about real world relationships that are given in tables.
https://www.khanacademy.org/e/interpreting-tables
Standard IF.5
Common Core Area - Interpreting Functions
Skill - Determine the domain of functions - Determine the domain of a function according to the algebraic limitations of that function.
https://www.khanacademy.org/e/domain-of-algebraic-functions
Standard IF.5
Common Core Area - Interpreting Functions
Skill - Function domain word problems - Use information about a situation to figure out the domain of the function which models it.
https://www.khanacademy.org/e/interpreting-domain
Standard IF.5
Common Core Area - Interpreting Functions
Skill - Domain and range from graph - Given the graph of a function, determine its domain or range.
https://www.khanacademy.org/e/domain_and_range_0.5
Standard IF.6
Common Core Area - Interpreting Functions
Skill - Average rate of change word problems - Find and represent the average rate of change of a real-world relationship.
https://www.khanacademy.org/e/average-rate-of-change-word-problems
Standard IF.6
Common Core Area - Interpreting Functions
Skill - Average rate of change: graphs & tables - Find a function's average rate of change over a specific interval, given the function's graph or a table of values.
https://www.khanacademy.org/e/avg-rate-of-change-graphs-tables
Standard IF.6
Common Core Area - Interpreting Functions
Skill - Average rate of change - Find the average rate of change of a function over a given interval.
https://www.khanacademy.org/e/avg-rate-of-change
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Positive & negative intervals of polynomials - Given a polynomial, determine the intervals in which it is positive or negative.
https://www.khanacademy.org/e/positive-and-negative-intervals-of-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Increasing and decreasing intervals - Highlight intervals on the domain of a function where it's only increasing or only decreasing.
https://www.khanacademy.org/e/increasing-decreasing-intervals-of-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in factored form - Graph quadratic functions that are given in factored form. For example, graph y=(x-4)(x+2).
https://www.khanacademy.org/e/graph-quadratic-functions-in-factored-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Radical functions & their graphs - Given the formula of a square-root or a cube-root function, find the appropriate graph.
https://www.khanacademy.org/e/graphs-of-radical-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from a table - Find the intercepts of a line given a table of values.
https://www.khanacademy.org/e/intercepts-from-table
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Amplitude of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its amplitude.
https://www.khanacademy.org/e/find-amplitude-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Positive and negative intervals - Highlight intervals on the domain of a function where it's entirely positive or entirely negative.
https://www.khanacademy.org/e/positive_and_negative_parts_of_functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Midline of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its midline equation.
https://www.khanacademy.org/e/find-midline-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Amplitude of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its amplitude.
https://www.khanacademy.org/e/amplitude-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph sinusoidal functions - Given the formula of a sinusoidal function of the form a*f(bx)+d, draw its graph.
https://www.khanacademy.org/e/graphs_of_sine_and_cosine
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Analyze vertical asymptotes of rational functions - Given the formula of a rational function, determine how it behaves around its vertical asymptote.
https://www.khanacademy.org/e/analyze-vertical-asymptotes-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in standard form - Graph quadratic functions given in the standard form ax²+bx+c. For example, graph y=5x²-20x+15.
https://www.khanacademy.org/e/graphing_parabolas_0.5
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope-intercept intro - Practice your basic understanding of slope-intercept form for linear equations.
https://www.khanacademy.org/e/slope-from-an-equation-in-slope-intercept-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope from two points - Find the slope of the line that goes through the two points that are given to you.
https://www.khanacademy.org/e/slope-from-two-points
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph absolute value functions - Graph absolute value functions like f(x)=|x+3|+2.
https://www.khanacademy.org/e/graphs-of-absolute-value-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Absolute maxima and minima - Given the graph of a function, find its absolute maximum and minimum points.
https://www.khanacademy.org/e/recognize-absolute-maxima-and-minima
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphing linear functions word problems - Graph the line that represents a real-world relationship that is given verbally.
https://www.khanacademy.org/e/graphing-linear-functions-word-problems
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Evaluate piecewise functions - Given the formula of a piecewise function, evaluate it for a specific input.
https://www.khanacademy.org/e/evaluating-piecewise-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Horizontal & vertical lines - Practice your knowledge of horizontal and vertical lines: their graphical presentation, their slopes, and their equations.
https://www.khanacademy.org/e/horizontal-and-vertical-lines
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Piecewise functions graphs - Match the formula of a piecewise function to its graph.
https://www.khanacademy.org/e/piecewise-graphs-linear
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Midline of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its midline equation.
https://www.khanacademy.org/e/midline-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope-intercept intro - Practice your basic understanding of slope-intercept form for linear equations.
https://www.khanacademy.org/e/slope-from-an-equation-in-slope-intercept-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in factored form - Graph quadratic functions that are given in factored form. For example, graph y=(x-4)(x+2).
https://www.khanacademy.org/e/graph-quadratic-functions-in-factored-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Radical functions & their graphs - Given the formula of a square-root or a cube-root function, find the appropriate graph.
https://www.khanacademy.org/e/graphs-of-radical-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from a table - Find the intercepts of a line given a table of values.
https://www.khanacademy.org/e/intercepts-from-table
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Amplitude of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its amplitude.
https://www.khanacademy.org/e/find-amplitude-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Positive and negative intervals - Highlight intervals on the domain of a function where it's entirely positive or entirely negative.
https://www.khanacademy.org/e/positive_and_negative_parts_of_functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Midline of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its midline equation.
https://www.khanacademy.org/e/find-midline-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Amplitude of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its amplitude.
https://www.khanacademy.org/e/amplitude-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph sinusoidal functions - Given the formula of a sinusoidal function of the form a*f(bx)+d, draw its graph.
https://www.khanacademy.org/e/graphs_of_sine_and_cosine
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Analyze vertical asymptotes of rational functions - Given the formula of a rational function, determine how it behaves around its vertical asymptote.
https://www.khanacademy.org/e/analyze-vertical-asymptotes-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in standard form - Graph quadratic functions given in the standard form ax²+bx+c. For example, graph y=5x²-20x+15.
https://www.khanacademy.org/e/graphing_parabolas_0.5
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Positive & negative intervals of polynomials - Given a polynomial, determine the intervals in which it is positive or negative.
https://www.khanacademy.org/e/positive-and-negative-intervals-of-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope from two points - Find the slope of the line that goes through the two points that are given to you.
https://www.khanacademy.org/e/slope-from-two-points
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph absolute value functions - Graph absolute value functions like f(x)=|x+3|+2.
https://www.khanacademy.org/e/graphs-of-absolute-value-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Absolute maxima and minima - Given the graph of a function, find its absolute maximum and minimum points.
https://www.khanacademy.org/e/recognize-absolute-maxima-and-minima
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphing linear functions word problems - Graph the line that represents a real-world relationship that is given verbally.
https://www.khanacademy.org/e/graphing-linear-functions-word-problems
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Evaluate piecewise functions - Given the formula of a piecewise function, evaluate it for a specific input.
https://www.khanacademy.org/e/evaluating-piecewise-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Horizontal & vertical lines - Practice your knowledge of horizontal and vertical lines: their graphical presentation, their slopes, and their equations.
https://www.khanacademy.org/e/horizontal-and-vertical-lines
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Piecewise functions graphs - Match the formula of a piecewise function to its graph.
https://www.khanacademy.org/e/piecewise-graphs-linear
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Midline of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its midline equation.
https://www.khanacademy.org/e/midline-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Relative maxima and minima - Given the graph of a function, find all of its relative maximum and minimum points.
https://www.khanacademy.org/e/recognize-maxima-and-minima
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Horizontal & vertical lines - Practice your knowledge of horizontal and vertical lines: their graphical presentation, their slopes, and their equations.
https://www.khanacademy.org/e/horizontal-and-vertical-lines
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Evaluate step functions - Given the graph of a step function, find the function's outputs for given specific inputs.
https://www.khanacademy.org/e/evaluate-step-functions-from-their-graph
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Increasing and decreasing intervals - Highlight intervals on the domain of a function where it's only increasing or only decreasing.
https://www.khanacademy.org/e/increasing-decreasing-intervals-of-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Rational function points of discontinuity - Given a rational function, sort given input values according to zeros, vertical asymptotes, and removable discontinuities.
https://www.khanacademy.org/e/points-of-discontinuity-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope from equation - Find the slopes of lines whose equations are given in various forms. For example, find the slope of 2x+3y=5.
https://www.khanacademy.org/e/slope-from-an-equation-in-standard-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of logarithmic functions - Graph logarithmic functions and find the appropriate graph given the function.
https://www.khanacademy.org/e/graphs-of-exponentials-and-logarithms
Standard IF.7
Common Core Area - Interpreting Functions
Skill - End behavior of rational functions - Given a rational function, determine how it behaves as x approaches +∞ or -∞.
https://www.khanacademy.org/e/end-behavior-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - End behavior of polynomials - Analyze polynomial functions to determine how they behave as the input variable increases to positive infinity or decreases to negative infinity.
https://www.khanacademy.org/e/determine-the-end-behavior-of-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph parabolas in all forms - Graph quadratic functions given in any form.
https://www.khanacademy.org/e/graphing_parabolas_2
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from a graph - Look at the graph of an equation to find x-intercepts and y-intercepts
https://www.khanacademy.org/e/linear-function-intercepts
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of exponential functions - Graph exponential functions and find the appropriate graph given the function.
https://www.khanacademy.org/e/graphs-of-exponential-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Relative maxima and minima - Given the graph of a function, find all of its relative maximum and minimum points.
https://www.khanacademy.org/e/recognize-maxima-and-minima
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in vertex form - Graph quadratic functions that are given in the vertex form a(x+b)²+c. For example, graph y=-2(x-2)²+5.
https://www.khanacademy.org/e/graphing_parabolas_1
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of rational functions - Determine which of four graphs fits the formula of a given function.
https://www.khanacademy.org/e/graphs-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph from linear standard form - Find the graph of a linear equation given in standard form.
https://www.khanacademy.org/e/graph-from-standard-form-equation
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Period of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its period.
https://www.khanacademy.org/e/period-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphing exponential growth & decay - Graph exponential functions of the basic form f(x)=a⋅rˣ.
https://www.khanacademy.org/e/graphs-of-basic-exponential-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Period of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its period.
https://www.khanacademy.org/e/find-period-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of nonlinear piecewise functions - Given the graph of a nonlinear piecewise function, find its formula.
https://www.khanacademy.org/e/graphing-piecewise-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from an equation - Solve linear equations for the x-intercept and y-intercept
https://www.khanacademy.org/e/solving_for_the_x-intercept
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph from slope-intercept form - Practice drawing the graph of a line given in slope-intercept form. For example, graph y = 3x + 2.
https://www.khanacademy.org/e/graph-from-slope-intercept-equation
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of rational functions - Determine which of four graphs fits the formula of a given function.
https://www.khanacademy.org/e/graphs-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Amplitude of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its amplitude.
https://www.khanacademy.org/e/amplitude-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Midline of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its midline equation.
https://www.khanacademy.org/e/find-midline-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Positive and negative intervals - Highlight intervals on the domain of a function where it's entirely positive or entirely negative.
https://www.khanacademy.org/e/positive_and_negative_parts_of_functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Amplitude of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its amplitude.
https://www.khanacademy.org/e/find-amplitude-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from a table - Find the intercepts of a line given a table of values.
https://www.khanacademy.org/e/intercepts-from-table
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Radical functions & their graphs - Given the formula of a square-root or a cube-root function, find the appropriate graph.
https://www.khanacademy.org/e/graphs-of-radical-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in factored form - Graph quadratic functions that are given in factored form. For example, graph y=(x-4)(x+2).
https://www.khanacademy.org/e/graph-quadratic-functions-in-factored-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Positive & negative intervals of polynomials - Given a polynomial, determine the intervals in which it is positive or negative.
https://www.khanacademy.org/e/positive-and-negative-intervals-of-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph from slope-intercept form - Practice drawing the graph of a line given in slope-intercept form. For example, graph y = 3x + 2.
https://www.khanacademy.org/e/graph-from-slope-intercept-equation
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from an equation - Solve linear equations for the x-intercept and y-intercept
https://www.khanacademy.org/e/solving_for_the_x-intercept
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of nonlinear piecewise functions - Given the graph of a nonlinear piecewise function, find its formula.
https://www.khanacademy.org/e/graphing-piecewise-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Period of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its period.
https://www.khanacademy.org/e/find-period-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphing exponential growth & decay - Graph exponential functions of the basic form f(x)=a⋅rˣ.
https://www.khanacademy.org/e/graphs-of-basic-exponential-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Period of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its period.
https://www.khanacademy.org/e/period-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph from linear standard form - Find the graph of a linear equation given in standard form.
https://www.khanacademy.org/e/graph-from-standard-form-equation
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph sinusoidal functions - Given the formula of a sinusoidal function of the form a*f(bx)+d, draw its graph.
https://www.khanacademy.org/e/graphs_of_sine_and_cosine
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in vertex form - Graph quadratic functions that are given in the vertex form a(x+b)²+c. For example, graph y=-2(x-2)²+5.
https://www.khanacademy.org/e/graphing_parabolas_1
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Evaluate step functions - Given the graph of a step function, find the function's outputs for given specific inputs.
https://www.khanacademy.org/e/evaluate-step-functions-from-their-graph
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of exponential functions - Graph exponential functions and find the appropriate graph given the function.
https://www.khanacademy.org/e/graphs-of-exponential-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from a graph - Look at the graph of an equation to find x-intercepts and y-intercepts
https://www.khanacademy.org/e/linear-function-intercepts
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph parabolas in all forms - Graph quadratic functions given in any form.
https://www.khanacademy.org/e/graphing_parabolas_2
Standard IF.7
Common Core Area - Interpreting Functions
Skill - End behavior of polynomials - Analyze polynomial functions to determine how they behave as the input variable increases to positive infinity or decreases to negative infinity.
https://www.khanacademy.org/e/determine-the-end-behavior-of-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - End behavior of rational functions - Given a rational function, determine how it behaves as x approaches +∞ or -∞.
https://www.khanacademy.org/e/end-behavior-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of logarithmic functions - Graph logarithmic functions and find the appropriate graph given the function.
https://www.khanacademy.org/e/graphs-of-exponentials-and-logarithms
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope from equation - Find the slopes of lines whose equations are given in various forms. For example, find the slope of 2x+3y=5.
