### 1: Seeing Structure in Expressions

#### 1.1: Interpret the structure of expressions.

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.

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

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.

#### 1.2: Write expressions in equivalent forms to solve problems.

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.

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

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

### 2: Arithmetic with Polynomials and Rational Expressions

#### 2.1: Perform arithmetic operations on polynomials.

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

#### 2.2: Understand the relationship between zeros and factors of polynomials.

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

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 ??(??).

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.

#### 2.3: Use polynomial identities to solve problems.

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.

#### 2.4: Rewrite rational expressions.

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

### 3: Creating Equations

#### 3.1: Create equations that describe numbers or relationships.

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

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.

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.

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

### 4: Reasoning with Equations and Inequalities

#### 4.1: Understand solving equations as a process of reasoning and explain the reasoning.

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.

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.

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

#### 4.2: Solve equations and inequalities in one variable.

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

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.

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.

#### 4.3: Solve systems of equations.

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.

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

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.

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

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

#### 4.4: Represent and solve equations and inequalities graphically.

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.

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.

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.

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

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).

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

Correlation last revised: 9/15/2020

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