*The Calculus Bible* is a guide to the Advanced Placement tests in AB and BC Calculus. It can serve as a review packet before quizzes or tests and is also a great review of the entire year's matieral before the AP.

Combined, the two cover:

- functions (domain, range, asymptotes, and fundamental properties)
- graphs you must know
- the derivative (definition, formulas, theorems, etc.)
- applications of the derivative (slope of a curve, slope of the normal line, curve sketching, max-min word problems, related rates, motion along a line, etc.)
- antiderivatives (the definition and applications)
- techniques of integration (including u-substituion, the inverse chain rule, and integration by parts)
- approximations of the definite integral
- the definite integral as area
- applications of the integral (motion along a line, mean value of a function, area between two curves, and volume of a solid of revolution)
- advanced techniques of integration (reduction formulas, power formualas, etc.)
- trigonometric substitutions
- partial fractions
- improper integrals
- further applications of the definite integral (volumes of known cross-sections, length of a plane curve, and work)
- parametrically-defined equations (definition, derivative, and length of the plane curve)
- polar functions (lines, circles, and rectangular hyperbolas)
- limacons
- lemniscates
- spirals
- roses
- sequences and series (convergence and tests for convergence)
- function approximations by infinite series