### HS.A-SSE: Seeing Structure in Expressions

#### 1.1: Interpret the structure of expressions

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

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

HS.A-SSE.1.b: Interpret complicated expressions by examining one or more of their parts as a single entity.

HS.A-SSE.2: Use the structure of an expression to identify ways to rewrite it.

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

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

HA.A.SSE.3.a: Factor a quadratic expression to reveal the zeros of the function it defines.

HA.A.SSE.3.b: Complete the square in a quadratic expression to produce an equivalent expression.

HA.A.SSE.3.c: Use the properties of exponents to transform exponential expressions.

### HS.A-APR: Arithmetic with Polynomials and Rational Expressions

#### 2.1: Perform arithmetic operations on polynomials

HS.A-APR.1.i: Add, subtract, and multiply polynomials.

HS.A-APR.1.ii: Understand that polynomials form a system comparable to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.

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

HS.A-APR.2: Apply the Remainder Theorem.

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

HS.A-APR.3.i: Identify zeros of polynomials when suitable factorizations are available.

HS.A-APR.3.ii: Use the zeros to construct a rough graph of the function defined by the polynomial.

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

HS.A-APR.5: Apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n.

2.3.2.1: Coefficients in the expansion of (?? + ??)? can be determined using Pascal’s Triangle or combinations.

### HS.A-CED: Creating Equations and Inequalities

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

HS.A-CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

HS.A-CED.2.i: Create equations in two or more variables to represent relationships between quantities.

HS.A-CED.2.ii: Graph equations on coordinate axes with appropriate labels and scales.

HS.A-CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

HS.A-CED.4: Rearrange formulas to isolate a quantity of interest, using the same reasoning as in solving equations.

### HS.A-REI: Reasoning with Equations and Inequalities

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

HS.A-REI.1: Explain 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.

HS.A-REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

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

HS.A-REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

HS.A-REI.4: Solve quadratic equations in one variable.

HS.A-REI.4.a.i: 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.

HS.A-REI.4.a.ii: Derive the quadratic formula from this form.

HS.A-REI.4.b.i: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.

HS.A-REI.4.b.ii: Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.

#### 4.3: Solve systems of equations

HS.A-REI.6: Solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables.

HS.A-REI.8: Represent a system of linear equations as a single matrix equation.

HS.A-REI.9: Find the inverse of a matrix, if it exists, and use it 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

HS.A-REI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

HS.A-REI.11: Using graphs, technology, tables, or successive approximations, show that the solution(s) to the equation f(x) = g(x) are the x-value(s) that result in the y-values of f(x) and g(x) being the same.

HS.A-REI.12.i: Graph the solutions to a linear inequality in two variables as a half-plane.

HS.A-REI.12.ii: Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Correlation last revised: 9/22/2020

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