https://www.khanacademy.org/e/slope-from-an-equation-in-standard-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Rational function points of discontinuity - Given a rational function, sort given input values according to zeros, vertical asymptotes, and removable discontinuities.
https://www.khanacademy.org/e/points-of-discontinuity-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Increasing and decreasing intervals - Highlight intervals on the domain of a function where it's only increasing or only decreasing.
https://www.khanacademy.org/e/increasing-decreasing-intervals-of-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Relative maxima and minima - Given the graph of a function, find all of its relative maximum and minimum points.
https://www.khanacademy.org/e/recognize-maxima-and-minima
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Midline of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its midline equation.
https://www.khanacademy.org/e/midline-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Piecewise functions graphs - Match the formula of a piecewise function to its graph.
https://www.khanacademy.org/e/piecewise-graphs-linear
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope from equation - Find the slopes of lines whose equations are given in various forms. For example, find the slope of 2x+3y=5.
https://www.khanacademy.org/e/slope-from-an-equation-in-standard-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from an equation - Solve linear equations for the x-intercept and y-intercept
https://www.khanacademy.org/e/solving_for_the_x-intercept
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of nonlinear piecewise functions - Given the graph of a nonlinear piecewise function, find its formula.
https://www.khanacademy.org/e/graphing-piecewise-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Period of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its period.
https://www.khanacademy.org/e/find-period-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphing exponential growth & decay - Graph exponential functions of the basic form f(x)=a⋅rˣ.
https://www.khanacademy.org/e/graphs-of-basic-exponential-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Period of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its period.
https://www.khanacademy.org/e/period-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph from linear standard form - Find the graph of a linear equation given in standard form.
https://www.khanacademy.org/e/graph-from-standard-form-equation
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of rational functions - Determine which of four graphs fits the formula of a given function.
https://www.khanacademy.org/e/graphs-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in vertex form - Graph quadratic functions that are given in the vertex form a(x+b)²+c. For example, graph y=-2(x-2)²+5.
https://www.khanacademy.org/e/graphing_parabolas_1
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Evaluate step functions - Given the graph of a step function, find the function's outputs for given specific inputs.
https://www.khanacademy.org/e/evaluate-step-functions-from-their-graph
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of exponential functions - Graph exponential functions and find the appropriate graph given the function.
https://www.khanacademy.org/e/graphs-of-exponential-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from a graph - Look at the graph of an equation to find x-intercepts and y-intercepts
https://www.khanacademy.org/e/linear-function-intercepts
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph parabolas in all forms - Graph quadratic functions given in any form.
https://www.khanacademy.org/e/graphing_parabolas_2
Standard IF.7
Common Core Area - Interpreting Functions
Skill - End behavior of polynomials - Analyze polynomial functions to determine how they behave as the input variable increases to positive infinity or decreases to negative infinity.
https://www.khanacademy.org/e/determine-the-end-behavior-of-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - End behavior of rational functions - Given a rational function, determine how it behaves as x approaches +∞ or -∞.
https://www.khanacademy.org/e/end-behavior-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of logarithmic functions - Graph logarithmic functions and find the appropriate graph given the function.
https://www.khanacademy.org/e/graphs-of-exponentials-and-logarithms
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph from slope-intercept form - Practice drawing the graph of a line given in slope-intercept form. For example, graph y = 3x + 2.
https://www.khanacademy.org/e/graph-from-slope-intercept-equation
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Rational function points of discontinuity - Given a rational function, sort given input values according to zeros, vertical asymptotes, and removable discontinuities.
https://www.khanacademy.org/e/points-of-discontinuity-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Increasing and decreasing intervals - Highlight intervals on the domain of a function where it's only increasing or only decreasing.
https://www.khanacademy.org/e/increasing-decreasing-intervals-of-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Relative maxima and minima - Given the graph of a function, find all of its relative maximum and minimum points.
https://www.khanacademy.org/e/recognize-maxima-and-minima
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Midline of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its midline equation.
https://www.khanacademy.org/e/midline-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Piecewise functions graphs - Match the formula of a piecewise function to its graph.
https://www.khanacademy.org/e/piecewise-graphs-linear
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Horizontal & vertical lines - Practice your knowledge of horizontal and vertical lines: their graphical presentation, their slopes, and their equations.
https://www.khanacademy.org/e/horizontal-and-vertical-lines
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Evaluate piecewise functions - Given the formula of a piecewise function, evaluate it for a specific input.
https://www.khanacademy.org/e/evaluating-piecewise-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphing linear functions word problems - Graph the line that represents a real-world relationship that is given verbally.
https://www.khanacademy.org/e/graphing-linear-functions-word-problems
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Absolute maxima and minima - Given the graph of a function, find its absolute maximum and minimum points.
https://www.khanacademy.org/e/recognize-absolute-maxima-and-minima
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph absolute value functions - Graph absolute value functions like f(x)=|x+3|+2.
https://www.khanacademy.org/e/graphs-of-absolute-value-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope from two points - Find the slope of the line that goes through the two points that are given to you.
https://www.khanacademy.org/e/slope-from-two-points
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope-intercept intro - Practice your basic understanding of slope-intercept form for linear equations.
https://www.khanacademy.org/e/slope-from-an-equation-in-slope-intercept-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in standard form - Graph quadratic functions given in the standard form ax²+bx+c. For example, graph y=5x²-20x+15.
https://www.khanacademy.org/e/graphing_parabolas_0.5
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Analyze vertical asymptotes of rational functions - Given the formula of a rational function, determine how it behaves around its vertical asymptote.
https://www.khanacademy.org/e/analyze-vertical-asymptotes-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Absolute maxima and minima - Given the graph of a function, find its absolute maximum and minimum points.
https://www.khanacademy.org/e/recognize-absolute-maxima-and-minima
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope from two points - Find the slope of the line that goes through the two points that are given to you.
https://www.khanacademy.org/e/slope-from-two-points
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph absolute value functions - Graph absolute value functions like f(x)=|x+3|+2.
https://www.khanacademy.org/e/graphs-of-absolute-value-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Absolute maxima and minima - Given the graph of a function, find its absolute maximum and minimum points.
https://www.khanacademy.org/e/recognize-absolute-maxima-and-minima
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphing linear functions word problems - Graph the line that represents a real-world relationship that is given verbally.
https://www.khanacademy.org/e/graphing-linear-functions-word-problems
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Evaluate piecewise functions - Given the formula of a piecewise function, evaluate it for a specific input.
https://www.khanacademy.org/e/evaluating-piecewise-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Rational function points of discontinuity - Given a rational function, sort given input values according to zeros, vertical asymptotes, and removable discontinuities.
https://www.khanacademy.org/e/points-of-discontinuity-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Increasing and decreasing intervals - Highlight intervals on the domain of a function where it's only increasing or only decreasing.
https://www.khanacademy.org/e/increasing-decreasing-intervals-of-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Relative maxima and minima - Given the graph of a function, find all of its relative maximum and minimum points.
https://www.khanacademy.org/e/recognize-maxima-and-minima
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Midline of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its midline equation.
https://www.khanacademy.org/e/midline-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Piecewise functions graphs - Match the formula of a piecewise function to its graph.
https://www.khanacademy.org/e/piecewise-graphs-linear
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Horizontal & vertical lines - Practice your knowledge of horizontal and vertical lines: their graphical presentation, their slopes, and their equations.
https://www.khanacademy.org/e/horizontal-and-vertical-lines
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Evaluate piecewise functions - Given the formula of a piecewise function, evaluate it for a specific input.
https://www.khanacademy.org/e/evaluating-piecewise-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphing linear functions word problems - Graph the line that represents a real-world relationship that is given verbally.
https://www.khanacademy.org/e/graphing-linear-functions-word-problems
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope-intercept intro - Practice your basic understanding of slope-intercept form for linear equations.
https://www.khanacademy.org/e/slope-from-an-equation-in-slope-intercept-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph absolute value functions - Graph absolute value functions like f(x)=|x+3|+2.
https://www.khanacademy.org/e/graphs-of-absolute-value-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope from two points - Find the slope of the line that goes through the two points that are given to you.
https://www.khanacademy.org/e/slope-from-two-points
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope-intercept intro - Practice your basic understanding of slope-intercept form for linear equations.
https://www.khanacademy.org/e/slope-from-an-equation-in-slope-intercept-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in standard form - Graph quadratic functions given in the standard form ax²+bx+c. For example, graph y=5x²-20x+15.
https://www.khanacademy.org/e/graphing_parabolas_0.5
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Analyze vertical asymptotes of rational functions - Given the formula of a rational function, determine how it behaves around its vertical asymptote.
https://www.khanacademy.org/e/analyze-vertical-asymptotes-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph sinusoidal functions - Given the formula of a sinusoidal function of the form a*f(bx)+d, draw its graph.
https://www.khanacademy.org/e/graphs_of_sine_and_cosine
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Amplitude of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its amplitude.
https://www.khanacademy.org/e/amplitude-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Midline of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its midline equation.
https://www.khanacademy.org/e/find-midline-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Positive and negative intervals - Highlight intervals on the domain of a function where it's entirely positive or entirely negative.
https://www.khanacademy.org/e/positive_and_negative_parts_of_functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Amplitude of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its amplitude.
https://www.khanacademy.org/e/find-amplitude-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from a table - Find the intercepts of a line given a table of values.
https://www.khanacademy.org/e/intercepts-from-table
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Radical functions & their graphs - Given the formula of a square-root or a cube-root function, find the appropriate graph.
https://www.khanacademy.org/e/graphs-of-radical-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in factored form - Graph quadratic functions that are given in factored form. For example, graph y=(x-4)(x+2).
https://www.khanacademy.org/e/graph-quadratic-functions-in-factored-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Positive & negative intervals of polynomials - Given a polynomial, determine the intervals in which it is positive or negative.
https://www.khanacademy.org/e/positive-and-negative-intervals-of-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of nonlinear piecewise functions - Given the graph of a nonlinear piecewise function, find its formula.
https://www.khanacademy.org/e/graphing-piecewise-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope from equation - Find the slopes of lines whose equations are given in various forms. For example, find the slope of 2x+3y=5.
https://www.khanacademy.org/e/slope-from-an-equation-in-standard-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of logarithmic functions - Graph logarithmic functions and find the appropriate graph given the function.
https://www.khanacademy.org/e/graphs-of-exponentials-and-logarithms
Standard IF.7
Common Core Area - Interpreting Functions
Skill - End behavior of rational functions - Given a rational function, determine how it behaves as x approaches +∞ or -∞.
https://www.khanacademy.org/e/end-behavior-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - End behavior of polynomials - Analyze polynomial functions to determine how they behave as the input variable increases to positive infinity or decreases to negative infinity.
https://www.khanacademy.org/e/determine-the-end-behavior-of-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph parabolas in all forms - Graph quadratic functions given in any form.
https://www.khanacademy.org/e/graphing_parabolas_2
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from a graph - Look at the graph of an equation to find x-intercepts and y-intercepts
https://www.khanacademy.org/e/linear-function-intercepts
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of exponential functions - Graph exponential functions and find the appropriate graph given the function.
https://www.khanacademy.org/e/graphs-of-exponential-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Evaluate step functions - Given the graph of a step function, find the function's outputs for given specific inputs.
https://www.khanacademy.org/e/evaluate-step-functions-from-their-graph
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in vertex form - Graph quadratic functions that are given in the vertex form a(x+b)²+c. For example, graph y=-2(x-2)²+5.
https://www.khanacademy.org/e/graphing_parabolas_1
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of rational functions - Determine which of four graphs fits the formula of a given function.
https://www.khanacademy.org/e/graphs-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph from linear standard form - Find the graph of a linear equation given in standard form.
https://www.khanacademy.org/e/graph-from-standard-form-equation
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Period of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its period.
https://www.khanacademy.org/e/period-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphing exponential growth & decay - Graph exponential functions of the basic form f(x)=a⋅rˣ.
https://www.khanacademy.org/e/graphs-of-basic-exponential-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Period of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its period.
https://www.khanacademy.org/e/find-period-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Rational function points of discontinuity - Given a rational function, sort given input values according to zeros, vertical asymptotes, and removable discontinuities.
https://www.khanacademy.org/e/points-of-discontinuity-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from an equation - Solve linear equations for the x-intercept and y-intercept
https://www.khanacademy.org/e/solving_for_the_x-intercept
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph from slope-intercept form - Practice drawing the graph of a line given in slope-intercept form. For example, graph y = 3x + 2.
https://www.khanacademy.org/e/graph-from-slope-intercept-equation
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Positive & negative intervals of polynomials - Given a polynomial, determine the intervals in which it is positive or negative.
https://www.khanacademy.org/e/positive-and-negative-intervals-of-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in factored form - Graph quadratic functions that are given in factored form. For example, graph y=(x-4)(x+2).
https://www.khanacademy.org/e/graph-quadratic-functions-in-factored-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Radical functions & their graphs - Given the formula of a square-root or a cube-root function, find the appropriate graph.
https://www.khanacademy.org/e/graphs-of-radical-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from a table - Find the intercepts of a line given a table of values.
https://www.khanacademy.org/e/intercepts-from-table
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Amplitude of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its amplitude.
https://www.khanacademy.org/e/find-amplitude-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Positive and negative intervals - Highlight intervals on the domain of a function where it's entirely positive or entirely negative.
https://www.khanacademy.org/e/positive_and_negative_parts_of_functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Midline of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its midline equation.
https://www.khanacademy.org/e/find-midline-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Amplitude of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its amplitude.
https://www.khanacademy.org/e/amplitude-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph sinusoidal functions - Given the formula of a sinusoidal function of the form a*f(bx)+d, draw its graph.
https://www.khanacademy.org/e/graphs_of_sine_and_cosine
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Analyze vertical asymptotes of rational functions - Given the formula of a rational function, determine how it behaves around its vertical asymptote.
https://www.khanacademy.org/e/analyze-vertical-asymptotes-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in standard form - Graph quadratic functions given in the standard form ax²+bx+c. For example, graph y=5x²-20x+15.
https://www.khanacademy.org/e/graphing_parabolas_0.5
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Period of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its period.
https://www.khanacademy.org/e/find-period-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in standard form - Graph quadratic functions given in the standard form ax²+bx+c. For example, graph y=5x²-20x+15.
https://www.khanacademy.org/e/graphing_parabolas_0.5
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Analyze vertical asymptotes of rational functions - Given the formula of a rational function, determine how it behaves around its vertical asymptote.
