PDF First Edition Qishen Huang, Ph.D.
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SAT /ACT Math
And Beyond: Problems Book
A Standard High School Workbook
First Edition
Qishen Huang, Ph.D.
This book helps you
Score highly on SAT/ACT Math section,
Get ready for Calculus course, and
Win in high school math contests.
ISBN-10: 0-9819072-0-2
ISBN-13: 978-0-9819072-0-8
c Copyright 2008 by Qishen Huang.
It is unlawful for anyone to incorporate any part of the content into his works without the author's permission. Questions for the author should be sent to GoodMathBook@.
Limit of Liability/Disclaimer of Warranty: The author makes no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaims any implied warranties of anything for a particular purpose. The author shall not be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
ACT is a registered trademark of ACT, Inc. SAT is a registered trademark of the College Entrance Examination Board. Both companies were not involved in the creation and marketing of the book.
ISBN-10: 0-9819072-0-2 ISBN-13: 978-0-9819072-0-8
10900 Stonecutter Place, Gaithersburg, MD 20878-4805, USA.
c Qishen Huang
2
Preface
I performed most of groundwork for this workbook while my oldest son was in high school. With the book, I have three relevant goals for him.
1. To get a perfect or near perfect score on the SAT Math section. It is getting harder for high school students to gain acceptance to a decent college these days because of the large number of applicants across the country. Students can read the article Applications to Colleges Are Breaking Records by Karen W. Arenson dated January 17, 2008 in The New York Times. A top math score gives students an edge against competition.
2. To build a solid foundation for college level math. With the growing number of problems that need to be solved by advancements in science and technology, current and future generations cannot afford to have a weak foundation in mathematics. Johns Hopkins University Mathematics Professor W. Stephen Wilson gave his 2006 calculus class the same test his 1989 class had taken, and the 2006 students were wiped out by the old class. A stitch in time saves nine.
3. To be competitive internationally in math. According to the article U.S. Leaders Fret Over Students' Math and Science Weaknesses by Vaishali Honawar of Education Week, US high school students had lower math score than any other developed country. Rep. Vernon Ehlers of Michigan declares it a steadily worsening crisis. Central to the crisis is a popular culture that doesn't value math and science.
This problems book will be updated from time to time. A detailed Solutions Manual is available. Relevant inquires should be sent to GoodMathBook@..
c Qishen Huang
3
Contents
1 Tips on Math Homework
1
2 Algebraic Expressions: Basic
3
3 Algebraic Expressions: Intermediate
7
4 Rational Expressions
9
5 Linear Relations: Basic
13
6 Linear Relations: Intermediate
18
7 Linear Relations: Advanced
21
8 Word Problems: Basic
23
9 Word Problems: Intermediate
25
10 Word Problems: Advanced
27
11 Geometry: Basic
29
12 Geometry: Intermediate
34
13 Geometry: Advanced
39
14 Radicals
44
15 Exponentials: Basic
47
16 Exponentials: Intermediate
52
17 Exponentials: Advanced
54
18 General Functions
57
c Qishen Huang
4
CONTENTS
19 Inverse Functions 20 Quadratic Functions: Basic 21 Quadratic Functions: Intermediate 22 Quadratic Functions: Advanced 23 Polynomial and Rational Functions 24 Radical Equations and Functions 25 Circles 26 Ellipses 27 Hyperbolas 28 Sequences: Basic 29 Sequences: Intermediate 30 Sequences: Advanced 31 Trigonometry: Basic 32 Trigonometry: Intermediate 33 Trigonometry: Advanced 34 Complex Numbers 35 Vectors and Matrices 36 Parameterized Equations 37 Polar Coordinates 38 Statistics 39 Limits
c Qishen Huang
CONTENTS
60 62 66 68 70 74 76 79 82 86 91 93 94 103 106 109 111 114 116 118 122
5
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