New SA Created for the SAT

1 Acing Acing the New SAT Math Understand the Basic Concepts of Algebra I, II, Geometry, Statistics, and Trigonometry. Learn Problem Solving the Techniques. This book covers all of the math New concepts you need to know for the New SAT, organized in twenty chapters Created by subject, so you can focus on areas you find especially challenging. Important vocabularies, definitions, and formulas are in the beginning of for the each section to teach you as directly New SAT. SAT. and clearly as possible. Accompanying examples and solutions show you how to apply your knowledge. Exam! A set of exercises in each section, and chapter test at the end of each chapter, come 3 Full-Length NEW SAT EXAM! Created FOR THE. with detailed step-by-step solutions. Practice Tests These realistic practice tests give you practical preparation, helping you get comfortable with the New SAT exam.

2 20 Chapter Tests Math Complete answers and explanations help you identify weaknesses and attain maximum benefits out of the practice test. Definitions, Theorems, and Key Formulas Hundreds of Examples and Exercises $ ISBN 978-0-9754753-6-2. * SAT is a registered trademark of the College Entrance Examination Board, which is not affiliated with this book 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.

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.

4 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.

5 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.

6 Chapter 9 Practice Test 145. Answers and Explanations 147. Contents iii III. Advanced Math Chapter 10: Law of Exponents and Polynomials 153. 10-1 Laws of Exponents and Scientific Notation 153. 10-2 Adding, Subtracting, Multiplying, and Dividing Polynomials 156. 10-3 FOIL Method and Special Products 159. 10-4 Prime Factorization, GCF, and LCM 161. 10-5 Factoring Using the Distributive Property 164. Chapter 10 Practice Test 166. Answers and Explanations 168. Chapter 11: Quadratic Functions 173. 11-1 Graphs of Quadratic Equations 173. 11-2 Factoring Trinomials 176. 11-3 Factoring Differences of Squares and Perfect Square Trinomials 179. 11-4 Solving Quadratic Equations by Completing the Square 181. 11-5 Quadratic Formula and the Discriminant 183. 11-6 Solving Systems Consisting Linear and Quadratic Equations 186. Chapter 11 Practice Test 188.

7 Answers and Explanations 190. Chapter 12: Composition, Recursion, and Exponential Functions 197. 12-1 Composition of Functions 197. 12-2 Recursive Formula 199. 12-3 Exponential Functions and Graphs 201. 12-4 Exponential Growth and Decay 203. Chapter 12 Practice Test 205. Answers and Explanations 207. Chapter 13: Polynomial and Radical Functions 213. 13-1 Polynomial Functions and Their Graphs 213. 13-2 Remainder Theorem and Factor Theorem 215. 13-3 Radical Expressions 217. 13-4 Solving Radical Equations 220. 13-5 Complex Numbers 222. Chapter 13 Practice Test 225. Answers and Explanations 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.

8 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.

9 18-2 Rectangles, Squares, and Trapezoids 297. 18-3 Regular Polygons 299. Chapter 18 Practice Test 301. Answers and Explanations 303. Contents v Chapter 19: Circles 309. 19-1 Arcs, Angles, and Tangents 309. 19-2 Arc Lengths and Areas of Sectors 311. 19-3 Inscribed Angles 313. 19-4 Arcs and Chords 315. 19-5 Equations of Circles 317. Chapter 19 Practice Test 319. Answers and Explanations 321. Chapter 20: Surface Areas and Volumes 327. 20-1 Prisms 327. 20-2 Cylinders and Spheres 329. 20-3 Pyramids and Cones 331. Chapter 20 Practice Test 333. Answers and Explanations 335. Part B Practice Tests PSAT 10 Practice Test 341. Answers and Explanations 360. SAT Practice Test 1 367. Answers and Explanations 388. SAT Practice Test 2 399. Answers and Explanations 421. vi To the Students To the Students . If you're reading this, you are on your way to a better score on the New SAT math!

10 Below are guidelines for getting the most out of this book, as well as information about changes to the math section of the New SAT. Using this Book This book helps students review and master mathematical concepts in the most concise and straightforward manner possible. Each of the twenty chapters in this book teaches a particular group of mathematical concepts you need to know for the New SAT. Each chapter contains lessons that convey key concepts along with illustrations and diagrams. Important vocabularies are printed in boldface. Next to the key terms and illustrations, you will find examples, with complete solutions, that apply the application of the concepts you have just learned. Keep a pencil and sheet of paper handy. Follow along, working out the sample questions yourself this will help you later in solving the practice problems.