https://www.khanacademy.org/e/analyze-vertical-asymptotes-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph sinusoidal functions - Given the formula of a sinusoidal function of the form a*f(bx)+d, draw its graph.
https://www.khanacademy.org/e/graphs_of_sine_and_cosine
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Amplitude of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its amplitude.
https://www.khanacademy.org/e/amplitude-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Midline of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its midline equation.
https://www.khanacademy.org/e/find-midline-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Positive and negative intervals - Highlight intervals on the domain of a function where it's entirely positive or entirely negative.
https://www.khanacademy.org/e/positive_and_negative_parts_of_functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Amplitude of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its amplitude.
https://www.khanacademy.org/e/find-amplitude-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from a table - Find the intercepts of a line given a table of values.
https://www.khanacademy.org/e/intercepts-from-table
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Radical functions & their graphs - Given the formula of a square-root or a cube-root function, find the appropriate graph.
https://www.khanacademy.org/e/graphs-of-radical-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in factored form - Graph quadratic functions that are given in factored form. For example, graph y=(x-4)(x+2).
https://www.khanacademy.org/e/graph-quadratic-functions-in-factored-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Positive & negative intervals of polynomials - Given a polynomial, determine the intervals in which it is positive or negative.
https://www.khanacademy.org/e/positive-and-negative-intervals-of-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph from slope-intercept form - Practice drawing the graph of a line given in slope-intercept form. For example, graph y = 3x + 2.
https://www.khanacademy.org/e/graph-from-slope-intercept-equation
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from an equation - Solve linear equations for the x-intercept and y-intercept
https://www.khanacademy.org/e/solving_for_the_x-intercept
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of nonlinear piecewise functions - Given the graph of a nonlinear piecewise function, find its formula.
https://www.khanacademy.org/e/graphing-piecewise-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from an equation - Solve linear equations for the x-intercept and y-intercept
https://www.khanacademy.org/e/solving_for_the_x-intercept
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphing exponential growth & decay - Graph exponential functions of the basic form f(x)=a⋅rˣ.
https://www.khanacademy.org/e/graphs-of-basic-exponential-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Period of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its period.
https://www.khanacademy.org/e/period-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph from linear standard form - Find the graph of a linear equation given in standard form.
https://www.khanacademy.org/e/graph-from-standard-form-equation
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of rational functions - Determine which of four graphs fits the formula of a given function.
https://www.khanacademy.org/e/graphs-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in vertex form - Graph quadratic functions that are given in the vertex form a(x+b)²+c. For example, graph y=-2(x-2)²+5.
https://www.khanacademy.org/e/graphing_parabolas_1
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Evaluate step functions - Given the graph of a step function, find the function's outputs for given specific inputs.
https://www.khanacademy.org/e/evaluate-step-functions-from-their-graph
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of exponential functions - Graph exponential functions and find the appropriate graph given the function.
https://www.khanacademy.org/e/graphs-of-exponential-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from a graph - Look at the graph of an equation to find x-intercepts and y-intercepts
https://www.khanacademy.org/e/linear-function-intercepts
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph parabolas in all forms - Graph quadratic functions given in any form.
https://www.khanacademy.org/e/graphing_parabolas_2
Standard IF.7
Common Core Area - Interpreting Functions
Skill - End behavior of polynomials - Analyze polynomial functions to determine how they behave as the input variable increases to positive infinity or decreases to negative infinity.
https://www.khanacademy.org/e/determine-the-end-behavior-of-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - End behavior of rational functions - Given a rational function, determine how it behaves as x approaches +∞ or -∞.
https://www.khanacademy.org/e/end-behavior-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of logarithmic functions - Graph logarithmic functions and find the appropriate graph given the function.
https://www.khanacademy.org/e/graphs-of-exponentials-and-logarithms
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope from equation - Find the slopes of lines whose equations are given in various forms. For example, find the slope of 2x+3y=5.
https://www.khanacademy.org/e/slope-from-an-equation-in-standard-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope from two points - Find the slope of the line that goes through the two points that are given to you.
https://www.khanacademy.org/e/slope-from-two-points
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph from slope-intercept form - Practice drawing the graph of a line given in slope-intercept form. For example, graph y = 3x + 2.
https://www.khanacademy.org/e/graph-from-slope-intercept-equation
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of nonlinear piecewise functions - Given the graph of a nonlinear piecewise function, find its formula.
https://www.khanacademy.org/e/graphing-piecewise-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Period of sinusoidal functions from equation - Given the formula of a sinusoidal function, determine its period.
https://www.khanacademy.org/e/find-period-of-a-sinusoid-from-formula
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphing exponential growth & decay - Graph exponential functions of the basic form f(x)=a⋅rˣ.
https://www.khanacademy.org/e/graphs-of-basic-exponential-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Period of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its period.
https://www.khanacademy.org/e/period-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph from linear standard form - Find the graph of a linear equation given in standard form.
https://www.khanacademy.org/e/graph-from-standard-form-equation
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of rational functions - Determine which of four graphs fits the formula of a given function.
https://www.khanacademy.org/e/graphs-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph quadratics in vertex form - Graph quadratic functions that are given in the vertex form a(x+b)²+c. For example, graph y=-2(x-2)²+5.
https://www.khanacademy.org/e/graphing_parabolas_1
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Evaluate step functions - Given the graph of a step function, find the function's outputs for given specific inputs.
https://www.khanacademy.org/e/evaluate-step-functions-from-their-graph
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of exponential functions - Graph exponential functions and find the appropriate graph given the function.
https://www.khanacademy.org/e/graphs-of-exponential-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Intercepts from a graph - Look at the graph of an equation to find x-intercepts and y-intercepts
https://www.khanacademy.org/e/linear-function-intercepts
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph parabolas in all forms - Graph quadratic functions given in any form.
https://www.khanacademy.org/e/graphing_parabolas_2
Standard IF.7
Common Core Area - Interpreting Functions
Skill - End behavior of polynomials - Analyze polynomial functions to determine how they behave as the input variable increases to positive infinity or decreases to negative infinity.
https://www.khanacademy.org/e/determine-the-end-behavior-of-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - End behavior of rational functions - Given a rational function, determine how it behaves as x approaches +∞ or -∞.
https://www.khanacademy.org/e/end-behavior-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope from equation - Find the slopes of lines whose equations are given in various forms. For example, find the slope of 2x+3y=5.
https://www.khanacademy.org/e/slope-from-an-equation-in-standard-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Slope-intercept intro - Practice your basic understanding of slope-intercept form for linear equations.
https://www.khanacademy.org/e/slope-from-an-equation-in-slope-intercept-form
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graph absolute value functions - Graph absolute value functions like f(x)=|x+3|+2.
https://www.khanacademy.org/e/graphs-of-absolute-value-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Absolute maxima and minima - Given the graph of a function, find its absolute maximum and minimum points.
https://www.khanacademy.org/e/recognize-absolute-maxima-and-minima
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphing linear functions word problems - Graph the line that represents a real-world relationship that is given verbally.
https://www.khanacademy.org/e/graphing-linear-functions-word-problems
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Evaluate piecewise functions - Given the formula of a piecewise function, evaluate it for a specific input.
https://www.khanacademy.org/e/evaluating-piecewise-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Horizontal & vertical lines - Practice your knowledge of horizontal and vertical lines: their graphical presentation, their slopes, and their equations.
https://www.khanacademy.org/e/horizontal-and-vertical-lines
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Midline of sinusoidal functions from graph - Given the graph of a sinusoidal function, determine its midline equation.
https://www.khanacademy.org/e/midline-of-trig-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Relative maxima and minima - Given the graph of a function, find all of its relative maximum and minimum points.
https://www.khanacademy.org/e/recognize-maxima-and-minima
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Increasing and decreasing intervals - Highlight intervals on the domain of a function where it's only increasing or only decreasing.
https://www.khanacademy.org/e/increasing-decreasing-intervals-of-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Rational function points of discontinuity - Given a rational function, sort given input values according to zeros, vertical asymptotes, and removable discontinuities.
https://www.khanacademy.org/e/points-of-discontinuity-of-rational-functions
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Graphs of logarithmic functions - Graph logarithmic functions and find the appropriate graph given the function.
https://www.khanacademy.org/e/graphs-of-exponentials-and-logarithms
Standard IF.7
Common Core Area - Interpreting Functions
Skill - Piecewise functions graphs - Match the formula of a piecewise function to its graph.
https://www.khanacademy.org/e/piecewise-graphs-linear
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Find zeros of polynomials - Use various methods in order to find all the zeros of polynomial expressions or functions.
https://www.khanacademy.org/e/find-the-zeros-of-polynomials
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Quadratics by factoring - Solve quadratic equations of the form ax^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring_2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor polynomials: quadratic methods - Factor polynomials that can be factored as the product of a monomial and a quadratic expression, then further factor the quadratic expression.
https://www.khanacademy.org/e/factoring_polynomials_2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Features of quadratic functions: strategy - Identify the form of a quadratic function that immediately reveals a given feature of that function. Features in question are the y-intercept of the graph, the zeroes ("roots") of the function, and the vertex of the parabola.
https://www.khanacademy.org/e/identifying-and-using-quadratic-forms
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Compare features of functions - Compare various features between two functions, each represented in a different way.
https://www.khanacademy.org/e/comparing-features-of-functions-2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor monomials - Factor monomials as products of smaller monomials.
https://www.khanacademy.org/e/factoring-monomials
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Interpret time in exponential models - Given a function that models an exponential situation, find the time interval over which the quantity changes by a given factor.
https://www.khanacademy.org/e/rewriting-and-interpreting-exponential-functions
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor polynomials: common factor - Practice finding the greatest common factors of polynomials and factoring them out of the polynomials.
https://www.khanacademy.org/e/factoring-polynomials
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Perfect squares - Factor quadratic expressions of the general perfect square forms: (ax)²+2abx+b² or (ax)²-2abx+b². The factored expressions have the general forms (ax+b)² or (ax-b)².
https://www.khanacademy.org/e/factoring-perfect-squares
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor quadratics by grouping - Factor quadratics of the form ax²+bx+c.
https://www.khanacademy.org/e/factoring_polynomials_by_grouping_1
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor polynomials: quadratic methods - Factor polynomials that can be factored as the product of a monomial and a quadratic expression, then further factor the quadratic expression.
https://www.khanacademy.org/e/factoring_polynomials_2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Features of quadratic functions: strategy - Identify the form of a quadratic function that immediately reveals a given feature of that function. Features in question are the y-intercept of the graph, the zeroes ("roots") of the function, and the vertex of the parabola.
https://www.khanacademy.org/e/identifying-and-using-quadratic-forms
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Compare features of functions - Compare various features between two functions, each represented in a different way.
https://www.khanacademy.org/e/comparing-features-of-functions-2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor monomials - Factor monomials as products of smaller monomials.
https://www.khanacademy.org/e/factoring-monomials
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Interpret time in exponential models - Given a function that models an exponential situation, find the time interval over which the quantity changes by a given factor.
https://www.khanacademy.org/e/rewriting-and-interpreting-exponential-functions
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor polynomials: common factor - Practice finding the greatest common factors of polynomials and factoring them out of the polynomials.
https://www.khanacademy.org/e/factoring-polynomials
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Perfect squares - Factor quadratic expressions of the general perfect square forms: (ax)²+2abx+b² or (ax)²-2abx+b². The factored expressions have the general forms (ax+b)² or (ax-b)².
https://www.khanacademy.org/e/factoring-perfect-squares
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Difference of squares - Factor quadratic expressions of the general difference of squares form: (ax)^2-b^2. The factored expressions have the general form (ax+b)(ax-b).
https://www.khanacademy.org/e/factoring_difference_of_squares_2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factoring quadratics intro - Factor quadratics of the form x²+bx+c.
https://www.khanacademy.org/e/factoring_polynomials_1
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Find zeros of polynomials - Use various methods in order to find all the zeros of polynomial expressions or functions.
https://www.khanacademy.org/e/find-the-zeros-of-polynomials
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Slope from equation - Find the slopes of lines whose equations are given in various forms. For example, find the slope of 2x+3y=5.
https://www.khanacademy.org/e/slope-from-an-equation-in-standard-form
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Interpret change in exponential models - Given a function that models an exponential situation, find the factor by which the quantity changes per unit time interval.
https://www.khanacademy.org/e/modeling-with-exponential-functions
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Features of quadratic functions - Find the zeroes ("roots") of quadratic functions and the vertex of their parabolas. Functions are given in standard, vertex, and factored form.
https://www.khanacademy.org/e/rewriting-expressions-to-reveal-information
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Completing the square (intermediate) - Solve quadratic equations of the form x^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_1
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Convert linear equations to standard form - Convert linear equations in various forms into standard form.
https://www.khanacademy.org/e/converting_between_slope_intercept_and_standard_form
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor polynomials: special product forms - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using special product factorization methods.
https://www.khanacademy.org/e/factoring_difference_of_squares_3
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Quadratic word problems (standard form) - Solve real-world word problems that involve quadratic models. In this exercise, that models are given in standard form.
https://www.khanacademy.org/e/key-features-quadratics
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Difference of squares intro - Factor quadratic expressions into the special products of the general form (x+a)(x-a).
https://www.khanacademy.org/e/factoring_difference_of_squares_1
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Completing the square - Solve quadratic equations of the form ax^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Equivalent forms of exponential expressions - Determine whether pairs of exponential expressions are equivalent.
https://www.khanacademy.org/e/equivalent-forms-of-expressions-with-variable-exponents
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Completing the square - Solve quadratic equations of the form ax^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factoring quadratics intro - Factor quadratics of the form x²+bx+c.
https://www.khanacademy.org/e/factoring_polynomials_1
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor quadratics by grouping - Factor quadratics of the form ax²+bx+c.
https://www.khanacademy.org/e/factoring_polynomials_by_grouping_1
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Slope from equation - Find the slopes of lines whose equations are given in various forms. For example, find the slope of 2x+3y=5.
https://www.khanacademy.org/e/slope-from-an-equation-in-standard-form
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Interpret change in exponential models - Given a function that models an exponential situation, find the factor by which the quantity changes per unit time interval.
https://www.khanacademy.org/e/modeling-with-exponential-functions
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Features of quadratic functions - Find the zeroes ("roots") of quadratic functions and the vertex of their parabolas. Functions are given in standard, vertex, and factored form.
https://www.khanacademy.org/e/rewriting-expressions-to-reveal-information
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Completing the square (intermediate) - Solve quadratic equations of the form x^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_1
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Convert linear equations to standard form - Convert linear equations in various forms into standard form.
