Contents

Introduction

1      Arithmetic to algebra

The real numbers

Properties of real numbers

Integers

Order of operations

Using variables

Evaluating expressions

Calculator notes #1

2      Linear equations

Addition and subtraction equations

Multiplication and division equations

Two-step equations

Variables on both sides

Simplifying before solving

Absolute value equations

Mixture problems: coffee, coins, and cars

Calculator notes #2

3      Linear inequalities

Simple inequalities

Compound inequalities

Absolute value inequalities

4      Coordinate graphing

The coordinate plane

Distance

Midpoints

Slope and rate of change

Graphing linear equations

Vertical and horizontal lines

Graphing linear inequalities

Graphing absolute value equations

Writing linear equations

Parallel and perpendicular lines

Calculator notes #3

5      Systems of linear equations and inequalities

Graphing systems of equations

Graphing systems of inequalities

Solving systems of equations by substitution

Solving systems of equations by combination

Combinations with multiplication

Dependent and inconsistent systems

Calculator notes #4

6      Powers and polynomials

Rules for exponents

More rules

Monomials and polynomials

Adding and subtracting polynomials

Multiplying polynomials

Dividing polynomials

Calculator notes #5

7      Factoring

Greatest common monomial factor

Factoring x2 + bx + c

Factoring ax2 + bx + c

Special factoring patterns

Factoring by grouping

Calculator notes #6

8      Radicals

Powers and roots

Estimating roots

Simplifying radical expressions

Adding and subtracting radicals

Solving radical equations

Graphing square root equations

9      Quadratic equations and their graphs

Solving by square roots

Completing the square

The quadratic formula

Solving by factoring

Graphing quadratic functions

Calculator notes #7

10   Proportion and variation

Using ratios and extended ratios

Solving proportions

Variation

Joint and combined variation

11   Rational equations and their graphs

Simplifying rational expressions

Multiplying rational expressions

Dividing rational expressions

Adding and subtracting rational expressions

Complex fractions

Solving rational equations

Graphing rational functions

Calculator notes #8

12   Exponential growth and decay

Evaluating exponential functions 107

Compound interest

Exponential growth and decay

Graphing the exponential functions

Calculator notes #9

13   Matrix algebra

Rows and columns

Addition and subtraction

Scalar multiplication

Matrix multiplication

Determinants

Inverses

Solving systems with matrices

Calculator notes #10

14   Problem solving

General strategies

Problems solved with linear equations

Problems solved with quadratic equations

Problems solved with rational equations

Problems solved with systems

Answers