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
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Calculus Topic: Circles, Parabolas, etc.
2. Completing the Square
Completing the square in one and two variables
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Calculus Topic: Equations
3. Solving Equations
Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property
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Calculus Topic: Functions and Graphs
4. Functions and Their Graphs
Introduction, equations of lines, power functions, shifting graphs, intersection of curves
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Calculus Topic: Limits
5. Changing the Form of a Function
Factoring, canceling, long division, rationalizing, extracting a factor from under a radical
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Calculus Topic: Derivatives
6. Simplifying Algebraic Expressions
Working with difference quotients and rational functions, canceling common factors, rationalizing expressions
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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
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Calculus Topic: The Chain Rule
8. Composition and Decomposition of Functions
Composite functions, inner, outer, and outermost functions, decomposing composite functions
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Calculus Topic: Implicit Differentiation
9. Equations of Degree 1 Revisited
Solving linear equations involving derivatives
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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
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Calculus Topic: Integrating Trigonometric Functions
11. Trigonometric Identities
Rewriting trigonometric expressions using identities
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Appendices
A. Exponential Functions
B. Inverse Functions
C. Logarithmic Functions
D. Inverse Trigonometric Functions
E. The Binomial Theorem
E. Derivation of the Quadratic Formula
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Answers to Exercises
Index