https://www.khanacademy.org/e/converting_between_slope_intercept_and_standard_form
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor polynomials: special product forms - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using special product factorization methods.
https://www.khanacademy.org/e/factoring_difference_of_squares_3
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Quadratic word problems (standard form) - Solve real-world word problems that involve quadratic models. In this exercise, that models are given in standard form.
https://www.khanacademy.org/e/key-features-quadratics
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Difference of squares intro - Factor quadratic expressions into the special products of the general form (x+a)(x-a).
https://www.khanacademy.org/e/factoring_difference_of_squares_1
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Difference of squares - Factor quadratic expressions of the general difference of squares form: (ax)^2-b^2. The factored expressions have the general form (ax+b)(ax-b).
https://www.khanacademy.org/e/factoring_difference_of_squares_2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Equivalent forms of exponential expressions - Determine whether pairs of exponential expressions are equivalent.
https://www.khanacademy.org/e/equivalent-forms-of-expressions-with-variable-exponents
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Quadratics by factoring - Solve quadratic equations of the form ax^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring_2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Rewrite exponential expressions - Rewrite a given exponential expression in a specific desired form.
https://www.khanacademy.org/e/rewrite-exponential-expressions
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor polynomials: quadratic methods (challenge) - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using quadratic factorization methods.
https://www.khanacademy.org/e/factoring_polynomials_with_two_variables
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Interpret change in exponential models: with manipulation - Given a function that models an exponential situation, rewrite the function in order to analyze its rate of change.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-with-manipulation
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Interpret change in exponential models: changing units - Given a function that models an exponential situation, rewrite the function in order to find its change for a different time unit.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-for-a-different-unit
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Quadratics by factoring (intro) - Solve quadratic equations of the form x^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Completing the square (intro) - Practice the method of completing the square with quadratic expressions.
https://www.khanacademy.org/e/completing_the_square_in_quadratic_expressions
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Solve equations using structure - Solve advanced equations by strategically using quadratic factorization methods.
https://www.khanacademy.org/e/solving-quadratics-by-using-structure
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Slope from equation - Find the slopes of lines whose equations are given in various forms. For example, find the slope of 2x+3y=5.
https://www.khanacademy.org/e/slope-from-an-equation-in-standard-form
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Compare features of functions - Compare various features between two functions, each represented in a different way.
https://www.khanacademy.org/e/comparing-features-of-functions-2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor monomials - Factor monomials as products of smaller monomials.
https://www.khanacademy.org/e/factoring-monomials
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Interpret time in exponential models - Given a function that models an exponential situation, find the time interval over which the quantity changes by a given factor.
https://www.khanacademy.org/e/rewriting-and-interpreting-exponential-functions
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor polynomials: common factor - Practice finding the greatest common factors of polynomials and factoring them out of the polynomials.
https://www.khanacademy.org/e/factoring-polynomials
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Zeros of polynomials & their graphs - Select the graph that best suits a polynomial equation by considering the zeros of the polynomial.
https://www.khanacademy.org/e/using-zeros-to-graph-polynomials
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Perfect squares - Factor quadratic expressions of the general perfect square forms: (ax)²+2abx+b² or (ax)²-2abx+b². The factored expressions have the general forms (ax+b)² or (ax-b)².
https://www.khanacademy.org/e/factoring-perfect-squares
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Difference of squares - Factor quadratic expressions of the general difference of squares form: (ax)^2-b^2. The factored expressions have the general form (ax+b)(ax-b).
https://www.khanacademy.org/e/factoring_difference_of_squares_2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factoring quadratics intro - Factor quadratics of the form x²+bx+c.
https://www.khanacademy.org/e/factoring_polynomials_1
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor quadratics by grouping - Factor quadratics of the form ax²+bx+c.
https://www.khanacademy.org/e/factoring_polynomials_by_grouping_1
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Completing the square (intro) - Practice the method of completing the square with quadratic expressions.
https://www.khanacademy.org/e/completing_the_square_in_quadratic_expressions
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Interpret change in exponential models - Given a function that models an exponential situation, find the factor by which the quantity changes per unit time interval.
https://www.khanacademy.org/e/modeling-with-exponential-functions
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Features of quadratic functions - Find the zeroes ("roots") of quadratic functions and the vertex of their parabolas. Functions are given in standard, vertex, and factored form.
https://www.khanacademy.org/e/rewriting-expressions-to-reveal-information
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Completing the square (intermediate) - Solve quadratic equations of the form x^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_1
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Convert linear equations to standard form - Convert linear equations in various forms into standard form.
https://www.khanacademy.org/e/converting_between_slope_intercept_and_standard_form
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor polynomials: special product forms - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using special product factorization methods.
https://www.khanacademy.org/e/factoring_difference_of_squares_3
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Quadratic word problems (standard form) - Solve real-world word problems that involve quadratic models. In this exercise, that models are given in standard form.
https://www.khanacademy.org/e/key-features-quadratics
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Difference of squares intro - Factor quadratic expressions into the special products of the general form (x+a)(x-a).
https://www.khanacademy.org/e/factoring_difference_of_squares_1
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Completing the square - Solve quadratic equations of the form ax^2+bx+c by completing the square.
https://www.khanacademy.org/e/completing_the_square_2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor polynomials: quadratic methods - Factor polynomials that can be factored as the product of a monomial and a quadratic expression, then further factor the quadratic expression.
https://www.khanacademy.org/e/factoring_polynomials_2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Solve equations using structure - Solve advanced equations by strategically using quadratic factorization methods.
https://www.khanacademy.org/e/solving-quadratics-by-using-structure
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Quadratics by factoring (intro) - Solve quadratic equations of the form x^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Interpret change in exponential models: changing units - Given a function that models an exponential situation, rewrite the function in order to find its change for a different time unit.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-for-a-different-unit
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Interpret change in exponential models: with manipulation - Given a function that models an exponential situation, rewrite the function in order to analyze its rate of change.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-with-manipulation
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor polynomials: quadratic methods (challenge) - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using quadratic factorization methods.
https://www.khanacademy.org/e/factoring_polynomials_with_two_variables
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Rewrite exponential expressions - Rewrite a given exponential expression in a specific desired form.
https://www.khanacademy.org/e/rewrite-exponential-expressions
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Quadratics by factoring - Solve quadratic equations of the form ax^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring_2
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Equivalent forms of exponential expressions - Determine whether pairs of exponential expressions are equivalent.
https://www.khanacademy.org/e/equivalent-forms-of-expressions-with-variable-exponents
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Factor polynomials: quadratic methods (challenge) - Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using quadratic factorization methods.
https://www.khanacademy.org/e/factoring_polynomials_with_two_variables
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Interpret change in exponential models: with manipulation - Given a function that models an exponential situation, rewrite the function in order to analyze its rate of change.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-with-manipulation
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Interpret change in exponential models: changing units - Given a function that models an exponential situation, rewrite the function in order to find its change for a different time unit.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-for-a-different-unit
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Quadratics by factoring (intro) - Solve quadratic equations of the form x^2+bx+c=0 that can be rewritten according to their linear factors.
https://www.khanacademy.org/e/solving_quadratics_by_factoring
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Completing the square (intro) - Practice the method of completing the square with quadratic expressions.
https://www.khanacademy.org/e/completing_the_square_in_quadratic_expressions
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Solve equations using structure - Solve advanced equations by strategically using quadratic factorization methods.
https://www.khanacademy.org/e/solving-quadratics-by-using-structure
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Find zeros of polynomials - Use various methods in order to find all the zeros of polynomial expressions or functions.
https://www.khanacademy.org/e/find-the-zeros-of-polynomials
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Features of quadratic functions: strategy - Identify the form of a quadratic function that immediately reveals a given feature of that function. Features in question are the y-intercept of the graph, the zeroes ("roots") of the function, and the vertex of the parabola.
https://www.khanacademy.org/e/identifying-and-using-quadratic-forms
Standard IF.8
Common Core Area - Interpreting Functions
Skill - Rewrite exponential expressions - Rewrite a given exponential expression in a specific desired form.
https://www.khanacademy.org/e/rewrite-exponential-expressions
Standard IF.9
Common Core Area - Interpreting Functions
Skill - Compare features of functions - Compare various features between two functions, each represented in a different way.
https://www.khanacademy.org/e/comparing-features-of-functions-2
Standard IF.9
Common Core Area - Interpreting Functions
Skill - Comparing linear functions word problem - Compare features of two real-world relationships that can be modeled by linear functions, where the functions are represented in different ways.
https://www.khanacademy.org/e/comparing-features-of-functions-1
Standard IF.9
Common Core Area - Interpreting Functions
Skill - Compare linear functions - Compare features of two linear functions represented in different ways.
https://www.khanacademy.org/e/comparing-features-of-functions-0-5
Standard IF.9
Common Core Area - Interpreting Functions
Skill - Compare quadratic functions - Compare the properties of two quadratic functions, each represented in a different way.
https://www.khanacademy.org/e/compare-properties-quadratic-functions
Standard LE.1
Common Core Area - Linear Quadratic and Exponential Models
Skill - Sequences word problems - Given a verbal description of a real-world relationship, determine the sequence that models that relationship.
https://www.khanacademy.org/e/recursive_explicit
Standard LE.1
Common Core Area - Linear Quadratic and Exponential Models
Skill - Exponential vs. linear. models - Given a description of a real-world relationship, determine whether that relationship is linear or exponential.
https://www.khanacademy.org/e/understanding-linear-and-exponential-models
Standard LE.1
Common Core Area - Linear Quadratic and Exponential Models
Skill - Linear vs. exponential growth: from data - Given a table with values of two quantities over time, determine whether the quantities form grow linearly or exponentially.
https://www.khanacademy.org/e/distinguish-between-linear-and-exponential-growth-from-tables
Standard LE.1
Common Core Area - Linear Quadratic and Exponential Models
Skill - Sequences word problems - Given a verbal description of a real-world relationship, determine the sequence that models that relationship.
https://www.khanacademy.org/e/recursive_explicit
Standard LE.1
Common Core Area - Linear Quadratic and Exponential Models
Skill - Exponential vs. linear. models - Given a description of a real-world relationship, determine whether that relationship is linear or exponential.
https://www.khanacademy.org/e/understanding-linear-and-exponential-models
Standard LE.1
Common Core Area - Linear Quadratic and Exponential Models
Skill - Linear vs. exponential growth: from data - Given a table with values of two quantities over time, determine whether the quantities form grow linearly or exponentially.
https://www.khanacademy.org/e/distinguish-between-linear-and-exponential-growth-from-tables
Standard LE.1
Common Core Area - Linear Quadratic and Exponential Models
Skill - Sequences word problems - Given a verbal description of a real-world relationship, determine the sequence that models that relationship.
https://www.khanacademy.org/e/recursive_explicit
Standard LE.1
Common Core Area - Linear Quadratic and Exponential Models
Skill - Exponential vs. linear. models - Given a description of a real-world relationship, determine whether that relationship is linear or exponential.
https://www.khanacademy.org/e/understanding-linear-and-exponential-models
Standard LE.1
Common Core Area - Linear Quadratic and Exponential Models
Skill - Linear vs. exponential growth: from data - Given a table with values of two quantities over time, determine whether the quantities form grow linearly or exponentially.
https://www.khanacademy.org/e/distinguish-between-linear-and-exponential-growth-from-tables
Standard LE.1
Common Core Area - Linear Quadratic and Exponential Models
Skill - Sequences word problems - Given a verbal description of a real-world relationship, determine the sequence that models that relationship.
https://www.khanacademy.org/e/recursive_explicit
Standard LE.1
Common Core Area - Linear Quadratic and Exponential Models
Skill - Exponential vs. linear. models - Given a description of a real-world relationship, determine whether that relationship is linear or exponential.
https://www.khanacademy.org/e/understanding-linear-and-exponential-models
Standard LE.1
Common Core Area - Linear Quadratic and Exponential Models
Skill - Linear vs. exponential growth: from data - Given a table with values of two quantities over time, determine whether the quantities form grow linearly or exponentially.
https://www.khanacademy.org/e/distinguish-between-linear-and-exponential-growth-from-tables
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Slope-intercept equation from graph - Practice finding the slope-intercept equation of a line from its graph.
https://www.khanacademy.org/e/slope-intercept-equation-from-graph
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Slope-intercept from two points - Practice finding the equation of a line passing through two points
https://www.khanacademy.org/e/slope-intercept-equation-from-two-points
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Linear equations in any form - You've had practice with a few different forms of linear equations. Now use your skills.
https://www.khanacademy.org/e/writing-the-equation-of-a-line-in-any-form
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Explicit formulas for arithmetic sequences - Solve problems such as: The first four terms in an arithmetic sequence are 12, 5, -2, and -9. Find an explicit formula for the sequence.
https://www.khanacademy.org/e/explicit-formulas-for-arithmetic-sequences
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Horizontal & vertical lines - Practice your knowledge of horizontal and vertical lines: their graphical presentation, their slopes, and their equations.
https://www.khanacademy.org/e/horizontal-and-vertical-lines
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Slope from graph - Find the slope of a line on the coordinate plane.
https://www.khanacademy.org/e/slope-from-a-graph
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Exponential functions from tables & graphs - Write exponential functions of the basic form f(x)=a⋅rˣ, either when given a table with two input-output pairs, or when given the graph of the function.
https://www.khanacademy.org/e/construct-basic-exponential-functions-from-table-or-graph
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Sequences word problems - Given a verbal description of a real-world relationship, determine the sequence that models that relationship.
https://www.khanacademy.org/e/recursive_explicit
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Construct exponential models - Given a verbal description of the rate of change of a real world situation, find the exponential function that models it.
https://www.khanacademy.org/e/construct-exponential-models-according-to-rate-of-change
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Recursive formulas for arithmetic sequences - Find the recursive formula of an arithmetic sequence given the first few terms.
https://www.khanacademy.org/e/recursive-formulas-for-arithmetic-sequences
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Recursive formulas for geometric sequences - Find the recursive formula of a geometric sequence given the first few terms or given an explicit formula.
https://www.khanacademy.org/e/recursive-formulas-for-geometric-sequences
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Explicit formulas for geometric sequences - Solve problems such as: The first four terms in a geometric sequence are 1/3, 1, 3, and 9. Find an explicit formula for the sequence.
https://www.khanacademy.org/e/sequences-as-functions
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Point-slope form - Write equations in point-slope form given two pairs of values, and convert the equation into slope-intercept form.
