Algebra

Concept Map

Concepts
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Real Numbers, Variables, and Expressions

The Real Numbers

The Evolution of Number System

Order Real Numbers

Roman Numerals

Integers

Absolute Value of Integers

Integer Addition

Integer Subtraction

Integer Multiplication

Integer Division

The Order of Operations

Order of Operations

PEMDAS in Numerical Expressions

Algebra Expressions with Exponents

Algebra Expressions with Fraction Bars

Order of Operations and Variable Substitution

Algebra Expressions and Variables

Expressions and Variables

Evaluate Single Variable Expressions

Evaluate Expressions with One or More Variables

Words that Describe Mathematical Operations

Translate Between English Phrases and Algebraic Expressions

Equivalent Expressions

Calculator Use with Algebra Expressions

Properties and Axioms of Real Numbers

Real Number Properties and Axioms

Distributive Property

Expressions and the Distributive Property

When to Use the Distributive Property

Distributive Property to Evaluate Formulas with Decimals

Additive inverses and Absolute Values

Associative and Commutative Property with Decimals

Associative and Commutative Property with Fractions

Addition and Multiplication Properties with Real Numbers

Applications of the Commutative and Associative Properties of Addition

Applications of the Commutative and Associative Properties of Multiplication

Fraction and Mixed Number Applications

Simplifying Expressions

Simplify Variable Expressions Involving Addition and Subtraction

Simplify Variable Expressions Involving Multiplication and Division

Simplify Variable Expressions Involving Multiple Operations

Simplify Algebraic Expressions

Linear Equations

Basic Equations

Writing Basic Equations

Sentences as Single Variable Equations

Addition and Subtraction Phrases as Equations

Multiplication and Division Phrases as Equations

Independent and Dependent Variables

Input-Output Tables

Function Rules for Input-Output Tables

Input-Output Tables for Function Rules

One-Step Equations and the Properties of Equality

One-Step Equations and Properties of Equality

Single Variable Equations with Addition and Subtraction

Properties of Equality with Fractions

Single Variable Equations with Multiplication and Division

Properties of Equality with Decimals

Checking Solutions to Equations

Solve Two-Step Equations

Two-Step Equations

Two-Step Equations from Verbal Models

Two-Step Equations with Addition and Multiplication

Two-Step Equations with Addition and Division

Two-Step Equations with Subtraction and Multiplication

Two-Step Equations with Subtraction and Division

Applications of Two-Step Equations

Solve Multi-Step Equations

Multi-Step Equations

Multi-Step Equations with Like Terms and Distribution

Multi-Step Equations with Fractions

Multi-Step Equations with Decimals

Multi-Step Equations with Decimals, Fractions, and Parentheses

Applications of Multi-Step Equations

Equations with Variables on Both Sides

Determining the Number of Solutions to a Multi-Step Equation

Solving for a Variable

Absolute Value Equations

Linear Equations in the Real World

Applications of Linear Equations

Problem-Solving Models

Guess and Check, Work Backward

Cryptarithms

Applications Using Linear Models

Distance, Rate, and Time

D = RT

Solving for Elapsed Time Related to Rate

Finding the Total Time Given a Distance between Two Objects

Applications of Finding Time Using Multiple Steps

Finding Total Distance Using Multiple Steps Word Problems

Find the Rate, Given Time and Distance

Solving Length and Distance Problems Involving Time

Linear Inequalities

Solve One Step Linear Inequalities

Inequalities on a Number Line

Inequalities that Describe Patterns

Inequality Expressions

Inequalities with Addition and Subtraction

Inequalities with Multiplication and Division

Multi-Step Inequalities

Two-Step Inequality Expressions

Two-Step Inequalities

Applications of Two-Step Inequalities

Checking Solutions to Inequalities

Compound Inequalities

Write Compound Inequalities

Graph and Solve Absolute Value Inequalities

Intervals and Interval Notation

Applications with Inequalities

Graphs and Functions

Graphing in the Coordinate Plane

Graphs in the Coordinate Plane

Points in the Coordinate Plane

Ordered Pairs in Four Quadrants

Symmetry on the Coordinate Plane

Plotting Figures in the Coordinate Plane

Coordinate Locations on a Map

Functions on a Coordinate Plane

Graphs Based on Rules

Rules Based on Graphs

Understand Representations of Functions

Compare Representations of Functions

