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
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