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Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. Answers to all of your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. They're perfect for undergraduate and graduate studies.
This highly useful reference provides thorough coverage of first-year college math, including algebraic, trigonometric, exponential, and logarithmic functions and their graphs. Includes solutions of linear and quadratic equations, analytic geometry, elementary statistics, differentiation and integration, determinants, matrices, and systems of equations. Problem-solving strategies are included at the beginning of every chapter for each topic covered.
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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 ContentsChapter 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
24 VECTORS, MATRICES AND DETERMINANTS
25 DETERMINANTS, MATRICES AND
SYSTEMS OF EQUATIONS
26 PARTIAL FRACTIONS
SECTION 2: PLANE TRIGONOMETRY
28 ANGLES AND ARCS
29 DEFINITIONS OF THE
30 TABLES AND LOGARITHMS OF THE
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
SECTION 3: ANALYTIC GEOMETRY
39 STRAIGHT LINES AND FAMILIES
OF STRAIGHT LINES
44 TRANSFORMATION OF COORDINATES
45 POLAR COORDINATES
46 PARAMETRIC EQUATIONS
47 SPACE-RELATED PROBLEMS
SECTION 4: INTRODUCTION TO CALCULUS
50 D - FUNCTION
51 THE DERIVATIVE
52 DIFFERENTIATION OF ALGEBRAIC FUNCTIONS
55 ELEMENTARY STATISTICS