Practice Makes Perfect: Algebra I Review and Workbook, Third Edition

by Carolyn Wheater

Overview

The ideal study guide for success in Algebra I—with updated review and hundreds of practice questions

Practice makes perfect—and this study guide gives you all the practice you need to gain mastery over Algebra I. Whether you’re a high school or college student, or a self-studying adult, the hundreds of exercises in Practice Makes Perfect: Algebra I Review and Workbook, Third Edition will help you become comfortable, and ultimately gain confidence with the material.

Written by an expert algebra educator with decades of experience, this updated edition of Practice Makes Perfect: Algebra I Review and Workbook features the latest strategies and lesson instruction in an accessible format, with thorough review followed immediately by a variety of practice questions. Covering all the essential algebra topics, this book will give you everything you need to help with your schoolwork, exams, and everyday life!

Features:

• The most updated Algebra I lesson instruction and practice questions
• Use of the latest question types and Algebra strategies
• More than 900 practice exercises to reinforce Algebra I concepts
• Coverage of all the most important Algebra topics, from linear equations to solving word problems
• Answer Key to help check your work
• Lessons presented in an easy-to-use format, with review followed by lots of practice

Product Details

ISBN-13:	9781264285778
Publisher:	McGraw Hill LLC
Publication date:	05/13/2022
Edition description:	3rd ed.
Pages:	240
Sales rank:	990,802
Product dimensions:	8.40(w) x 10.80(h) x 0.50(d)

About the Author

Carolyn Wheater teaches middle school and upper school mathematics at the Nightingale-Bamford School in New York City. Educated at Marymount Manhattan College and the University of Massachusetts, Amherst, she has taught math and computer technology for 30 years, and is a member of the National Council of Teachers of Mathematics (NCTM) and the Association of Teachers in Independent Schools.

Table of Contents

Introduction ix

1 Arithmetic to algebra 1

The real numbers 1

Properties of real numbers 2

Integers 4

Order of operations 7

Using variables 7

Evaluating expressions 9

Calculator notes #1 9

2 Equations with one variable 11

Addition and subtraction equations 11

Multiplication and division equations 12

Two-step equations 13

Variables on both sides 13

Simplifying before solving 14

Putting equations to work 15

Calculator notes #2 17

3 Problems solved with equations 19

Mixture problems 19

Percentage problems 22

Perimeter problems 23

Consecutive integer problems 23

4 Functions 25

Domain and range 26

Another way to represent relations and functions 27

Vertical line test 28

Function notation 31

Evaluating functions 31

Working backwards 32

Restricting domains 33

5 Coordinate graphing 35

The coordinate plane 35

Distance 36

Midpoints 38

Graphing equations 38

Slope and rate of change 40

Vertical and horizontal lines 43

Writing linear equations 44

Parallel and perpendicular lines 45

Calculator notes #3 46

6 Absolute value 49

Absolute value equations 50

Absolute value functions 51

Graphing absolute value functions 53

7 Inequalities 57

Simple inequalities 57

Compound inequalities 59

Absolute value inequalities 60

Graphing inequalities in two variables 62

8 Systems of linear equations and inequalities 65

Solving systems of equations by graphing 65

Graphing systems of inequalities 66

Solving systems of equations by substitution 68

Solving systems of equations by elimination 69

Elimination with multiplication 70

Dependent and inconsistent systems 71

Problems solved with systems 73

Calculator notes #4 74

9 Powers and polynomials 77

Rules for exponents 77

More rules 79

Monomials and polynomials 80

Adding and subtracting polynomials 81

Multiplying polynomials 82

Dividing polynomials 87

Calculator notes #5 89

10 Factoring 91

Greatest common monomial factor 91

Factoring x² + bx + c 93

Factoring ax² + bx + c 96

Special factoring patterns 98

Factoring by grouping 99

Calculator notes #6 100

11 Radicals 103

Powers and roots 103

Estimating roots 104

Simplifying radical expressions 105

Adding and subtracting radicals 108

Solving radical equations 108

Graphing square root equations 110

12 Quadratic equations and their graphs 111

Solving by square roots 111

Completing the square 112

The quadratic formula 113

Solving by factoring 115

Graphing quadratic functions 116

Problems solved with quadratic equations 118

Calculator notes #7 122

13 Proportion and variation 125

Using ratios and extended ratios 125

Solving proportions 126

Variation 127

Joint and combined variation 129

14 Rational equations and their graphs 131

Simplifying rational expressions 131

Multiplying rational expressions 132

Dividing rational expressions 133

Adding and subtracting rational expressions 134

Complex fractions 135

Solving rational equations 137

Graphing rational functions 140

Problems solved with rational equations 142

Calculator notes #8 145

15 Exponential growth and decay 147

Evaluating exponential functions 149

Compound interest 150

Exponential growth and decay 151

Graphing exponential functions 152

Calculator notes #9 153

16 Matrix algebra 155

Rows and columns 156

Addition and subtraction 157

Scalar multiplication 160

Matrix multiplication 163

Determinants 168

Inverses 169

Solving systems with matrices 172

Calculator notes #10 176

Answers 179