Real Functions

Graphs of Inequalities in One Variable

Graphs of Inequalities in Two Variables

Identify Types of Linear and Nonlinear Graphs

Function Families

Classes of Functions

Functions and Function Notation

Function Notation

Domain and Range of a Function

Applications of Functions

Identify Functions and the Vertical Line Test

Even and Odd Functions and Function Symmetry

Operations on Functions

Composition of Functions

Graph Linear Equations in Two Variables

Graph of a Linear Equation in Two Variables

Graphs of Linear Equations

Horizontal and Vertical Line Graphs

Graph Using Intercepts

Problem Solving with Linear Graphs

Linear Functions

Graphs of Absolute Value Equations

Linear and Absolute Value Function Families

Interpreting Linear Models

Function Transformations

Overview of Function Transformations

Vertical and Horizontal Transformations

Stretching and Reflecting Transformations

Combining Transformations

Notation for Transformations

Graphing Slope

Slope

Rates of Change

Comparing Slope and Constant of Proportionality

Slope of a Line Using Two Points

Graph Using Slope-Intercept Form

The Forms of a Linear Equation

Standard Form of Linear Equations

Slope-Intercept Form of Linear Equations

Two-Point Form of the Equation of a Line

Intercept Form of the Equation of a Line

Normal Form of the Equation of a Line

Distance of a Point from a Line

Point-Slope Form of Linear Equations

Forms of Linear Equations

Parallel and Perpendicular Lines

Equations of Parallel and Perpendicular Lines

Equations of Parallel Lines

Equations of Perpendicular Lines

Families of Lines

Shifting of Origin

The Equation of a Line

Determining the Equation of a Line

Write an Equation Given the Slope and a Point

Write an Equation Given Two Points

Write a Function in Slope-Intercept Form

Fitting Lines to Data

Write Linear Equations to Approximate a Line of Fit

Linear Interpolation and Extrapolation

Applications of Linear Interpolation and Extrapolation

Systems of Equations and Inequalities

Consistent and Inconsistent Linear Systems

Checking a Solution for a Linear System

Understand Solutions of Systems of Linear Equations

Graphs of Linear Systems

Systems of Linear Equations in Two Variables

Solving Linear Systems

Linear Systems by Elimination

Solving Systems by Multiplying One Equation

Solving Systems by Multiplying Both Equations

Linear Systems by Elimination Using Multiplication

Systems Using Substitution

Comparing Methods for Solving Linear Systems

Applications of Linear Systems

Mixture Problems

Systems of Linear Equations in Three Variables

Linear Programming

Solving Systems of Linear Inequalities

Graphs of Systems of Linear Inequalities in Two Variables

Evaluate Solutions for Linear Inequalities in Two Variables

Graphing to Check Solutions to Systems of Linear Inequalities

Systems of Inequalities

Quadratic Inequalities

Polynomial and Rational Inequalities

Polynomials and Factoring

Polynomials

Monomials, Binomials, and Trinomials

Polynomials in Standard Form

Addition and Subtraction of Polynomials

Polynomial Multiplication

Multiply Polynomials by Monomials

Multiply Binomials by Binomials

Multiply Polynomials by Binomials

Multiply Polynomials by Polynomials

Polynomial Factoring

Factoring Polynomials

Monomial Factors of Polynomials

Polynomial Special Products

Special Products of Polynomials

Factor Difference of Squares

Factor Perfect Square Trinomials

Sum and Difference of Cubes

Quadratic Expressions

Factor Quadratics with a Leading Coefficient of 1

Factor Quadratic Expressions with Negative Coefficients

Factor Quadratics

Factor by Grouping

Zero Product Principle

Applications of Factoring

Solve Quadratic Equations

Polynomial Division

Dividing Polynomials

Long Division of Polynomials

Synthetic Division of Polynomials

Find Factors of Polynomials

Finding Zeros of Polynomials

Zeroes and Intercepts of Polynomials

Graphing Polynomials

Identify Parts of Polynomial Graphs

Graphs of Polynomials Using Transformations

Graphs of Polynomials Using Zeros

Graphing Calculator to Analyze Polynomial Functions

Rational Expressions

Working with Rational Expressions

Simplifying Rational Expressions

Excluded Values for Rational Expressions

Restricted Domain and Range

Multiply and Divide Rational Expressions

Products and Quotients of Rational Expressions

Multiplication of Rational Expressions

Division of Rational Expressions

Complex Fractions

Add and Subtract Rational Expressions

Addition and Subtraction of Rational Expressions

Adding and Subtracting Rational Expressions where One Denominator is the LCD

