1. AP Calculus AB
1.0 Foundations for Calculus
- 1.1 Algebra Review: linear equations, quadratic equations, polynomial operations, rational expressions, radical expressions, exponential and logarithmic functions.
- 1.2 Function Foundations: function notation, domain and range, composition, inverse functions, and piecewise functions.
- 1.3 Graphical Analysis: transformations, symmetry, intercepts, asymptotes, and end behavior.
- 1.4 Trigonometric Foundations: unit circle, trigonometric functions, trig identities, and inverse trig functions.
2.0 Limits and Continuity
- 2.1 Limits & Graphing Visualization 12% Free Preview
- 2.1.1 Numerical limits.
- 2.1.2 Graphical limits.
- 2.1.3 Analytical limits.
- 2.1.4 One-sided limits.
- 2.1.5 Infinite limits.
- 2.2 Limit Laws: sum, product, quotient, and power laws.
- 2.3 Techniques for Evaluating Limits: factoring, rationalization, common denominators, and squeeze theorem.
- 2.4 Continuity: definition of continuity, discontinuities, and Intermediate Value Theorem.
3.0 Differentiation
f′(x) = limh→0 [f(x+h) − f(x)] / h
- 3.1 Derivative Concepts: average rate of change, instantaneous rate of change, tangent lines, and velocity interpretation.
- 3.2 Difference quotient and derivative notation.
- 3.3 Differentiation rules: power, constant, sum, difference, product, quotient, and chain rule.
- 3.4 Derivatives of polynomial, rational, trigonometric, exponential, and logarithmic functions.
4.0 Applications of Derivatives
- 4.1 Motion analysis: position, velocity, and acceleration.
- 4.2 Curve analysis: critical points, increasing/decreasing intervals, concavity, and inflection points.
- 4.3 Optimization.
- 4.4 Related rates.
- 4.5 Mean Value Theorem and Rolle’s Theorem.
5.0 Integration and Accumulation
∫ab f(x) dx
- 5.1 Antiderivatives and indefinite integrals.
- 5.2 Definite integrals, area interpretation, and net change.
- 5.3 Fundamental Theorem of Calculus.
- 5.4 Applications of integration.
6.0 Differential Equations
- 6.1 Slope fields and exponential growth/decay.
- 6.2 Separation of variables and logistic models.
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