Calculus Topic: Review of Basics
1. Numbers and Their Disguises
Brackets, multiplying and dividing fractions, adding and subtracting fractions, exponents, roots, percent, scientific notation, calculators, rounding, intervals
Calculus Topic: Circles, Parabolas, etc.
2. Completing the Square
Completing the square in one and two variables
Calculus Topic: Equations
3. Solving Equations
Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property
Calculus Topic: Functions and Graphs
4. Functions and Their Graphs
Introduction, equations of lines, power functions, shifting graphs, intersection of curves
Calculus Topic: Limits
5. Changing the Form of a Function
Factoring, canceling, long division, rationalizing, extracting a factor from under a radical
Calculus Topic: Derivatives
6. Simplifying Algebraic Expressions
Working with difference quotients and rational functions, canceling common factors, rationalizing expressions
Calculus Topic: Derivatives of Trigonometric Functions
7. Cyclic Phenomena: The Six Basic Trigonometric Functions
Angles, definitions of the six trigonometric functions, special angles, graphs involving sin x and cos x, graphs of complex trigonometric functions
Calculus Topic: The Chain Rule
8. Composition and Decomposition of Functions
Composite functions, inner, outer, and outermost functions, decomposing composite functions
Calculus Topic: Implicit Differentiation
9. Equations of Degree 1 Revisited
Solving linear equations involving derivatives
Calculus Topic: Related Rates, Applied Max-Min Problems
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
Calculus Topic: Integrating Trigonometric Functions
11. Trigonometric Identities
Rewriting trigonometric expressions using identities
Appendices
A. Exponential Functions
B. Inverse Functions
C. Logarithmic Functions
D. Inverse Trigonometric Functions
E. The Binomial Theorem
E. Derivation of the Quadratic Formula
Answers to Exercises
Index