https://www.khanacademy.org/e/converting_between_point_slope_and_slope_intercept
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Linear models word problems - Solve general word problems about real-world relationships that can be modeled by linear equations or functions.
https://www.khanacademy.org/e/constructing-and-interpreting-linear-functions
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Writing linear functions word problems - Find a linear function that represents a real-world relationship that is given verbally.
https://www.khanacademy.org/e/constructing-linear-functions-word-problems
Standard LE.2
Common Core Area - Linear Quadratic and Exponential Models
Skill - Slope-intercept intro - Practice your basic understanding of slope-intercept form for linear equations.
https://www.khanacademy.org/e/slope-from-an-equation-in-slope-intercept-form
Standard LE.3
Common Core Area - Linear Quadratic and Exponential Models
Skill - Exponential vs. linear growth over time - Practice analyzing the end behavior of two functions that model similar real-world relationship, where one function is exponential and the other is polynomial.
https://www.khanacademy.org/e/comparing-growth-rates-of-exponentials-and-polynomials
Standard LE.4
Common Core Area - Linear Quadratic and Exponential Models
Skill - Solve exponential equations using logarithms: base-10 and base-e - Solve exponential equations that have 10 or e at the base of the exponential term.
https://www.khanacademy.org/e/using-logarithms-to-solve-exponential-equations
Standard LE.4
Common Core Area - Linear Quadratic and Exponential Models
Skill - Evaluate logarithms: change of base rule - Evaluate any logarithm in a calculator with the use of the change of base formula. Example: Evaluate logâ‚…(100).
https://www.khanacademy.org/e/evaluate-logarithms-using-the-change-of-base-rule
Standard LE.4
Common Core Area - Linear Quadratic and Exponential Models
Skill - Solve exponential equations using logarithms: base-2 and other bases - Solve exponential equations that have 2 or other numbers at the base of the exponential term.
https://www.khanacademy.org/e/solve-exponential-equations-using-logarithms-base-2
Standard LE.4
Common Core Area - Linear Quadratic and Exponential Models
Skill - Exponential model word problems - Solve word problems about exponential situations.
https://www.khanacademy.org/e/exponential-models-word-problems
Standard LE.5
Common Core Area - Linear Quadratic and Exponential Models
Skill - Interpret change in exponential models - Given a function that models an exponential situation, find the factor by which the quantity changes per unit time interval.
https://www.khanacademy.org/e/modeling-with-exponential-functions
Standard LE.5
Common Core Area - Linear Quadratic and Exponential Models
Skill - Linear equations word problems - Solve word problems about real world relationships that are given in formulas.
https://www.khanacademy.org/e/interpreting-features-of-linear-functions
Standard LE.5
Common Core Area - Linear Quadratic and Exponential Models
Skill - Interpret change in exponential models: with manipulation - Given a function that models an exponential situation, rewrite the function in order to analyze its rate of change.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-with-manipulation
Standard LE.5
Common Core Area - Linear Quadratic and Exponential Models
Skill - Comparing linear functions word problem - Compare features of two real-world relationships that can be modeled by linear functions, where the functions are represented in different ways.
https://www.khanacademy.org/e/comparing-features-of-functions-1
Standard LE.5
Common Core Area - Linear Quadratic and Exponential Models
Skill - Interpret change in exponential models: changing units - Given a function that models an exponential situation, rewrite the function in order to find its change for a different time unit.
https://www.khanacademy.org/e/interpret-rate-of-change-of-exponential-models-for-a-different-unit
Standard LE.5
Common Core Area - Linear Quadratic and Exponential Models
Skill - Interpret time in exponential models - Given a function that models an exponential situation, find the time interval over which the quantity changes by a given factor.
https://www.khanacademy.org/e/rewriting-and-interpreting-exponential-functions
Standard LE.5
Common Core Area - Linear Quadratic and Exponential Models
Skill - Linear models word problems - Solve general word problems about real-world relationships that can be modeled by linear equations or functions.
https://www.khanacademy.org/e/constructing-and-interpreting-linear-functions
Standard TF.1
Common Core Area - Trigonometric Functions
Skill - Coming Soon -
Standard TF.2
Common Core Area - Trigonometric Functions
Skill - Coming Soon -
Standard TF.3
Common Core Area - Trigonometric Functions
Skill - Trig values of special angles - Find the sine and cosine of special angles, which are angles whose trig values we can determine without the use of a calculator.
https://www.khanacademy.org/e/trigonometric-functions-of-special-angles
Standard TF.4
Common Core Area - Trigonometric Functions
Skill - Coming Soon -
Standard TF.5
Common Core Area - Trigonometric Functions
Skill - Modeling with sinusoidal functions: phase shift - Given the description of a real-world relationship, find the sinusoidal function that models it. The functions in this exercise have a phase (horizontal) shift.
https://www.khanacademy.org/e/modeling-with-periodic-functions-2
Standard TF.5
Common Core Area - Trigonometric Functions
Skill - Modeling with sinusoidal functions - Given the description of a real-world relationship, find the sinusoidal function that models it.
https://www.khanacademy.org/e/modeling-with-periodic-functions
Standard TF.5
Common Core Area - Trigonometric Functions
Skill - Construct sinusoidal functions - Given a few features of a sinusoidal function, find its formula.
https://www.khanacademy.org/e/construct-sinusoidal-functions
Standard TF.6
Common Core Area - Trigonometric Functions
Skill - Evaluate inverse trig functions - Given a sine, cosine, or tangent value, find the principle angle who has this value. In other words, find the arcsine, arccosine, or arctangent of that value.
https://www.khanacademy.org/e/inverse_trig_functions
Standard TF.7
Common Core Area - Trigonometric Functions
Skill - Solve sinusoidal equations (basic) - Solve equations of the form sin(x)=d or cos(x)=d where d is any number.
https://www.khanacademy.org/e/solve-basic-sinusoidal-equations
Standard TF.7
Common Core Area - Trigonometric Functions
Skill - Evaluate inverse trig functions - Given a sine, cosine, or tangent value, find the principle angle who has this value. In other words, find the arcsine, arccosine, or arctangent of that value.
https://www.khanacademy.org/e/inverse_trig_functions
Standard TF.7
Common Core Area - Trigonometric Functions
Skill - Sinusoidal models word problems - Solve word problems that involve real-world contexts that are modeled by sinusoidal functions.
https://www.khanacademy.org/e/inverse-trig-word-problems
Standard TF.7
Common Core Area - Trigonometric Functions
Skill - Solve sinusoidal equations - Solve equations of the form a*sin(bx+c)=d or a*cos(bx+c)=d where a, b, c, and d are any number.
https://www.khanacademy.org/e/solve-advanced-sinusoidal-equations
Standard TF.8
Common Core Area - Trigonometric Functions
Skill - Use the Pythagorean identity - Given the sine (or cosine) of an angle, find its cosine (or sine) using the Pythagorean identity.
https://www.khanacademy.org/e/circles-and-pythagorean-identities
Standard TF.9
Common Core Area - Trigonometric Functions
Skill - Find trig values using angle addition identities - Find the trigonometric values of various angles that (while they are not special angles) can be expressed as the sum or difference of special angles.
https://www.khanacademy.org/e/applying-angle-addition-formulas
Standard TF.9
Common Core Area - Trigonometric Functions
Skill - Using the trig angle addition identities - Find the trig values of sums of angles whose individual trig values are known.
Standard C.1
Common Core Area - Circles
Skill - Coming Soon -
Standard C.2
Common Core Area - Circles
Skill - Inscribed angles - Practice the relationship between inscribed & central angles that are subtended by the same arc length.
https://www.khanacademy.org/e/inscribed_angles_1
Standard C.2
Common Core Area - Circles
Skill - Inscribed shapes - Find missing angles and lengths in inscribed shapes.
https://www.khanacademy.org/e/inscribed-angle-problem-solving
Standard C.2
Common Core Area - Circles
Skill - Tangents of circles problems - Solve problems related to tangents of circles.
https://www.khanacademy.org/e/central--inscribed--and-circumscribed-angles
Standard C.3
Common Core Area - Circles
Skill - Quiz: Inscribed quadrilaterals - Use the fact that opposite angles in an inscribed quadrilateral are supplementary to solve a few problems.
https://www.khanacademy.org/e/inscribed-quadrilaterals
Standard C.4
Common Core Area - Circles
Skill - Coming Soon -
Standard C.5
Common Core Area - Circles
Skill - Radians & arc length - Solve problems related to radians and arc length like finding an arc length given the central angle and radius.
https://www.khanacademy.org/e/cc-radians-and-arc-length
Standard C.5
Common Core Area - Circles
Skill - Arc measure - Use the fact that the arc measures of a circle must sum to 360 degrees to find missing arc measures.
https://www.khanacademy.org/e/arc-measure
Standard C.5
Common Core Area - Circles
Skill - Arc length - Relate the length of an arc to the circumference of a whole circle and the central angle subtended by the arc.
https://www.khanacademy.org/e/arc-length-of-functions-in-one-variable
Standard C.5
Common Core Area - Circles
Skill - Radians & degrees - Convert angle measures given in degrees to radians and vice versa.
https://www.khanacademy.org/e/degrees_to_radians
Standard C.5
Common Core Area - Circles
Skill - Area of a sector - Relate the area of a sector to the area of a whole circle.
https://www.khanacademy.org/e/areas_of_circles_and_sectors
Standard C.5
Common Core Area - Circles
Skill - Arc length - Relate the length of an arc to the circumference of a whole circle and the central angle subtended by the arc.
https://www.khanacademy.org/e/circles_and_arcs
Standard C.5
Common Core Area - Circles
Skill - Arc measure with equations - Use the fact that the arc measures of a circle must sum to 360 degrees to find missing arc measures by setting up equations.
https://www.khanacademy.org/e/arc-measure-with-equations
Standard CO.1
Common Core Area - Congruence
Skill - Geometric definitions -
https://www.khanacademy.org/e/geometric-definitions
Standard CO.2
Common Core Area - Congruence
Skill - Rigid transformations: preserved properties - Identify which properties of shapes remain the same after a rigid transformation (reflection, rotation, translation) has been applied.
https://www.khanacademy.org/e/transformation-preserved-properties
Standard CO.2
Common Core Area - Congruence
Skill - Find measures using rigid transformations - Use your knowledge about the effects of rigid transformations to solve problems about figures and their images under transformations.
https://www.khanacademy.org/e/find-measures-using-rigid-transformations
Standard CO.2
Common Core Area - Congruence
Skill - Sequences of transformations - Given a description of a sequence of transformations, determine whether it preserves segment length or angle measure.
https://www.khanacademy.org/e/analyze-sequences-of-transformations
Standard CO.2
Common Core Area - Congruence
Skill - Defining transformations - Given a description of the effect of a transformation, determine which rigid transformation it is.
https://www.khanacademy.org/e/qualitatively-defining-rigid-transformations
Standard CO.3
Common Core Area - Congruence
Skill - Symmetry of 2D shapes - Analyze various shapes according to their reflective and rotational symmetries.
https://www.khanacademy.org/e/symmetry-of-two-dimensional-shapes
Standard CO.4
Common Core Area - Congruence
Skill - Defining transformations - Given a description of the effect of a transformation, determine which rigid transformation it is.
https://www.khanacademy.org/e/qualitatively-defining-rigid-transformations
Standard CO.4
Common Core Area - Congruence
Skill - Identify transformations - Identify the transformation (translation, rotation, reflection, or dilation) that has been applied to a figure.
https://www.khanacademy.org/e/identify-transformations
Standard CO.5
Common Core Area - Congruence
Skill - Reflect shapes - Given a figure and a definition of a reflection, manually draw the image.
https://www.khanacademy.org/e/reflections-1
Standard CO.5
Common Core Area - Congruence
Skill - Rotate shapes - Given a figure on the coordinate plane and the definition of a rotation about the origin, manually draw the image of that rotation.
https://www.khanacademy.org/e/rotations-1
Standard CO.5
Common Core Area - Congruence
Skill - Determine reflections (advanced) - Given two figures on the coordinate plane, draw the line of reflection that takes one figure to another.
https://www.khanacademy.org/e/defining-reflections
Standard CO.5
Common Core Area - Congruence
Skill - Mapping shapes - Map a given shape into another using sequences of rigid transformations (translations, rotations, and/or reflections).
https://www.khanacademy.org/e/mapping-shapes
Standard CO.5
Common Core Area - Congruence
Skill - Translate shapes - Given a figure and a definition of a translation, manually draw the image.
https://www.khanacademy.org/e/translations
Standard CO.5
Common Core Area - Congruence
Skill - Advanced reflections - Find the reflection that maps a given figure to another and draw the image of a reflection. The lines of reflection in this exercise have a wide range of slopes.
https://www.khanacademy.org/e/reflections-2
Standard CO.5
Common Core Area - Congruence
Skill - Rotate shapes: center ≠(0,0) - Given a figure on the coordinate plane and the definition of a rotation about an arbitrary point, manually draw the image of that rotation.
https://www.khanacademy.org/e/rotations-2
Standard CO.5
Common Core Area - Congruence
Skill - Identify transformations - Identify the transformation (translation, rotation, reflection, or dilation) that has been applied to a figure.
https://www.khanacademy.org/e/identify-transformations
Standard CO.5
Common Core Area - Congruence
Skill - Reflect points - Given a point and a definition of a reflection, plot the reflection on a coordinate plane or identify the coordinates of the reflected point.
https://www.khanacademy.org/e/performing-reflections-on-the-coordinate-plane
Standard CO.5
Common Core Area - Congruence
Skill - Determine reflections - Given a shape and its image under a reflection, determine the line of reflection.
https://www.khanacademy.org/e/determine-reflections
Standard CO.5
Common Core Area - Congruence
Skill - Determine translations - Given two figures on the coordinate plane, find the formal definition of the translation that takes one figure to another.
https://www.khanacademy.org/e/defining-translations
Standard CO.5
Common Core Area - Congruence
Skill - Translate points - Given a point and a definition of a translation, plot the translation on a coordinate plane or identify the coordinates of the translated point.
https://www.khanacademy.org/e/performing-translations-on-the-coordinate-plane
Standard CO.5
Common Core Area - Congruence
Skill - Determine rotations - Given a figure on the coordinate plane and a center of a rotation, find the angle for the rotation that maps one figure to the other.
