CliffsNotes Algebra I Common Core Quick Review

by Kimberly Gores M.A.T.

Overview

A quick in, quick out review of Algebra I Common Core math

Relevant to high school students enrolled in their Algebra I class in those states adhering to the Common Core math standards, this quick review provides targeted chapter-level reviews of topics aligned to the Algebra I Common Core math standards, with practice problems throughout each review chapter and chapter-end quizzes.

This quick review is supplemented with 300+ multiple-choice questions available on CliffsNotes.com.

Product Details

ISBN-13:	9780544734104
Publisher:	Cliffs Notes Inc.
Publication date:	10/25/2016
Edition description:	First Edition, New edition
Pages:	288
Product dimensions:	5.30(w) x 7.60(h) x 0.80(d)

About the Author

KIMBERLY GORES, M.A.T., has been a mathematics educator and researcher for over 15 years. Gores has taught introductory and advanced algebra and mathematics classes at middle school, high school, and college levels. She is currently a math teacher at Coeur d’Alene High School, Idaho.

Table of Contents

Introduction 1

Common Core Slate Standards for Mathematics (CCSSM) 1

Connecting to Common Core Mathematics 2

Why You Need This Book 3

How to Use This Book 3

Hundreds of Practice Questions Online! 4

Chapter 1 Foundations for Understanding Algebra 5

Foundations for Understanding Numbers 6

Real numbers and the number system 6

Ways to show multiplication expressions 7

Common math symbols 8

Properties of Basic Mathematical Operations and Algebraic Thinking 9

Some properties of addition 10

Some properties of multiplication 11

The distributive property 12

Multiplying and dividing using zero 13

Powers and Exponents 14

Squares and cubes 15

Properties of exponents 16

Square Roots and Cube Roots 17

Square roots 17

Cube roots 17

Approximating square roots 18

Simplifying square roots 19

Evaluating Numerical Expressions with Grouping Symbols 21

Parentheses () 21

Brackets [ ] and braces {} 21

Order of operations 22

Divisibility Rules 23

Signed Numbers (Positive Numbers and Negative Numbers) 24

Number lines 24

Absolute Value 24

Addition of signed numbers 25

Subtraction of signed numbers 26

Minus sign preceding parenthesis 27

Multiplying and dividing signed numbers 27

Fractions 28

Negative fractions 28

Adding and subtracting fractions 28

Multiplying fractions 29

Simplifying (reducing) fractions 30

Multiplying mixed numbers 30

Dividing fractions 31

Dividing complex fractions 31

Dividing mixed numbers 32

Simplifying fractions and complex fractions 32

Decimals 33

Converting terminating decimals to fractions 33

Converting fractions to decimals 34

Converting repeating decimals to fractions 34

Percents, Fractions, and Proportions 36

Percents 36

Converting decimals to percents 37

Converting percents to decimals 37

Converting fractions to percents 38

Converting percents to fractions 39

Finding the percent of a quantity 40

Other applications of percent 41

Scientific Notation 43

Multiplication in scientific notation 44

Division in scientific notation 45

Chapter 2 Structure in Algebraic Expressions 51

Set Theory 51

Special sets 52

Types of sets 52

Describing sets 52

Comparing sets 54

Complement of a set 54

Operations with sets 54

Structure of Algebraic Expressions 55

Key words for operations 56

Evaluating Expressions 57

Chapter 3 Equations with One Variable 62

Equations 63

Properties of equality 63

Creating and solving equations 64

Literal equations 69

Ratios and Proportions 72

Ratios 72

Proportions 73

Solving proportions for value 74

Chapter 4 Equations with Two Variables 80

Solving Systems of Equations (Simultaneous Equations) 80

Elimination method 81

Substitution method 86

Graphing method 88

Chapter 5 Monomials, Polynomials, and Factoring 97

Monomials 97

Adding and subtracting monomials 98

Multiplying monomials 99

Dividing monomials 100

Working with negative exponents 101

Polynomials 101

Adding and subtracting polynomials 102

Multiplying polynomials 103

Dividing polynomials by monomials 105

Dividing polynomials by polynomials 105

Factoring 108

Factoring a monomial from a polynomial 109

Factoring the difference between two squares 109

Factoring trinomials of the form ax² + bx + c 109

Factoring by grouping 115

Summary of the factoring methods 117

Chapter 6 Rational Expressions 121

Operations with Rational Expressions 122

Simplifying rational expressions 122

Multiplying rational expressions 123

Dividing rational expressions 124

Adding or subtracting rational expressions 124

Chapter 7 Inequalities, Graphing, and Absolute Value 131

Inequalities 131

Axioms and properties of inequality 132

Solving inequalities 133

Graphing on a Number Line 135

Graphing inequalities 135

Interval 136

Absolute Value 138

Solving equations containing an absolute value 138

Solving inequalities containing an absolute value and graphing 140

Chapter 8 Coordinate Geometry 144

The Coordinate Plane 145

Graphing equations on the coordinate plane 147

Slope and Intercept of Linear Equations 151

Vertical and horizontal lines 155

Graphing linear equations using slope and intercept 156

Writing linear equations 159

Linear Inequalities and Half-Planes 164

Open half-plane 165

Closed half-plane 166

Chapter 9 Functions and Variations 173

Relations 174

Functions 174

Domain and range 174

Defining a Function 175

Vertical line test 177

Determining domain, range, and if the relation is a function 178

Evaluating functions 179

Variations 181

Direct variation 181

Inverse variation (indirect variation) 183

Chapter 10 Simplifying Radicals 189

Simplifying Square Roots 189

Operations with Square Roots 191

Under a single radical sign 191

When radical values are alike 191

When radical values are different 192

Addition and subtraction of square roots after simplifying 192

Products of nonnegative square roots 193

Quotients of nonnegative square roots 194

Chapter 11 Quadratic Equations 198

Solving Quadratic Equations 198

Factoring 199

The quadratic formula 202

Completing the square 206

Chapter 12 Application Problems 212

Problem-Solving Techniques 214

Key Words and Phrases 215

Simple Interest 216

Compound Interest 217

Ratio and Proportion 219

Percent 220

Percent Change 221

Number Problems 222

Absolute Value and Inequality Problems 224

Age Problems 226

Motion Problems 227

Coin Problems 229

Mixture Problems 231

Work Problems 232

Number Problems with Two Variables 233

Review Questions 239

Glossary 267

Index 274