College Board AP® Calculus AB
Exam Questions

Definition of a Limit, Infinite Limits & Limits at Infinity, Properties of Limits, Evaluating Limits Analytically, Evaluating Limits Numerically & Graphically, Squeeze Theorem & Trigonometric Limits

Continuity, Removable Discontinuities, Non-removable Discontinuities, Continuous Functions, Intermediate Value Theorem

Average Rate of Change, Instantaneous Rate of Change, Derivatives & Tangents, Estimating the Derivative at a Point, Differentiability & Continuity

Derivative Rules, Derivatives of Exponentials and Logarithms, Derivatives of Sine and Cosine Functions, The Product Rule, The Quotient Rule, Derivatives of Tangent and Reciprocal Trig Functions

The Chain Rule, The Inverse Function Theorem, Derivatives of Inverse Trigonometric Functions, Higher-Order Derivatives

Implicit Differentiation

Meaning of a Derivative in Context, Motion in a Straight Line, Related Rates

Approximating Values of a Function

L'Hospital's Rule

Mean Value Theorem, Extreme Value Theorem, Critical Points, Increasing & Decreasing Functions, First Derivative Test for Local Extrema, Candidates Test for Global Extrema, Concavity of Functions, Second Derivative Test for Local Extrema, Graphs of f, f' & f'', Optimization Problems

Second Derivatives of Implicit Functions, Critical Points of Implicit Relations

Indefinite Integrals, Derivatives & Antiderivatives, Indefinite Integral Rules, Constant of Integration

Accumulation of Change, Riemann Sums, Trapezoidal Sums, Accumulation Functions, Fundamental Theorem of Calculus, Properties of Definite Integrals, Evaluating Definite Integrals

Integrals of Composite Functions, Integration Using Substitution, Integration Using Completing the Square, Integration Using Long Division

Introduction to Differential Equations, Slope Fields, Separation of Variables, Finding Particular Solutions, Exponential Models

Average Value of a Function, Definite Integrals as Accumulated Change, Position, Velocity & Acceleration, Distance & Speed

Area Between a Curve & x-Axis, Area Between a Curve & y-Axis, Area Between Two Curves, Multiple Areas

Volumes from Areas of Known Cross Sections, Squares as Cross Sections, Rectangles as Cross Sections, Triangles as Cross Sections, Semicircles as Cross Sections

Disc Method Around the x-Axis, Disc Method Around the y-Axis, Disc Method Around Other Axes, Washer Method Around the x-Axis, Washer Method Around the y-Axis, Washer Method Around Other Axes