https://www.khanacademy.org/e/defining-rotations
Standard CO.6
Common Core Area - Congruence
Skill - Rigid transformations: preserved properties - Identify which properties of shapes remain the same after a rigid transformation (reflection, rotation, translation) has been applied.
https://www.khanacademy.org/e/transformation-preserved-properties
Standard CO.6
Common Core Area - Congruence
Skill - Find measures using rigid transformations - Use your knowledge about the effects of rigid transformations to solve problems about figures and their images under transformations.
https://www.khanacademy.org/e/find-measures-using-rigid-transformations
Standard CO.6
Common Core Area - Congruence
Skill - Congruence & transformations - Given a pair of figures in the coordinate plane, try to map one onto the other and determine whether they are congruent.
https://www.khanacademy.org/e/exploring-rigid-transformations-and-congruence
Standard CO.7
Common Core Area - Congruence
Skill - Coming Soon -
Standard CO.8
Common Core Area - Congruence
Skill - Coming Soon -
Standard CO.9
Common Core Area - Congruence
Skill - Proofs with transformations - Explore different ways of proving some theorems about lines and angles. Some transformations are used.
https://www.khanacademy.org/e/line-and-angle-proofs
Standard CO.10
Common Core Area - Congruence
Skill - Coming Soon -
Standard CO.11
Common Core Area - Congruence
Skill - Coming Soon -
Standard CO.12
Common Core Area - Congruence
Skill - Coming Soon -
Standard CO.13
Common Core Area - Congruence
Skill - Coming Soon -
Standard GMD.1
Common Core Area - Geometric Measurement and Dimension
Skill - Coming Soon -
Standard GMD.2
Common Core Area - Geometric Measurement and Dimension
Skill - Coming Soon -
Standard GMD.3
Common Core Area - Geometric Measurement and Dimension
Skill - Density word problems - Solve problems concerning real-world situations using your knowledge of volume, surface area, and density.
https://www.khanacademy.org/e/surface-and-volume-density-word-problems
Standard GMD.3
Common Core Area - Geometric Measurement and Dimension
Skill - Solid geometry - Find volumes and surface areas of boxes, cylinders, & triangular prisms.
https://www.khanacademy.org/e/solid_geometry
Standard GMD.3
Common Core Area - Geometric Measurement and Dimension
Skill - Solid geometry word problems - Solve problems concerning real-world situations with the volumes of cones, cylinders, and spheres.
https://www.khanacademy.org/e/volume-word-problems-with-cones--cylinders--and-spheres
Standard GMD.4
Common Core Area - Geometric Measurement and Dimension
Skill - Cross sections of 3D objects (basic) - Match 3D objects with their 2D cross-sections.
https://www.khanacademy.org/e/slicing-3d-figures
Standard GMD.4
Common Core Area - Geometric Measurement and Dimension
Skill - Cross sections of 3D objects - Practice your knowledge of all possible cross-sections of common 3D objects.
https://www.khanacademy.org/e/cross-sections-of-3d-shapes
Standard GMD.4
Common Core Area - Geometric Measurement and Dimension
Skill - Rotate 2D shapes in 3D - Practice your 3D visualization skills by rotating 2D shapes.
https://www.khanacademy.org/e/rotate-2d-shapes-to-make-3d-objects
Standard GPE.1
Common Core Area - Expressing Geometric Properties with Equations
Skill - Features of a circle from its expanded equation - Find the center and radius of a circle given the equation in expanded form.
https://www.khanacademy.org/e/equation_of_a_circle_2
Standard GPE.1
Common Core Area - Expressing Geometric Properties with Equations
Skill - Write standard equation of a circle - Given the graph of a circle or its features, find its standard equation.
https://www.khanacademy.org/e/write-the-equation-of-a-circle
Standard GPE.1
Common Core Area - Expressing Geometric Properties with Equations
Skill - Graph a circle from its expanded equation - Given the expanded equation of a circle, graph the circle. For example, graph the circle whose equation is x²+y²+4x+8y+16=0.
https://www.khanacademy.org/e/graphing_circles_2
Standard GPE.1
Common Core Area - Expressing Geometric Properties with Equations
Skill - Graph a circle from its standard equation - Given the standard form equation of a circle, graph the circle. For example, graph the circle who's equation is (x+5)²+(y+2)²=4.
https://www.khanacademy.org/e/graphing_circles
Standard GPE.1
Common Core Area - Expressing Geometric Properties with Equations
Skill - Features of a circle from its graph - Given the graph of a circle, find its center and radius.
https://www.khanacademy.org/e/find-the-features-of-a-circle-from-its-graph
Standard GPE.1
Common Core Area - Expressing Geometric Properties with Equations
Skill - Features of a circle from its standard equation - Find the center and radius of a circle given the equation in standard form.
https://www.khanacademy.org/e/equation_of_a_circle_1
Standard GPE.1
Common Core Area - Expressing Geometric Properties with Equations
Skill - Graph a circle from its features - Given information about the center and radius of a circle, graph it.
https://www.khanacademy.org/e/graph-a-circle-according-to-its-features
Standard GPE.2
Common Core Area - Expressing Geometric Properties with Equations
Skill - Equation of a parabola from focus & directrix - Given the focus and the directrix of a parabola, find its equation.
https://www.khanacademy.org/e/equation-of-parabola-from-focus-and-directrix
Standard GPE.3
Common Core Area - Expressing Geometric Properties with Equations
Skill - Equation of a hyperbola from features - Given some features of a hyperbola, find its equation.
https://www.khanacademy.org/e/equation_of_a_hyperbola
Standard GPE.3
Common Core Area - Expressing Geometric Properties with Equations
Skill - Foci of a hyperbola from equation - Given the equation of a hyperbola, find its foci.
https://www.khanacademy.org/e/foci-of-hyperbola-from-equation
Standard GPE.3
Common Core Area - Expressing Geometric Properties with Equations
Skill - Center & radii of ellipses from equation - Find the center and major and minor radius of an ellipse given its equation.
https://www.khanacademy.org/e/equation_of_an_ellipse
Standard GPE.3
Common Core Area - Expressing Geometric Properties with Equations
Skill - Foci of an ellipse from equation - Given the equation of an ellipse, find its foci.
https://www.khanacademy.org/e/foci-of-ellipse-from-equation
Standard GPE.3
Common Core Area - Expressing Geometric Properties with Equations
Skill - Graph & features of ellipses - Find the center and radii of an ellipse from its graph, and vice versa.
https://www.khanacademy.org/e/center-and-radii-of-an-ellipse-and-its-graph
Standard GPE.3
Common Core Area - Expressing Geometric Properties with Equations
Skill - Equation of an ellipse from features - Given the foci of an ellipse (and some other feature), find its equation.
https://www.khanacademy.org/e/equation-of-ellipse-from-foci
Standard GPE.3
Common Core Area - Expressing Geometric Properties with Equations
Skill - Foci of an ellipse from radii - Given the major and minor radii of an ellipse, find its foci.
https://www.khanacademy.org/e/find-foci-of-ellipse-from-radii
Standard GPE.3
Common Core Area - Expressing Geometric Properties with Equations
Skill - Ellipse standard equation & graph - Given the graph of an ellipse, find its equation, and vice versa.
https://www.khanacademy.org/e/equation-of-an-ellipse-from-its-graph
Standard GPE.3
Common Core Area - Expressing Geometric Properties with Equations
Skill - Vertices & direction of a hyperbola - Given the equation of a hyperbola, find its graph by considering its vertices and direction.
https://www.khanacademy.org/e/vertices-and-direction-of-hyperbola
Standard GPE.4
Common Core Area - Expressing Geometric Properties with Equations
Skill - Points inside/outside/on a circle - Given the center and radius of a circle, determine if a point is inside of the circle, on the circle, or outside of the circle
https://www.khanacademy.org/e/geometry-problems-on-the-coordinate-plane
Standard GPE.5
Common Core Area - Expressing Geometric Properties with Equations
Skill - Write equations of parallel & perpendicular lines - Write the equation for a line that is a parallel or perpendicular to a line given in slope-intercept form and goes through a specific point.
https://www.khanacademy.org/e/writing-equations-for-parallel-or-perpendicular-lines
Standard GPE.5
Common Core Area - Expressing Geometric Properties with Equations
Skill - Parallel & perpendicular lines from graph - Given points that two lines go through or the graph of each line, classify the lines as parallel, perpendicular, or neither.
https://www.khanacademy.org/e/classifying-lines-as-parallel--perpendicular--or-neither
Standard GPE.5
Common Core Area - Expressing Geometric Properties with Equations
Skill - Parallel & perpendicular lines from equation - Use your knowledge about the slopes of parallel and perpendicular lines to solve some problems. For example, what's the equation of the line perpendicular to y=3x-3 and passes through the point (-8, -2).
https://www.khanacademy.org/e/line_relationships
Standard GPE.6
Common Core Area - Expressing Geometric Properties with Equations
Skill - Divide line segments - Figure out the coordinates of a point between two other points that give a certain ratio. For example, find a point C so that it is two thirds of the way between point A and B.
https://www.khanacademy.org/e/dividing-line-segments
Standard GPE.6
Common Core Area - Expressing Geometric Properties with Equations
Skill - Midpoint formula - Find the midpoint of a segment on the coordinate plane, or find the endpoint of a segment given one point and the midpoint.
https://www.khanacademy.org/e/midpoint_formula
Standard GPE.7
Common Core Area - Expressing Geometric Properties with Equations
Skill - Area & perimeter on the coordinate plane - Find the area or perimeter of shapes like triangles, rectangles, parallelograms, and hexagons on the coordinate plane.
https://www.khanacademy.org/e/find-area-and-perimeter-on-the-coordinate-plane
Standard GPE.7
Common Core Area - Expressing Geometric Properties with Equations
Skill - Coordinate plane word problems: polygons - Solve all sorts of word problems with crazy contexts that use polygons on the coordinate plane.
https://www.khanacademy.org/e/coordinate-plane-word-problems-with-polygons
Standard MG.1
Common Core Area - Modeling with Geometry
Skill - Solid geometry word problems - Solve problems concerning real-world situations with the volumes of cones, cylinders, and spheres.
https://www.khanacademy.org/e/volume-word-problems-with-cones--cylinders--and-spheres
Standard MG.2
Common Core Area - Modeling with Geometry
Skill - Density word problems - Solve problems concerning real-world situations using your knowledge of volume, surface area, and density.
https://www.khanacademy.org/e/surface-and-volume-density-word-problems
Standard MG.3
Common Core Area - Modeling with Geometry
Skill - Coming Soon -
Standard SRT.1
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Dilate triangles - Given a figure and a definition of a dilation, manually draw the image.
https://www.khanacademy.org/e/dilations
Standard SRT.1
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Dilate points - Use the interactive transformation tool to perform dilations.
https://www.khanacademy.org/e/performing-dilations
Standard SRT.1
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Dilations: scale factor - Find both the center and the scale factor of a dilation that maps a given figure to another one.
https://www.khanacademy.org/e/defining-dilations-2
Standard SRT.1
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Dilate triangles - Given a figure and a definition of a dilation, manually draw the image.
https://www.khanacademy.org/e/dilations
Standard SRT.1
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Dilate points - Use the interactive transformation tool to perform dilations.
https://www.khanacademy.org/e/performing-dilations
Standard SRT.1
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Dilations: scale factor - Find both the center and the scale factor of a dilation that maps a given figure to another one.
https://www.khanacademy.org/e/defining-dilations-2
Standard SRT.1
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Dilate triangles - Given a figure and a definition of a dilation, manually draw the image.
https://www.khanacademy.org/e/dilations
Standard SRT.1
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Dilate points - Use the interactive transformation tool to perform dilations.
https://www.khanacademy.org/e/performing-dilations
Standard SRT.1
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Dilations: scale factor - Find both the center and the scale factor of a dilation that maps a given figure to another one.
https://www.khanacademy.org/e/defining-dilations-2
Standard SRT.2
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Dilate triangles - Given a figure and a definition of a dilation, manually draw the image.
https://www.khanacademy.org/e/dilations
Standard SRT.2
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Similarity & transformations - Given two polygons, try to map one onto the other using angle-preserving transformations, and determine whether they are similar.
https://www.khanacademy.org/e/exploring-angle-preserving-transformations-and-similarity
Standard SRT.2
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Dilations: scale factor - Find both the center and the scale factor of a dilation that maps a given figure to another one.
https://www.khanacademy.org/e/defining-dilations-2
Standard SRT.3
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Coming Soon -
Standard SRT.4
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Coming Soon -
Standard SRT.5
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Find angles in isosceles triangles - Find missing angles in isosceles triangles given just one angle.
https://www.khanacademy.org/e/find-angles-in-isosceles-triangles
Standard SRT.5
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Use similar & congruent triangles - Solve geometry problems with various polygons by using all you know about similarity and congruence.
https://www.khanacademy.org/e/solving-problems-with-similar-and-congruent-triangles
Standard SRT.5
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Solve similar triangles (basic) - Given two similar triangles and some of their side lengths, find a missing side length.
https://www.khanacademy.org/e/solving_similar_triangles_1
Standard SRT.5
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Find angles in congruent triangles - Given two triangles, determine whether they are congruent and use that to find missing angle measures.
https://www.khanacademy.org/e/congruent_triangles_2
Standard SRT.5
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Determine similar triangles: SSS - Given two triangles with some of their side measures, determine whether the triangles are similar or not.
https://www.khanacademy.org/e/similar_triangles_2
Standard SRT.5
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Solve similar triangles (advanced) - Given two similar triangles and some of their side lengths, find a missing side length.
https://www.khanacademy.org/e/solving_similar_triangles_2
Standard SRT.5
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Solve triangles: angle bisector theorem - Use the angle bisector theorem to find missing side lengths in triangles.
https://www.khanacademy.org/e/angle_bisector_theorem
Standard SRT.5
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Determine similar triangles: AA - Given two triangles with some of their angle measures, determine whether the triangles are similar or not.
https://www.khanacademy.org/e/similar_triangles_1
Standard SRT.5
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Determine congruent triangles - Use the triangle congruence criteria SSS, SAS, ASA, and AAS to determine that two triangles are congruent.
https://www.khanacademy.org/e/congruent_triangles_1
Standard SRT.6
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - DEPRECATED Trigonometry 1.5 - We took this down because we now have better material for you to use instead!
https://www.khanacademy.org/e/trigonometry_1.5
Standard SRT.6
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Solve for a side in right triangles - Given one side length and an acute angle in a right triangle, find another side using trigonometry.
