Academic Standards

KY.HS.A.1: Interpret expressions that represent a quantity in terms of its context.

KY.HS.A.1.a: Interpret parts of an expression, such as terms, factors and coefficients.

Compound Interest

Operations with Radical Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Formulas for any Variable

KY.HS.A.1.b: Interpret complicated expressions, given a context, by viewing one or more of their parts as a single entity.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Compound Interest

Exponential Growth and Decay

Geometric Sequences

Translating and Scaling Functions

Using Algebraic Expressions

KY.HS.A.2: Use the structure of an expression to identify ways to rewrite it and consistently look for opportunities to rewrite expressions in equivalent forms.

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Exponents and Power Rules

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Multiplying Exponential Expressions

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Simplifying Trigonometric Expressions

Solving Algebraic Equations II

Using Algebraic Expressions

KY.HS.A.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

KY.HS.A.3.a: Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient and constant term.

Addition of Polynomials

Quadratics in Polynomial Form

KY.HS.A.3.b: Factor a quadratic expression to reveal the zeros of the function it defines.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Quadratics in Factored Form

KY.HS.A.3.c: Use the properties of exponents to rewrite exponential expressions.

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

KY.HS.A.3.d: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

KY.HS.A.5: Add, subtract and multiply polynomials.

Addition and Subtraction of Functions

Addition of Polynomials

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

KY.HS.A.6: Know and apply the Remainder Theorem.

Dividing Polynomials Using Synthetic Division

Polynomials and Linear Factors

2.2.1.2: For a polynomial ??(??) and a number ??, the remainder on division by ?? – ?? is ??(a), so ??(??) = 0 if and only if (?? – ??) is a factor of ??(??).

Dividing Polynomials Using Synthetic Division

Polynomials and Linear Factors

KY.HS.A.7: Identify roots of polynomials when suitable factorizations are available. Know these roots become the zeros (x-intercepts) for the corresponding polynomial function.

Graphs of Polynomial Functions

Modeling the Factorization of *x*^{2}+*bx*+*c*

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Vertex Form

KY.HS.A.8: Prove polynomial identities and use them to describe numerical relationships.

KY.HS.A.9: Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.

KY.HS.A.10: Rewrite simple rational expressions in different forms.

Dividing Polynomials Using Synthetic Division

KY.HS.A.12: Create equations and inequalities in one variable and use them to solve problems.

Absolute Value Equations and Inequalities

Arithmetic Sequences

Compound Interest

Exploring Linear Inequalities in One Variable

Geometric Sequences

Linear Inequalities in Two Variables

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Quadratic Inequalities

Solving Equations on the Number Line

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

Using Algebraic Equations

KY.HS.A.13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Absolute Value Equations and Inequalities

Cat and Mouse (Modeling with Linear Systems)

Circles

Compound Interest

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Quadratics in Polynomial Form

Quadratics in Vertex Form

Slope-Intercept Form of a Line

Solving Equations by Graphing Each Side

Solving Equations on the Number Line

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

Standard Form of a Line

Using Algebraic Equations

KY.HS.A.14: Create a system of equations or inequalities to represent constraints within a modeling context. Interpret the solution(s) to the corresponding system as viable or nonviable options within the context.

Linear Inequalities in Two Variables

Linear Programming

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

KY.HS.A.15: Rearrange formulas to solve a literal equation, highlighting a quantity of interest, using the same reasoning as in solving equations.

Area of Triangles

Solving Formulas for any Variable

KY.HS.A.16: Understand each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations I

Solving Algebraic Equations II

Solving Equations by Graphing Each Side

Solving Equations on the Number Line

Solving Formulas for any Variable

Solving Two-Step Equations

KY.HS.A.17: Solve and justify equations in one variable. Justify the solutions and give examples showing how extraneous solutions may arise.

KY.HS.A.17.a: Solve rational equations written as proportions in one variable.

Percents and Proportions

Proportions and Common Multipliers

Radical Functions

KY.HS.A.17.b: Solve radical equations in one variable.

KY.HS.A.18: Solve linear equations and inequalities in one variable, including literal equations with coefficients represented by letters.

Area of Triangles

Compound Inequalities

Exploring Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations I

Solving Algebraic Equations II

Solving Equations by Graphing Each Side

Solving Equations on the Number Line

Solving Formulas for any Variable

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

KY.HS.A.19: Solve quadratic equations in one variable.

KY.HS.A.19.a: Solve quadratic equations by taking square roots, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Points in the Complex Plane

Quadratics in Factored Form

Roots of a Quadratic

KY.HS.A.19.b: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.

KY.HS.A.19.c: Solve quadratic equations by completing the square.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Points in the Complex Plane

Roots of a Quadratic

KY.HS.A.20: Solve systems of linear equations in two variables.

KY.HS.A.20.a: Understand a system of two equations in two variables has the same solution as a new system formed by replacing one of the original equations with an equivalent equation.

Solving Equations by Graphing Each Side

Solving Linear Systems (Standard Form)

KY.HS.A.20.b: Solve systems of linear equations with graphs, substitution and elimination, focusing on pairs of linear equations in two variables.

Cat and Mouse (Modeling with Linear Systems)

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

KY.HS.A.22: Use matrices to solve a system of equations.

KY.HS.A.22.a: Represent a system of linear equations as a single matrix equation in a vector variable.

Solving Linear Systems (Matrices and Special Solutions)

KY.HS.A.22.b: Find the inverse of a matrix if it exists.

Solving Linear Systems (Matrices and Special Solutions)

KY.HS.A.22.c: Use matrices to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

Solving Linear Systems (Matrices and Special Solutions)

KY.HS.A.23: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

Absolute Value Equations and Inequalities

Cat and Mouse (Modeling with Linear Systems)

Circles

Ellipses

Hyperbolas

Parabolas

Point-Slope Form of a Line

Points, Lines, and Equations

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

Standard Form of a Line

KY.HS.A.24: Justify that the solutions of the equations f(x) = g(x) are the x-coordinates of the points where the graphs of y = f(x) and y = g(x) intersect. Find the approximate solutions graphically, using technology or tables.

Cat and Mouse (Modeling with Linear Systems)

Point-Slope Form of a Line

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Standard Form of a Line

4.4.2.1: Students justify solutions for equations which Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential and logarithmic functions.

Cat and Mouse (Modeling with Linear Systems)

Point-Slope Form of a Line

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Standard Form of a Line

KY.HS.A.25: Graph linear inequalities in two variables.

Linear Inequalities in Two Variables

Linear Programming

Systems of Linear Inequalities (Slope-intercept form)

KY.HS.A.25.a: Graph the solutions to a linear inequality as a half-plane (excluding the boundary in the case of a strict inequality).

Linear Inequalities in Two Variables

Systems of Linear Inequalities (Slope-intercept form)

KY.HS.A.25.b: Graph the solution set to a system of linear inequalities as the intersection of the corresponding half-planes.

Linear Programming

Systems of Linear Inequalities (Slope-intercept form)

Correlation last revised: 9/15/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.