Applications of Adding and Subtracting Rational Expressions

Proportions and Percents

Proportions

Proportions using LCD

Proportions using Cross-Multiplication

Rational Equations and Proportions

Applications of Ratios and Proportions

Multi-Step Proportions

Proportion and Scale

Proportions and Scale

Dimensional Analysis

Applications of Scale and Indirect Measurement

Applications Using Direct Variation

Graphs of Linear Models of Direct Variation

Identifying Proportional Relationships in Graphs

Compare Models of Direct Variation in Different Forms

Compare Direct Variation Models and Linear Models

Inverse Variation and Rational Functions

Direct and Inverse Variation

Inverse Variation Models

Estimate Graphs of Rational Functions

Horizontal and Vertical Asymptotes

Vertical Asymptotes

Horizontal Asymptotes

Oblique Asymptotes

Determining Asymptotes by Division

Inverse Variation Problems

Joint and Combined Variation

Applications Using Rational Equations

Roots and Irrational Numbers

Exponents and Irrational Numbers

Negative and Zero Exponents

Fractional Exponents

Zero, Negative, and Fractional Exponents

Operations with Roots and Irrational Numbers

The Pythagorean Theorem

Pythagorean Theorem and its Converse

Pythagorean Triples

Converse of the Pythagorean Theorem

Solving Equations Using the Pythagorean Theorem

Applications Using the Pythagorean Theorem

Vertical and Horizontal Distance on a Coordinate Plane

Distance Formula

Absolute Value as Distance on the Coordinate Plane

Midpoint Formula

Radical Expressions

Simplify Expressions with Radicals

Multiplication and Division of Radicals

Raising a Product or Quotient to a Power

Addition and Subtraction of Radicals

nth Roots

Radical Equations

Equations with Radicals

Equations with Square Roots

Equations with Radicals on Both Sides

Equations with Variables Under and not Under a Radical

Graphs of Square Root Functions

Shifts of Square Root Functions

Graphing Cube Root Functions

Square and Cube Root Function Families

Applications Using Radicals

Solving Quadratic and Exponential Equations and Functions

Quadratic and Exponential Equations and Functions

Solving Quadratic Equations

Use Square Roots to Solve Quadratic Equations

Square Root Applications

Completing the Square

Completing the Square when the Leading Coefficient Equals 1

Vertex Form of a Quadratic Equation by Completing the Square

Use Graphs and Technology to Solve Quadratic Equations

The Quadratic Formula

The Discriminant

Quadratic Equation Applications

Graphing Quadratic Functions and Equations

Graph Quadratic Functions and Equations

Understand Quadratic Functions

Graphing with the Vertex Form of Quadratic Functions

Graphs of Quadratic Functions in Intercept Form

Roots to Determine a Quadratic Function

Quadratic Functions and Equations

Exponential Functions and Properties of Exponents

Properties of Exponents in Variable Expressions

Exponential Properties Involving Products

Exponential Properties Involving Quotients

Exponential Terms Raised to an Exponent

Exponential Properties in Variable Expressions

Exponential Growth and Decay Functions

Exponential Functions

Solving Equations with Exponents

Exponential Growth and Decay

Exponential Growth

Exponential Decay

Geometric Sequences and Exponential Functions

Graphs of Exponential Functions

Applications of Exponential Functions

Logarithms

Common and Natural Logarithms

Analysis of Logarithmic Graphs

Logarithm Properties

Change of Base

Product and Quotient Properties of Logarithms

Power Property of Logarithms

Inverse Properties of Logarithms

Logistic Functions

Linear, Exponential and Quadratic Models

Identifying Linear, Exponential, and Quadratic Models

Piecewise Function Models

Greatest Integer Functions and Smallest Integer Functions

Linear, Quadratic, and Cubic Models

Cubic Models

Applications of Function Models

Matrices

Matrix Algebra

Introduction to Matrices

Types of Matrices

Addition of Matrices

Adding and Subtracting Matrices

Multiplying Matrices by a Scalar

Matrix Multiplication

Matrix Operations

Transpose of a Matrix

Symmetric and Skew-Symmetric Matrices

Determinants

Properties of Determinants

Cramer's Rule

Area of a Triangle in Determinant Form

Matrix Equations

Solving Matrix Equations

Augmented Matrices

Row Operations and Row Echelon Forms

Writing and Solving a Matrix Equation for a Linear System

Solving Linear Systems Using Matrices and Technology

Inverse Matrices

Applications of Matrices

Partial Fraction Expansions

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