Contents 

0. A REVIEW OF BASIC ALGEBRA 

Sets of Real Numbers 

Integer Exponents and Scientific Notation 

Rational Exponents and Radicals 

Polynomials 

Factoring Polynomials 

Algebraic Fractions 

1. EQUATIONS AND INEQUALITIES 

Equations 

Applications of Linear Equations 

Quadratic Equations 

Applications of Quadratic Equations 

Complex Numbers 

Polyomial and Radical Equations 

Inequalities 

Absolute Value 

2. THE RECTANGULAR COORDINATE SYSTEM AND GRAPHS OF EQUATIONS 

The Rectangular Coordinate System 

The Slope of a Nonvertical Line 

Writing Equations of Lines 

Graphs of Equations 

Proportion and Variation 

3. FUNCTIONS 

Functions and Function Notation 

Quadratic Functions 

Polynomial and Other Functions 

Translating and Stretching Graphs 

Rational Functions 

Operations on Functions 

Inverse Functions 

4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS 

Exponential Functions and Their Graphs 

Applications of Exponential Functions 

Logarithmic Functions and Their Graphs 

Applications of Logarithmic Functions 

Properties of Logarithms 

Exponential and Logarithmic Equations 

5. SOLVING POLYNOMIAL EQUATIONS 

The Remainder and Factor Theorems; Synthetic Division 

Descartes' Rule of Signs and Bounds on Roots 

Rational Roots of Polynomial Equations 

Irrational Roots of Polynomial Equations 

6. LINEAR SYSTEMS 

Systems of Linear Equations 

Gaussian Eliminations and Matrix Methods 

Matrix Algebra 

Matrix Inversion 

Determinants 

Partial Fractions 

Graphs of Linear Inequalities 

Linear Programming 

7. CONIC SECTIONS AND QUADRATIC SYSTEMS 

The Circle and the Parabola 

The Ellipse 

The Hyperbola 

Solving Simultaneous SecondDegree Equations 

8. NATURAL NUMBER FUNCTIONS AND PROBABILITY 

The Binomial Theorem 

Sequences, Series, and Summation Notation 

Arithmetic Sequences 

Geometric Sequences 

Mathematical Induction 

Permutations and Combinations 

Probability 

Computation of Compound Probabilities 

Odds and Mathematical Expectation 

9. THE MATHEMATICS OF FINANCE 

Compound Interest 

Annuities and Future Value 

Present Value of an Annuity; Amortization 

Appendix 1: A Proof of the Binomial Theorem 

Appendix 2: Tables 

Table A 

Powers and Roots 

Table B 

Base10 Logarithms 

Table C 

Basee Logarithms 

Appendix 3: Answers to Selected Exercises 

Index 

Index of Applications 
