APC Contents
Prerequisites
| Category Title | Problems |
|---|---|
| Solving polynomial inequations algebraically | 22 |
| Solving absolute value equations and inequations algebraically | 20 |
| Trigonometry | 66 |
| Logarithmic and exponential | 24 |
Functions
| Category Title | Problems |
|---|---|
| Solving equations and inequations graphically | 17 |
| Domain and range | 42 |
| Zeros and intercepts | 18 |
| Symmetry, oddness, and evenness | 12 |
| Asymptotes | 24 |
| Composition and inverses | 39 |
| Shifting, scaling, periodicity | 36 |
Graphs and Limits
| Category Title | Problems |
|---|---|
| Estimation of limits from graphs and tables of value | 16 |
| Finding limits | 27 |
| Special limits | 23 |
| One-sided limits | 33 |
| Continuity—including removable, jump, and infinite discontinuities | 7 |
| Limits at positive and negative infinity | 20 |
Derivatives
| Category Title | Problems |
|---|---|
| Definitions (including simple power rule) | 16 |
| Sums and differences | 8 |
| Products and quotients | 13 |
| Compositions, The Chain Rule | 40 |
| Inverse functions | 5 |
| Trigonometric and inverse trigonometric | 30 |
| Exponential and logarithmic | 86 |
| Parametric, polar, and vector functions | 24 |
| Evaluated at a given point | 35 |
| Mean Value Theorem and Rolle's Theorem | 8 |
| Higher order | 27 |
| Indeterminate forms of L'Hopital's Rule | 39 |
| Implicit differentiation | 28 |
Derivatives and Applications
| Category Title | Problems |
|---|---|
| Tangents and normals | 52 |
| Linerarization as approximation, local linearity, differentials | 7 |
| Newton's Method | 22 |
| Monotonocity | 13 |
| Concavity | 23 |
| Global and local extrema | 55 |
| Inflection points | 28 |
| Relating f, f', and f'' | 32 |
| Curve analysis using parametric form | 9 |
| Curve analysis using polar form | 5 |
| Critical value problems and optimization | 35 |
| Related rates | 42 |
| Rate of change—distance, velocity, acceleration | 3 |
Integrals and Integration
| Category Title | Problems |
|---|---|
| Anti-differentiation: polynomials, absolute value, and greatest integer | 31 |
| Anti-differentiation: trigonometric, inverse trigonometric | 14 |
| Anti-differentiation: exponential and logarithmic | 7 |
| Substitution | 78 |
| Integration by parts | 24 |
| Trigonometric integrals | 4 |
| Trigonometric substitution | 5 |
| Partial functions | 35 |
| Rectangle approximations | 3 |
| Trapezoidal approximations | 7 |
| Simpson's Rule | 2 |
| Fundamental theorem of Calculus to evaluate definite integrals | 129 |
| Fundamental theorem of Calculus of representative anti-derivatives | 8 |
| Mean Value Theorem of Integrals | 18 |
| Area between a curve and the x-axis | 42 |
| Area between curves | 29 |
| Improper integrals | 23 |
Integrals and Applications
| Category Title | Problems |
|---|---|
| Position, velocity, and acceleration | 33 |
| Separable differential equations including exponential growth and decay | 41 |
| Volume of solids of revolution (disks and washers, cylindrical shells) | 58 |
| Volume of solids with known cross-sections | 2 |
| Arc length, length of curves | 8 |
Polynomial Approximations and Series
| Category Title | Problems |
|---|---|
| Definition of series | 18 |
| Convergence of a series | 12 |
| Taylor Series, MacLaurin Series | 2 |