https://www.khanacademy.org/e/trigonometry_2
Standard SRT.6
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Trigonometric ratios in right triangles - Given the side lengths of a right triangle, find the sine, cosine, or tangent of one of the acute angles.
https://www.khanacademy.org/e/trigonometry_1
Standard SRT.6
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - DEPRECATED Trigonometry 0.5 - We took this down because we now have better material for you to use instead!
https://www.khanacademy.org/e/trigonometry_0.5
Standard SRT.6
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Reciprocal trig ratios - Understand the right triangle definition of sec, csc, and cot ratios.
https://www.khanacademy.org/e/reciprocal_trig_funcs
Standard SRT.7
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Coming Soon -
Standard SRT.8
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Right triangle word problems - Solve word problems by modeling real-world (and not-so-real) situations as right triangles and using trigonometry.
https://www.khanacademy.org/e/applying-right-triangles
Standard SRT.8
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Solve for a side in right triangles - Given one side length and an acute angle in a right triangle, find another side using trigonometry.
https://www.khanacademy.org/e/trigonometry_2
Standard SRT.8
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Trigonometric ratios in right triangles - Given the side lengths of a right triangle, find the sine, cosine, or tangent of one of the acute angles.
https://www.khanacademy.org/e/trigonometry_1
Standard SRT.8
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Special right triangles - Use your knowledge of 30-60-90 and 45-45-90 triangles to solve some problems.
https://www.khanacademy.org/e/pythagorean_theorem_2
Standard SRT.8
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Solve for an angle in right triangles - Given two sides in a right triangle, find one of the acute angles using trigonometry.
https://www.khanacademy.org/e/solve-for-an-angle-in-a-right-triangle
Standard SRT.9
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Coming Soon -
Standard SRT.10
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Solve triangles using the law of sines - Solve missing triangle measures using the law of sines.
https://www.khanacademy.org/e/law_of_sines
Standard SRT.10
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - General triangle word problems - Solve word problems that involve general triangles using trigonometry.
https://www.khanacademy.org/e/law-of-sines-and-cosines-word-problems
Standard SRT.10
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Solve triangles using the law of cosines - Solve missing triangle measures using the law of cosines.
https://www.khanacademy.org/e/law_of_cosines
Standard SRT.11
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Solve triangles using the law of sines - Solve missing triangle measures using the law of sines.
https://www.khanacademy.org/e/law_of_sines
Standard SRT.11
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - General triangle word problems - Solve word problems that involve general triangles using trigonometry.
https://www.khanacademy.org/e/law-of-sines-and-cosines-word-problems
Standard SRT.11
Common Core Area - Similarity Right Triangles and Trigonometry
Skill - Solve triangles using the law of cosines - Solve missing triangle measures using the law of cosines.
https://www.khanacademy.org/e/law_of_cosines
Standard CN.1
Common Core Area - The Complex Number System
Skill - Simplify roots of negative numbers - Rewrite square roots of negative numbers as imaginary numbers.
https://www.khanacademy.org/e/simplify-square-roots-of-negative-numbers
Standard CN.1
Common Core Area - The Complex Number System
Skill - Parts of complex numbers - Determine the real and the imaginary parts of complex numbers
https://www.khanacademy.org/e/real-and-imaginary-parts-of-complex-numbers
Standard CN.1
Common Core Area - The Complex Number System
Skill - Classify complex numbers - Classify numbers as real, pure imaginary, or complex.
https://www.khanacademy.org/e/the-imaginary-unit-and-complex-numbers
Standard CN.2
Common Core Area - The Complex Number System
Skill - Powers of the imaginary unit - Simplify expressions with base i (the imaginary unit) raised to a positive exponent.
https://www.khanacademy.org/e/imaginary_unit_powers
Standard CN.2
Common Core Area - The Complex Number System
Skill - Multiply complex numbers (basic) - Multiply complex numbers by single terms that are either real or pure imaginary.
https://www.khanacademy.org/e/multiply-complex-numbers-by-real-or-imaginary-numbers
Standard CN.2
Common Core Area - The Complex Number System
Skill - Multiply complex numbers - Given two complex numbers, find their product.
https://www.khanacademy.org/e/multiplying_complex_numbers
Standard CN.2
Common Core Area - The Complex Number System
Skill - Add & subtract complex numbers - Practice addition and subtraction with complex numbers.
https://www.khanacademy.org/e/adding_and_subtracting_complex_numbers
Standard CN.3
Common Core Area - The Complex Number System
Skill - Divide complex numbers - Given a complex number division, express the result as a complex number of the form a+bi.
https://www.khanacademy.org/e/dividing_complex_numbers
Standard CN.3
Common Core Area - The Complex Number System
Skill - Complex number conjugates - Given a complex number, find its conjugate or plot it in the complex plane.
https://www.khanacademy.org/e/find-conjugates-of-complex-numbers
Standard CN.4
Common Core Area - The Complex Number System
Skill - Graphically add & subtract complex numbers - Add or subtract complex numbers, and plot the result in the complex plane.
https://www.khanacademy.org/e/complex_plane_operations
Standard CN.4
Common Core Area - The Complex Number System
Skill - Polar & rectangular forms of complex numbers - Given a complex number in rectangular form, write it in polar form. Given a complex number in polar form, write it in rectangular form.
https://www.khanacademy.org/e/rectangular-and-polar-forms-of-complex-numbers
Standard CN.4
Common Core Area - The Complex Number System
Skill - Absolute value of complex numbers - Given a complex number in the form a+bi, find its absolute value.
https://www.khanacademy.org/e/absolute_value_of_complex_numbers
Standard CN.4
Common Core Area - The Complex Number System
Skill - Plot numbers on the complex plane - Given a complex number, plot its corresponding point on the complex plane.
https://www.khanacademy.org/e/the_complex_plane
Standard CN.4
Common Core Area - The Complex Number System
Skill - Complex numbers from absolute value & angle - Given the absolute value and the angle of a complex number, express the number in the form a+bi.
https://www.khanacademy.org/e/find-complex-numbers-according-to-absolute-value-and-angle
Standard CN.4
Common Core Area - The Complex Number System
Skill - Angle of complex numbers - Given a complex number of the form a+bi, find its angle.
https://www.khanacademy.org/e/find-the-angle-of-complex-numbers
Standard CN.5
Common Core Area - The Complex Number System
Skill - Complex number conjugates - Given a complex number, find its conjugate or plot it in the complex plane.
https://www.khanacademy.org/e/find-conjugates-of-complex-numbers
Standard CN.5
Common Core Area - The Complex Number System
Skill - Graphically add & subtract complex numbers - Add or subtract complex numbers, and plot the result in the complex plane.
https://www.khanacademy.org/e/complex_plane_operations
Standard CN.5
Common Core Area - The Complex Number System
Skill - Powers of complex numbers - Simplify a power of a complex number z^n, or solve an equation of the form z^n=k.
https://www.khanacademy.org/e/powers_of_complex_numbers_1
Standard CN.5
Common Core Area - The Complex Number System
Skill - Multiply & divide complex numbers in polar form - Given two complex numbers in polar form, find their product or quotient.
https://www.khanacademy.org/e/multiplying_and_dividing_complex_number_polar_forms
Standard CN.6
Common Core Area - The Complex Number System
Skill - Midpoint of complex numbers - Given two complex numbers (either algebraically or graphically), find their midpoint.
https://www.khanacademy.org/e/find-the-midpoint-of-two-complex-numbers
Standard CN.6
Common Core Area - The Complex Number System
Skill - Distance of complex numbers - Given two complex numbers (either algebraically or graphically), find their distance.
https://www.khanacademy.org/e/distance-and-midpoint-on-the-complex-plane
Standard CN.7
Common Core Area - The Complex Number System
Skill - Solve quadratic equations: complex solutions - Solve quadratic equations using the quadratic formula. Some of the equations have real solutions while others have complex solutions.
https://www.khanacademy.org/e/quadratic-formula-with-complex-solutions
Standard CN.8
Common Core Area - The Complex Number System
Skill - Factor polynomials: complex numbers - Identify correctly factored forms of given polynomials. Factorizations may use complex numbers.
https://www.khanacademy.org/e/equivalent-forms-of-expressions-with-complex-numbers
Standard CN.9
Common Core Area - The Complex Number System
Skill - Coming Soon -
Standard Q.1
Common Core Area - Quantities
Skill - Interpret units in formulas - Determine the appropriate unit of a quantity based on a formula containing that quantity.
https://www.khanacademy.org/e/working-with-units
Standard Q.1
Common Core Area - Quantities
Skill - Multiple units word problems - Solve word problems that contain multiple quantities that are measured in different units.
https://www.khanacademy.org/e/units
Standard Q.2
Common Core Area - Quantities
Skill - Coming Soon -
Standard Q.3
Common Core Area - Quantities
Skill - Coming Soon -
Standard RN.1
Common Core Area - The Real Number System
Skill - Coming Soon -
Standard RN.2
Common Core Area - The Real Number System
Skill - Properties of exponents challenge (rational exponents) - Rewrite some elaborate exponential expressions that involve fractional exponents and radicals.
https://www.khanacademy.org/e/rational-exp-prop-challenge
Standard RN.2
Common Core Area - The Real Number System
Skill - Unit-fraction exponents - Evaluate numerical expressions with unit-fraction exponents or radicals, and convert between the two forms of representations.
https://www.khanacademy.org/e/understanding-fractional-exponents
Standard RN.2
Common Core Area - The Real Number System
Skill - Evaluate radical expressions challenge - Evaluate numerical radical expressions using the properties of exponents.
https://www.khanacademy.org/e/simplify-radicals-and-exponentials
Standard RN.2
Common Core Area - The Real Number System
Skill - Properties of exponents (rational exponents) - Rewrite exponential expressions (where the exponent can be a fraction) using the properties of exponents.
https://www.khanacademy.org/e/exponents_4
Standard RN.2
Common Core Area - The Real Number System
Skill - Simplify square roots - For example, simplify √18 as 3√2.
https://www.khanacademy.org/e/simplifying_radicals
Standard RN.2
Common Core Area - The Real Number System
Skill - Simplify square-root expressions - Practice simplifying expressions with multiple radical terms.
https://www.khanacademy.org/e/adding_and_subtracting_radicals
Standard RN.2
Common Core Area - The Real Number System
Skill - Rational exponents challenge - Choose equivalent forms of radical and exponential expressions.
https://www.khanacademy.org/e/manipulating-fractional-exponents
Standard RN.2
Common Core Area - The Real Number System
Skill - Fractional exponents - Evaluate numerical expressions with rational exponents, and convert between equivalent forms of exponential and radical expressions.
https://www.khanacademy.org/e/exponents_3
Standard RN.2
Common Core Area - The Real Number System
Skill - 4th & 5th roots - Radicals are also known as roots. The most common are square root √ and cube root ∛, but there are more. Evaluate higher-degree radicals like ∜81.
https://www.khanacademy.org/e/radicals
Standard RN.2
Common Core Area - The Real Number System
Skill - Simplify square-roots (variables) - Simplify square roots that contain variables in them, like √(8x³)
https://www.khanacademy.org/e/multiplying_radicals
Standard RN.3
Common Core Area - The Real Number System
Skill - Rational vs. irrational expressions - Determine whether an expression that is the combination of two rational/irrational numbers is rational or irrational itself.
https://www.khanacademy.org/e/recognizing-rational-and-irrational-expressions
Standard VM.1
Common Core Area - Vector and Matrix Quantities
Skill - Magnitude of vectors - Find the magnitude of a vector. You'll see vectors given in graphs, given in component form, and given by initial and terminal points.
https://www.khanacademy.org/e/magnitude-of-vectors
Standard VM.1
Common Core Area - Vector and Matrix Quantities
Skill - Equivalent vectors - Determine if two vectors shown on a graph are equivalent.
https://www.khanacademy.org/e/equivalent-vectors
Standard VM.2
Common Core Area - Vector and Matrix Quantities
Skill - Components of vectors - Find the components of a vector.
https://www.khanacademy.org/e/components_of_vectors
Standard VM.3
Common Core Area - Vector and Matrix Quantities
Skill - Vector word problems - Apply what you've learned about vectors to solve some word problems!
https://www.khanacademy.org/e/vector-word-problems
Standard VM.4
Common Core Area - Vector and Matrix Quantities
Skill - Add & subtract vectors - Add and subtract vectors given in component form.
https://www.khanacademy.org/e/adding_vectors
Standard VM.4
Common Core Area - Vector and Matrix Quantities
Skill - Graphically add & subtract vectors - Analyze graphs that represent vector addition & subtraction.
https://www.khanacademy.org/e/graphically-adding-and-subtracting-vectors
Standard VM.4
Common Core Area - Vector and Matrix Quantities
Skill - Add & subtract vectors - Add and subtract vectors given in component form.
https://www.khanacademy.org/e/adding_vectors
Standard VM.4
Common Core Area - Vector and Matrix Quantities
Skill - Add vectors: magnitude & direction to component - Add two vectors in magnitude and direction form to get a new vector in component form.
https://www.khanacademy.org/e/adding-vectors-in-magnitude-and-direction-form
Standard VM.4
Common Core Area - Vector and Matrix Quantities
Skill - Graphically add & subtract vectors - Analyze graphs that represent vector addition & subtraction.
https://www.khanacademy.org/e/graphically-adding-and-subtracting-vectors
Standard VM.4
Common Core Area - Vector and Matrix Quantities
Skill - Add & subtract vectors - Add and subtract vectors given in component form.
https://www.khanacademy.org/e/adding_vectors
Standard VM.4
Common Core Area - Vector and Matrix Quantities
Skill - Add vectors: magnitude & direction to component - Add two vectors in magnitude and direction form to get a new vector in component form.
https://www.khanacademy.org/e/adding-vectors-in-magnitude-and-direction-form
Standard VM.4
Common Core Area - Vector and Matrix Quantities
Skill - Graphically add & subtract vectors - Analyze graphs that represent vector addition & subtraction.
https://www.khanacademy.org/e/graphically-adding-and-subtracting-vectors
Standard VM.4
Common Core Area - Vector and Matrix Quantities
Skill - Add & subtract vectors - Add and subtract vectors given in component form.
https://www.khanacademy.org/e/adding_vectors
Standard VM.4
Common Core Area - Vector and Matrix Quantities
Skill - Add vectors: magnitude & direction to component - Add two vectors in magnitude and direction form to get a new vector in component form.
