Academic standards list

High School: Algebra — Mathematics


Academic standards define the expectations for knowledge and skills that students are to learn in a subject by a certain age or at the end of a school grade level. This page contains a list of standards for a specific content area, grade level, and/or course. The list of standards may be structured using categories and sub-categories.

Seeing Structure in Expressions

Interpret the structure of expressions
Interpret expressions that represent a quantity in terms of its context.*
     There are 2 components within this standard.
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
Write expressions in equivalent forms to solve problems
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*
     There are 3 components within this standard.
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

Arithmetic with Polynomials and Rational Functions

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
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
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined
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 +
(+) 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
Rewrite rational functions
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
(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication,

Creating Equations

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,
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V

Reasoning with Equations and Inequalities

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
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Solve equations and inequalities in one variable
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Solve quadratic equations in one variable.
     There are 2 components within this standard.
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
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find
(+) Represent a system of linear equations as a single matrix equation in a vector variable.
(+) 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 x 3
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
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and
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