# Government Standards

## Common Core

Assessment Exam - Common Core Math - High School: Algebra
Seeing Structure in Expressions eTAP Lesson
Interpret the structure of expressions.
Interpret parts of an expression, such as terms, factors, and coefficients.
CCSS.Math.Content.HSA.SSE.A.1.a
Variables and Expressions
Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
CCSS.Math.Content.HSA.SSE.A.1.b
Open Sentences
Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).
CCSS.Math.Content.HSA.SSE.A.2
Perfect Square Factoring

Factoring Differences of Squares
Write expressions in equivalent forms to solve problems.
Factor a quadratic expression to reveal the zeros of the function it defines.
CCSS.Math.Content.HSA.SSE.B.3.a
Factoring by Grouping
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
CCSS.Math.Content.HSA.SSE.B.3.b
Completing the Square
Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
CCSS.Math.Content.HSA.SSE.B.3.c
Negative and Rational Exponents

Exponential Functions and Data

Graphs of Exponential Functions
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.*
CCSS.Math.Content.HSA.SSE.B.4
Arithmetic and Geometric Series

Sums of Geometric Series

Sums of Arithmetic Series
Arithmetic with Polynomials and Rational Expressions eTAP Lesson
Perform arithmetic operations on polynomials.
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
CCSS.Math.Content.HSA.APR.A.1
Polynomials

Understand the relationship between zeros and factors of polynomials.
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).
CCSS.Math.Content.HSA.APR.B.2
Zeros of Polynomial Functions
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
CCSS.Math.Content.HSA.APR.B.3
Graphs of Polynomial Functions
Use polynomial identities to solve problems.
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 - y2)2 + (2xy)2 can be used to generate Pythagorean triples.
CCSS.Math.Content.HSA.APR.C.4
Cubic Equations
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.
CCSS.Math.Content.HSA.APR.C.5
Pascal's Triangle
Rewrite rational expressions.
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
CCSS.Math.Content.HSA.APR.D.6
Multiplying and Dividing Monomials

Dividing Polynomials
Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
CCSS.Math.Content.HSA.APR.D.7
Multiplying and Dividing Polynomials
Creating Equations eTAP Lesson
Create equations that describe numbers or relationships.
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.
CCSS.Math.Content.HSA.CED.A.1
Simplifying Rational Expressions
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
CCSS.Math.Content.HSA.CED.A.2
How to Use Graphs
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
CCSS.Math.Content.HSA.CED.A.3
Graphing Systems of Inequalities
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
CCSS.Math.Content.HSA.CED.A.4
Solving Equations Using Several Operations
Reasoning with Equations and Inequalities eTAP Lesson
Understand solving equations as a process of reasoning and explain the reasoning.
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.
CCSS.Math.Content.HSA.REI.A.1
Substitution
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
CCSS.Math.Content.HSA.REI.A.2
Elimination
Solve equations and inequalities in one variable.
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
CCSS.Math.Content.HSA.REI.B.3
Solving Equations by Multiplication and Division
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.
CCSS.Math.Content.HSA.REI.B.4.a
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. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
CCSS.Math.Content.HSA.REI.B.4.b
Solve systems of equations.
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
CCSS.Math.Content.HSA.REI.C.5
Solving Equations by Addition and Subtraction
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
CCSS.Math.Content.HSA.REI.C.6
Graphing Systems of Equations
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x2 + y2 = 3.
CCSS.Math.Content.HSA.REI.C.7
Represent a system of linear equations as a single matrix equation in a vector variable
CCSS.Math.Content.HSA.REI.C.8
Solving Linear Systems with Matrices
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).
CCSS.Math.Content.HSA.REI.C.9
What are Matrices
Represent and solve equations and inequalities graphically.
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
CCSS.Math.Content.HSA.REI.D.10