https://www.khanacademy.org/e/adding-vectors-in-magnitude-and-direction-form
Standard VM.4
Common Core Area - Vector and Matrix Quantities
Skill - Graphically add & subtract vectors - Analyze graphs that represent vector addition & subtraction.
https://www.khanacademy.org/e/graphically-adding-and-subtracting-vectors
Standard VM.4
Common Core Area - Vector and Matrix Quantities
Skill - Add vectors: magnitude & direction to component - Add two vectors in magnitude and direction form to get a new vector in component form.
https://www.khanacademy.org/e/adding-vectors-in-magnitude-and-direction-form
Standard VM.5
Common Core Area - Vector and Matrix Quantities
Skill - Analyze scalar multiplication - Match vectors to images based on scalars to show that you understand scalar multiplication.
https://www.khanacademy.org/e/understanding-scalar-multiplication
Standard VM.5
Common Core Area - Vector and Matrix Quantities
Skill - Unit vectors - Find a unit vector in the direction of a given vector.
https://www.khanacademy.org/e/unit-vector
Standard VM.5
Common Core Area - Vector and Matrix Quantities
Skill - Analyze scalar multiplication - Match vectors to images based on scalars to show that you understand scalar multiplication.
https://www.khanacademy.org/e/understanding-scalar-multiplication
Standard VM.5
Common Core Area - Vector and Matrix Quantities
Skill - Unit vectors - Find a unit vector in the direction of a given vector.
https://www.khanacademy.org/e/unit-vector
Standard VM.5
Common Core Area - Vector and Matrix Quantities
Skill - Analyze scalar multiplication - Match vectors to images based on scalars to show that you understand scalar multiplication.
https://www.khanacademy.org/e/understanding-scalar-multiplication
Standard VM.5
Common Core Area - Vector and Matrix Quantities
Skill - Unit vectors - Find a unit vector in the direction of a given vector.
https://www.khanacademy.org/e/unit-vector
Standard VM.6
Common Core Area - Vector and Matrix Quantities
Skill - Matrix elements - Find specific elements (also called entries) of given matrices.
https://www.khanacademy.org/e/understand-matrix-coordinates
Standard VM.7
Common Core Area - Vector and Matrix Quantities
Skill - Multiply matrices by scalars - Find the matrix that is a result of multiplying a given matrix by a given scalar.
https://www.khanacademy.org/e/scalar_matrix_multiplication
Standard VM.7
Common Core Area - Vector and Matrix Quantities
Skill - Matrix equations: scalar multiplication - Solve equations where the unknown is a matrix, by using matrix multiplication by a scalar.
https://www.khanacademy.org/e/solve-matrix-equations-scalar-multiplication
Standard VM.8
Common Core Area - Vector and Matrix Quantities
Skill - Multiply matrices - Find the result of a multiplication of two given matrices.
https://www.khanacademy.org/e/multiplying_a_matrix_by_a_matrix
Standard VM.8
Common Core Area - Vector and Matrix Quantities
Skill - Matrix equations: addition & subtraction - Solve equations where the unknown is a matrix, by using matrix addition and subtraction.
https://www.khanacademy.org/e/solve-matrix-equations-add-sub
Standard VM.8
Common Core Area - Vector and Matrix Quantities
Skill - Determinant of a 2x2 matrix - Find the determinant of a given 2x2 matrix.
https://www.khanacademy.org/e/matrix_determinant
Standard VM.8
Common Core Area - Vector and Matrix Quantities
Skill - Add & subtract matrices - Find the matrix that is the result of the addition or subtraction of two given matrices.
https://www.khanacademy.org/e/matrix_addition_and_subtraction
Standard VM.9
Common Core Area - Vector and Matrix Quantities
Skill - Coming Soon -
Standard VM.10
Common Core Area - Vector and Matrix Quantities
Skill - Determine invertible matrices - Given a 2x2 matrix, determine whether it has an inverse.
https://www.khanacademy.org/e/determine-invertibile-2x2-matrices
Standard VM.11
Common Core Area - Vector and Matrix Quantities
Skill - Transform vectors using matrices - Find the result (both algebraically and graphically) of transforming a vector using a transformation matrix.
https://www.khanacademy.org/e/multiplying_a_matrix_by_a_vector
Standard VM.12
Common Core Area - Vector and Matrix Quantities
Skill - Matrices as transformations - Match transformation matrices with a visual representation of their effect on the plane.
https://www.khanacademy.org/e/transformation-matrices-1
Standard VM.12
Common Core Area - Vector and Matrix Quantities
Skill - Transform polygons using matrices - Find the image of a given polygon under a transformation defined by a given matrix.
https://www.khanacademy.org/e/transform-polygons-with-matrices
Standard CP.1
Common Core Area - Conditional Probability & the Rules of Probability
Skill - Subsets of sample spaces - Answer interesting questions about subsets of sample spaces.
https://www.khanacademy.org/e/describing-subsets-of-sample-spaces
Standard CP.1
Common Core Area - Conditional Probability & the Rules of Probability
Skill - Basic set notation - The union, complement, and intersection of sets.
https://www.khanacademy.org/e/basic_set_notation
Standard CP.2
Common Core Area - Conditional Probability & the Rules of Probability
Skill - Dependent and independent events - Determine if two events are dependent or independent.
https://www.khanacademy.org/e/identifying-dependent-and-independent-events
Standard CP.3
Common Core Area - Conditional Probability & the Rules of Probability
Skill - Dependent and independent events - Determine if two events are dependent or independent.
https://www.khanacademy.org/e/identifying-dependent-and-independent-events
Standard CP.4
Common Core Area - Conditional Probability & the Rules of Probability
Skill - Trends in categorical data - Analyze categorical data to find some trends.
https://www.khanacademy.org/e/trends-in-categorical-data
Standard CP.5
Common Core Area - Conditional Probability & the Rules of Probability
Skill - Trends in categorical data - Analyze categorical data to find some trends.
https://www.khanacademy.org/e/trends-in-categorical-data
Standard CP.6
Common Core Area - Conditional Probability & the Rules of Probability
Skill - Dependent probability - Find dependent probabilities like P(A | B) or P(B | A) for a variety of contexts.
https://www.khanacademy.org/e/dependent_probability
Standard CP.6
Common Core Area - Conditional Probability & the Rules of Probability
Skill - Trends in categorical data - Analyze categorical data to find some trends.
https://www.khanacademy.org/e/trends-in-categorical-data
Standard CP.7
Common Core Area - Conditional Probability & the Rules of Probability
Skill - Adding probabilities - Find four probabilities for each problem: P(A), P(B), P(A and B), and P(A or B).
https://www.khanacademy.org/e/adding-probability
Standard CP.8
Common Core Area - Conditional Probability & the Rules of Probability
Skill - Multiplying dependent probabilities - Use properties of dependent probability like P(A | B) * P(B) = P(A and B) to solve some tricky probability problems!
https://www.khanacademy.org/e/multiplying-dependent-probabilities
Standard CP.9
Common Core Area - Conditional Probability & the Rules of Probability
Skill - Permutations & combinations - Permutations and Combinations with overcounting
https://www.khanacademy.org/e/permutations_and_combinations_2
Standard CP.9
Common Core Area - Conditional Probability & the Rules of Probability
Skill - Combinations - Introductory combination problems like if you have 5 friends and can pick 2 of them to join you on a boat ride, how many different groups of friends could you take with you?
https://www.khanacademy.org/e/combinations_1
Standard CP.9
Common Core Area - Conditional Probability & the Rules of Probability
Skill - Permutations - Introductory permutation problems.
https://www.khanacademy.org/e/permutations_1
Standard CP.9
Common Core Area - Conditional Probability & the Rules of Probability
Skill - Probability with permutations and combinations - Probability questions using permutations and combinations of objects
Standard IC.1
Common Core Area - Making Inferences and Justifying Conclusions
Skill - Coming Soon -
Standard IC.2
Common Core Area - Making Inferences and Justifying Conclusions
Skill - Simple hypothesis testing - Show that you have mastery over the idea behind hypothesis testing by calculating some probabilities and drawing conclusions.
https://www.khanacademy.org/e/hypothesis-testing-with-simulations
Standard IC.3
Common Core Area - Making Inferences and Justifying Conclusions
Skill - Types of statistical studies - Determines if a statistical study is a sample study, an experiment, or an observational study.
https://www.khanacademy.org/e/types-of-statistical-studies
Standard IC.4
Common Core Area - Making Inferences and Justifying Conclusions
Skill - Coming Soon -
Standard IC.5
Common Core Area - Making Inferences and Justifying Conclusions
Skill - Hypothesis testing in experiments - Look at the results of different experiments, and determine if they are statistically significant.
https://www.khanacademy.org/e/hypothesis-testing-in-experiments
Standard IC.6
Common Core Area - Making Inferences and Justifying Conclusions
Skill - Types of statistical studies - Determines if a statistical study is a sample study, an experiment, or an observational study.
https://www.khanacademy.org/e/types-of-statistical-studies
Standard ID.1
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Comparing data distributions - Take a look at two different data distributions and draw some comparisons.
https://www.khanacademy.org/e/interpreting-and-comparing-data-distributions
Standard ID.2
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Comparing data distributions - Take a look at two different data distributions and draw some comparisons.
https://www.khanacademy.org/e/interpreting-and-comparing-data-distributions
Standard ID.2
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Standard deviation of a population - Calculate the standard deviation of a population.
https://www.khanacademy.org/e/standard_deviation_of_a_population
Standard ID.3
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Comparing data distributions - Take a look at two different data distributions and draw some comparisons.
https://www.khanacademy.org/e/interpreting-and-comparing-data-distributions
Standard ID.4
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Normal distribution: Area above or below a point - Use a z-table to find the area above or below a given point in some Normal distribution.
https://www.khanacademy.org/e/z_scores_2
Standard ID.4
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Empirical rule - Practice applying the 68-95-99.7 empirical rule.
https://www.khanacademy.org/e/empirical_rule
Standard ID.4
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Z-scores 1 - Find the z-score of a particular measurement given the mean and standard deviation.
https://www.khanacademy.org/e/z_scores_1
Standard ID.4
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Normal distribution: Area between two points - Use a z-table to find the area between two given points in some normal distribution.
https://www.khanacademy.org/e/z_scores_3
Standard ID.5
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Trends in categorical data - Analyze categorical data to find some trends.
https://www.khanacademy.org/e/trends-in-categorical-data
Standard ID.6
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Fitting quadratic and exponential functions to scatter plots - Determine if a quadratic or exponential model fits a data set better, then use the model to make a prediction.
https://www.khanacademy.org/e/fitting-functions-to-scatter-plots
Standard ID.6
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Fitting quadratic and exponential functions to scatter plots - Determine if a quadratic or exponential model fits a data set better, then use the model to make a prediction.
https://www.khanacademy.org/e/fitting-functions-to-scatter-plots
Standard ID.6
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Fitting quadratic and exponential functions to scatter plots - Determine if a quadratic or exponential model fits a data set better, then use the model to make a prediction.
https://www.khanacademy.org/e/fitting-functions-to-scatter-plots
Standard ID.6
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Fitting quadratic and exponential functions to scatter plots - Determine if a quadratic or exponential model fits a data set better, then use the model to make a prediction.
https://www.khanacademy.org/e/fitting-functions-to-scatter-plots
Standard ID.7
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Coming Soon -
Standard ID.8
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Correlation coefficient intuition - Match correlation coefficients to scatterplots to build a deeper intuition behind correlation coefficients.
https://www.khanacademy.org/e/correlation-coefficient-intuition
Standard ID.9
Common Core Area - Interpreting Categorical and Quantitative Data
Skill - Types of statistical studies - Determines if a statistical study is a sample study, an experiment, or an observational study.
https://www.khanacademy.org/e/types-of-statistical-studies
Standard MD.1
Common Core Area - Using Probability to Make Decisions
Skill - Constructing probability distributions - Given a context, create a probability distribution.
https://www.khanacademy.org/e/constructing-probability-distributions
Standard MD.2
Common Core Area - Using Probability to Make Decisions
Skill - Expected value - Compute the expected value given a set of outcomes, probabilities, and payoffs
https://www.khanacademy.org/e/expected_value
Standard MD.3
Common Core Area - Using Probability to Make Decisions
Skill - Expected value with calculated probabilities - Find expected value based on calculated probabilities.
https://www.khanacademy.org/e/expected-value-with-calculated-probabilities
Standard MD.4
Common Core Area - Using Probability to Make Decisions
Skill - Expected value with empirical probabilities - Find expected value based on empirical probabilities.
https://www.khanacademy.org/e/expected-value-with-empirical-probabilities
Standard MD.5
Common Core Area - Using Probability to Make Decisions
Skill - Expected value - Compute the expected value given a set of outcomes, probabilities, and payoffs
https://www.khanacademy.org/e/expected_value
Standard MD.5
Common Core Area - Using Probability to Make Decisions
Skill - Making decisions with expected values - Calculate expected values and then use them to make decisions.
https://www.khanacademy.org/e/making-decisions-with-expected-values
Standard MD.5
Common Core Area - Using Probability to Make Decisions
Skill - Expected value - Compute the expected value given a set of outcomes, probabilities, and payoffs
https://www.khanacademy.org/e/expected_value
Standard MD.5
Common Core Area - Using Probability to Make Decisions
Skill - Making decisions with expected values - Calculate expected values and then use them to make decisions.
https://www.khanacademy.org/e/making-decisions-with-expected-values
Standard MD.5
Common Core Area - Using Probability to Make Decisions
Skill - Expected value - Compute the expected value given a set of outcomes, probabilities, and payoffs
https://www.khanacademy.org/e/expected_value
Standard MD.5
Common Core Area - Using Probability to Make Decisions
Skill - Making decisions with expected values - Calculate expected values and then use them to make decisions.
https://www.khanacademy.org/e/making-decisions-with-expected-values
Standard MD.6
Common Core Area - Using Probability to Make Decisions
Skill - Using probability to make fair decisions - Determine if different methods are fair or unfair.
https://www.khanacademy.org/e/using-probability-to-make-fair-decisions
Standard MD.7
Common Core Area - Using Probability to Make Decisions
Skill - Using probability to make fair decisions - Determine if different methods are fair or unfair.
https://www.khanacademy.org/e/using-probability-to-make-fair-decisions
Standard MD.7
Common Core Area - Using Probability to Make Decisions
Skill - Making decisions with expected values - Calculate expected values and then use them to make decisions.
https://www.khanacademy.org/e/making-decisions-with-expected-values