Pre-Calculus Problem Solver

Pre-Calculus Problem Solver

by The Editors of REA, Dennis C. Smolarski, Rea

Paperback(REV)

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Product Details

ISBN-13: 9780878915569
Publisher: Research & Education Association
Publication date: 10/28/1984
Series: Problem Solvers Solution Guides
Edition description: REV
Pages: 1104
Product dimensions: 6.66(w) x 9.98(h) x 1.85(d)
Age Range: 16 Years

About the Author

Dennis Smolarski, Ph.D., is associate professor of mathematics at Santa Clara University, Santa Clara, CA.

Founded in 1959, Research & Education Association is dedicated to producing the finest and most effective digital and print materials in educational publishing, including some of America’s most popular test preps and study aids. REA’s wide-ranging catalog is a leading resource for teachers, students, and professionals.

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HOW TO USE THIS BOOK

This book can be an invaluable aid to students in pre-calculus as a supplement to their textbooks. The book is subdivided into 55 chapters, each dealing with a separate topic. The subject matter is developed beginning with algebraic, trigonmetric, exponential, logarithmic functions and their graphs and extends through linear and quadratic equations, analytic geometry, elementary statistics, differentiation and integration, determinants, matrices, and systems of equations. An extensive number of applications have been included, since these appear to be most troublesome to students.

Each chapter in the book begins with a section entitled "Basic Attacks and Strategies for Solving Problems in this Chapter." This section explains the principles which are applicable to the topics in the chapter. By reviewing these principles, the student can acquire a good grasp of the underlying techniques and strategies through which problems related to the chapter may be solved.

HOW TO LEARN AND UNDERSTAND
A TOPIC THOROUGHLY

1. Refer to your class text and read the section pertaining to the topic. You should become acquainted with the principles discussed there. These principles, however, may not be clear to you at the time.

2. Then locate the topic you are looking for by referring to the "Table of Contents" in the front of this book. After turning to the appropriate chapter, read the section "Basic Attacks and Strategies for Solving Problems in this Chapter." This section is a review of the important principles related to the chapter, and it will help you to understand further how and why problems in the chapter are solved in the manner shown.

3. Turn to the page where the topic begins and review the problems under each topic, in the order given. For each topic, the problems are arranged in order of complexity, from the simplest to the more difficult. Some problems may appear similar to others, but each problem has been selected to illustrate a different point or solution method.

Table of Contents

Chapter No. Page No.

SECTION 1: ALGEBRA

1 THE NUMBER SYSTEM

2 DEFINITIONS AND NOTATION OF SETS
  AND SET OPERATIONS

3 FUNDAMENTAL ALGEBRAIC LAWS AND
  OPERATIONS WITH NUMBERS

4 FUNDAMENTAL ALGEBRAIC LAWS AND
  OPERATIONS WITH ALGEBRAIC EXPRESSIONS

5 FACTORING EXPRESSIONS

6 EXPONENT, RADICAL AND POWER

7 FUNCTIONS AND GRAPHS

8 RATIOS, PROPORTIONS AND VARIATIONS

9 EQUATIONS AND GRAPHS

10 LINEAR FUNCTIONS AND EQUATIONS

11 SYSTEMS OF LINEAR EQUATIONS

12 QUADRATIC FUNCTIONS AND GRAPHS

13 QUADRATIC EQUATIONS AND SYSTEMS OF
  EQUATIONS INVOLVING QUADRATICS

14 EQUATIONS OF DEGREE GREATER THAN 2

15 THEORY OF EQUATIONS

16 INEQUALITIES AND GRAPHS

17 PROGRESSIONS AND SEQUENCES

18 MATHEMATICAL INDUCTION

19 THE BINOMIAL THEOREM

20 LOGARITHMS AND EXPONENTIALS

21 PERMUTATIONS

22 COMBINATIONS

23 PROBABILITY

24 VECTORS, MATRICES AND DETERMINANTS

25 DETERMINANTS, MATRICES AND
  SYSTEMS OF EQUATIONS

26 PARTIAL FRACTIONS

27 SERIES

SECTION 2: PLANE TRIGONOMETRY

28 ANGLES AND ARCS

29 DEFINITIONS OF THE
  TRIGONOMETRIC FUNCTIONS

30 TABLES AND LOGARITHMS OF THE
  TRIGONOMETRIC FUNCTIONS

31 PROPERTIES, GRAPHS AND SPECIAL VALUES
  OF TRIGONOMETRIC FUNCTIONS

32 TRIGONOMETRIC IDENTITIES AND FORMULAS

33 SOLVING TRIANGLES

34 INVERSE TRIGONOMETRIC FUNCTIONS

35 TRIGONOMETRIC EQUATIONS

36 COMPLEX NUMBERS

37 THE HYPERBOLIC AND INVERSE
  HYPERBOLIC FUNCTIONS

SECTION 3: ANALYTIC GEOMETRY

38 COORDINATES

39 STRAIGHT LINES AND FAMILIES
  OF STRAIGHT LINES

40 CIRCLES

41 PARABOLAS

42 ELLIPSES

43 HYPERBOLAS

44 TRANSFORMATION OF COORDINATES

45 POLAR COORDINATES

46 PARAMETRIC EQUATIONS

47 SPACE-RELATED PROBLEMS

SECTION 4: INTRODUCTION TO CALCULUS

48 LIMITS

49 CONTINUITY

50 D - FUNCTION

51 THE DERIVATIVE

52 DIFFERENTIATION OF ALGEBRAIC FUNCTIONS

53 APPLICATIONS

54 INTEGRAL

SECTION 5

55 ELEMENTARY STATISTICS

  INDEX

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