1. Numbers and Their Disguises.
Brackets, multiplying and dividing fractions, adding and subtracting fractions, exponents, roots, percent, scientific notation, calculators, rounding, intervals.
2. Completing the Square.
Completing the square in one and two variables.
3. Solving Equations.
Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property.
4. Functions and Their Graphs.
Introduction, equations of lines, power functions, shifting graphs, intersection of curves.
5. Changing the Form of a Function.
Factoring, canceling, long division, rationalizing, extracting a factor from under a radical.
6. Simplifying Algebraic Expressions.
Working with difference quotients and rational functions, canceling common factors, rationalizing expressions.
7. Cyclic Phenomena: The Six Basic Trigonometric Functions.
Angles, definitions of the six trigonometric functions, special angles, graphs involving sin x and cos x.
8. Composition and Decomposition of Functions.
Composite functions, inner, outer, and outermost functions, decomposing composite functions.
9. Equations of Degree 1 Revisited.
Solving linear equations involving derivatives.
10. Word Problems.
Algebraic word problems; the geometry of rectangles, circles and spheres, trigonometric word problems, right angle triangles, the law of sines and the law of cosines.
11. Trigonometric Identities.
Rewriting trigonometric expressions using identities.
Appendices.
A. Exponential Functions.
B. Inverse Functions.
C. Logarithmic Functions.
D. The Binomial Theorem.
E. Derivation of the Quadratic Formula.
Answers to Exercises.
Index.
