R                    R
               SAT
/ACT
 Math
                 And Beyond: Problems Book
                      AStandard High School Workbook
           First Edition                                 Qishen Huang, Ph.D.
           This book helps you
            √Score highly on SAT/ACT Math section,
            √Getready for Calculus course, and
            √Winin high school math contests.
           ISBN-10: 0-9819072-0-2                 ISBN-13: 978-0-9819072-0-8
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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@Yahoo.com.
          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 Col-
        lege 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.
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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 Weak-
           nesses by Vaishali Honawar of Education Week, US high school students had lower
           math score than any other developed country. Rep. Vernon Ehlers of Michigan de-
           clares 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@Yahoo.com..
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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
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Qishen Huang                              4