New SA Created for the SAT - Glassboro Public Schools

Created for the New SAT Exam!

3 Full-Length Practice Tests 20 Chapter Tests Definitions, Theorems, and Key Formulas Hundreds of Examples and Exercises

*SAT is a registered trademark of the College Entrance Examination Board, which is not affiliated with this book

Acing

the

New

SAT

Math

PDF

Acing the New SAT Math

by Thomas Hyun

GREENHALL PUBLISHING

THOUSAND OAKS, CA

Copyright ? 2016 by Greenhall Publishing All rights reserved. No part of this book may be used or reproduced in any manner without the written permission of the publisher.

This edition published by Greenhall Publishing Greenhall Publishing Thousand Oaks, CA 91358 http:// Written by Thomas Hyun Cover design by Hespenheide Design Printed in the United States of America

ISBN-10: 0-9754753-6-3 ISBN-13: 978-0-9754753-6-2

SAT is a registered trademark of the College Entrance Examination Board, which is not affiliated with this book.

CONTENTS

To the Students

vi

Part A ? Math Review

I. Heart of Algebra

Chapter 1: The Language and Tools of Algebra

5

1-1 Variables and Expressions

5

1-2 Exponents and Order of Operations

7

1-3 Simplifying Algebraic Expressions

9

1-4 Rational, Irrational, and Decimal

11

Chapter 1 Practice Test

13

Answers and Explanations

15

Chapter 2: Solving Linear Equations

19

2-1 Writing Equations

19

2-2 Solving Equations

21

2-3 Solving Equations with Variables on Both Sides

23

2-4 Equations with No Solution and Identity

25

2-5 Solving for a Specific Variable

27

Chapter 2 Practice Test

29

Answers and Explanations

31

Chapter 3: Functionsand Linear Equations

37

3-1 Relations and Functions

37

3-2 Rate of Change and Slope

40

3-3 Slope-Intercept Form and Point-Slope Form

42

3-4 Parallel and Perpendicular Lines

44

3-5 Solving Systems of Linear Equations

46

3-6 Absolute Value Equations

50

Chapter 3 Practice Test

52

Answers and Explanations

54

Chapter 4: Linear Inequalities and Graphs

61

4-1 Solving Inequalities

61

4-2 Compound and Absolute Value Inequalities

63

4-3 Graphing Inequalities in Two Variables

65

4-4 Graphing Systems of Inequalities

67

Chapter 4 Practice Test

69

Answers and Explanations

71

ii ? Contents

Chapter 5: Word Problems in Real-Life Situation

77

5-1 Solving Word Problems Using Linear Models

77

5-2 Solving Word Problems with Equations

79

5-3 Solving Word Problems Using Systems of Equations

81

5-4 Solving Word Problems Using Inequalities

83

Chapter 5 Practice Test

85

Answers and Explanations

87

II. Statistics and Data Analysis

Chapter 6: Ratios, Rates, and Proportions

95

6-1 Ratios and Rates

95

6-2 Proportions

97

6-3 Ratios, Rates, and Proportions Word Problems

99

Chapter 6 Practice Test

101

Answers and Explanations

103

Chapter 7: Percents

109

7-1 Percent of Change

109

7-2 Percents and Equations

111

7-3 Percent Word Problems

113

Chapter 7 Practice Test

115

Answers and Explanations

117

Chapter 8: Statistics

121

8-1 Mean, Median, Mode, and Range

121

8-2 Standard Deviation

123

8-3 Graphical Displays

125

8-4 Scatter Plots

127

8-5 Populations, Samples, and Random Selection

129

Chapter 8 Practice Test

131

Answers and Explanations

133

Chapter 9: Categorical Data and Probability

139

9-1 Permutations and Combinations

139

9-2 Rules of Probability

141

9-3 Categorical Data and Conditional Probabilities

143

Chapter 9 Practice Test

145

Answers and Explanations

147

III. Advanced Math

Chapter 10: Law of Exponents and Polynomials

10-1 Laws of Exponents and Scientific Notation 10-2 Adding, Subtracting, Multiplying, and Dividing Polynomials 10-3 FOIL Method and Special Products 10-4 Prime Factorization, GCF, and LCM 10-5 Factoring Using the Distributive Property

Chapter 10 Practice Test Answers and Explanations

Chapter 11: Quadratic Functions

11-1 Graphs of Quadratic Equations 11-2 Factoring Trinomials 11-3 Factoring Differences of Squares and Perfect Square Trinomials 11-4 Solving Quadratic Equations by Completing the Square 11-5 Quadratic Formula and the Discriminant 11-6 Solving Systems Consisting Linear and Quadratic Equations

Chapter 11 Practice Test Answers and Explanations

Chapter 12: Composition, Recursion, and Exponential Functions

12-1 Composition of Functions 12-2 Recursive Formula 12-3 Exponential Functions and Graphs 12-4 Exponential Growth and Decay

Chapter 12 Practice Test Answers and Explanations

Chapter 13: Polynomial and Radical Functions

13-1 Polynomial Functions and Their Graphs 13-2 Remainder Theorem and Factor Theorem 13-3 Radical Expressions 13-4 Solving Radical Equations 13-5 Complex Numbers

Chapter 13 Practice Test Answers and Explanations

Contents ? iii

153 153 156 159 161 164 166 168

173 173 176 179 181 183 186 188 190

197 197 199 201 203 205 207

213 213 215 217 220 222 225 227

iv ? Contents

Chapter 14: Rational Expressions

233

14-1 Rational Expressions

233

14-2 Solving Rational Equations

236

14-3 Direct, Inverse, and Joint Variation

238

14-4 Solving Word Problems Using Rational Equations

240

Chapter 14 Practice Test

242

Answers and Explanations

244

Chapter 15: Trigonometric Functions

251

15-1 Trigonometric Ratios of Acute Angles

251

15-2 The Radian Measure of an Angle

253

15-3 Trigonometric Functions of General Angles and the Unit Circle

255

Chapter 15 Practice Test

259

Answers and Explanations

261

IV. Geometry

Chapter 16: Lines and Angles

267

16-1 Lines, Segments, and Rays

267

16-2 Angles

269

16-3 Parallel and Perpendicular Lines

271

Chapter 16 Practice Test

273

Answers and Explanations to Exercises and Practice Test

275

Chapter 17: Triangles

279

17-1 Angles of a Triangles

279

17-2 Pythagorean Theorem and Special Right Triangles

281

17-3 Similar Triangles and Proportional Parts

283

17-4 Area of a Triangle

285

Chapter 17 Practice Test

287

Answers and Explanations

289

Chapter 18: Polygons

295

18-1 Parallelograms

295

18-2 Rectangles, Squares, and Trapezoids

297

18-3 Regular Polygons

299

Chapter 18 Practice Test

301

Answers and Explanations

303

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download