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AP Calculus AB

AP Calculus AB

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This AP® Calculus AB mock exam covers the core AB curriculum: limits and continuity, differentiation, applications of derivatives, integration, differential equations, and applications of integration. Sub-units blend conceptual understanding with procedural fluency and modeling so students are ready for both multiple-choice and free-response sections.

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Units and Sub-Units

Unit 1 | Limits and Continuity

  • 1.1 Introducing Calculus: Instantaneous Change — 30 Qs
  • 1.2 Defining Limits & Notation — 20 Qs
  • 1.3 Estimating Limits from Graphs — 20 Qs
  • 1.4 Estimating Limits from Tables — 20 Qs
  • 1.5 Limits via Algebraic Properties — 20 Qs
  • 1.6 Limits via Algebraic Manipulation — 40 Qs
  • 1.7 Selecting Procedures for Limits — 20 Qs
  • 1.8 Squeeze Theorem — 20 Qs
  • 1.9 Connecting Multiple Representations — 20 Qs
  • 1.10 Types of Discontinuities — 20 Qs
  • 1.11 Continuity at a Point — 20 Qs
  • 1.12 Continuity on an Interval — 40 Qs
  • 1.13 Removing Discontinuities — 20 Qs
  • 1.14 Infinite Limits & Vertical Asymptotes — 20 Qs
  • 1.15 Limits at Infinity & Horizontal Asymptotes — 50 Qs
  • 1.16 Intermediate Value Theorem (IVT) — 20 Qs

Unit 2 | Differentiation: Definition & Fundamental Properties

  • 2.1 Average vs. Instantaneous Rates of Change — 20 Qs
  • 2.2 Defining the Derivative & Notation — 20 Qs
  • 2.3 Estimating Derivatives at a Point — 20 Qs
  • 2.4 Differentiability vs. Continuity — 50 Qs
  • 2.5 Power Rule — 20 Qs
  • 2.6 Constant, Sum/Difference, Constant Multiple Rules — 30 Qs
  • 2.7 Derivatives of cos x, sin x, e^x, ln x — 20 Qs
  • 2.8 Product Rule — 20 Qs
  • 2.9 Quotient Rule — 20 Qs
  • 2.10 Derivatives of tan, cot, sec, csc — 20 Qs

Unit 3 | Differentiation: Composite, Implicit, and Inverse Functions

  • 3.1 Chain Rule — 70 Qs
  • 3.2 Implicit Differentiation — 20 Qs
  • 3.3 Derivatives of Inverse Functions — 20 Qs
  • 3.4 Derivatives of Inverse Trig Functions — 20 Qs
  • 3.5 Choosing Procedures for Derivatives — 20 Qs
  • 3.6 Higher-Order Derivatives — 50 Qs

Unit 4 | Contextual Applications of Differentiation

  • 4.1 Meaning of the Derivative in Context — 20 Qs
  • 4.2 Motion: Position, Velocity, Acceleration — 20 Qs
  • 4.3 Rates of Change in Non-Motion Contexts — 20 Qs
  • 4.4 Introduction to Related Rates — 20 Qs
  • 4.5 Solving Related Rates — 20 Qs
  • 4.6 Local Linearity & Linearization — 20 Qs
  • 4.7 L’Hospital’s Rule — 20 Qs

Unit 5 | Analytical Applications of Differentiation

  • 5.1 Mean Value Theorem — 50 Qs
  • 5.2 EVT, Global vs. Local Extrema, Critical Points — 20 Qs
  • 5.3 Intervals of Increase/Decrease — 20 Qs
  • 5.4 First Derivative Test — 20 Qs
  • 5.5 Candidates Test (Absolute Extrema) — 20 Qs
  • 5.6 Concavity — 30 Qs
  • 5.7 Second Derivative Test — 20 Qs
  • 5.8 Sketching Functions & Derivatives — 20 Qs
  • 5.9 Connecting f, f′, and f″ — 60 Qs
  • 5.10 Intro to Optimization — 20 Qs
  • 5.11 Solving Optimization Problems — 20 Qs
  • 5.12 Behaviors of Implicit Relations — 20 Qs

Unit 6 | Integration and Accumulation of Change

  • 6.1 Accumulations of Change — 20 Qs
  • 6.2 Riemann Sum Approximations — 40 Qs
  • 6.3 Riemann Sums, Σ-Notation, Definite Integral — 20 Qs
  • 6.4 Fundamental Theorem of Calculus & Accumulation — 20 Qs
  • 6.5 Behavior of Accumulation Functions — 30 Qs
  • 6.6 Properties of Definite Integrals — 50 Qs
  • 6.7 FTC & Definite Integrals — 30 Qs
  • 6.8 Antiderivatives & Indefinite Integrals — 50 Qs
  • 6.9 Substitution — 50 Qs
  • 6.10 Long Division & Completing the Square — 20 Qs
  • 6.14 Selecting Antidifferentiation Techniques — 30 Qs

Unit 7 | Differential Equations

  • 7.1 Modeling with Differential Equations — 20 Qs
  • 7.2 Verifying Solutions — 20 Qs
  • 7.3 Sketching Slope Fields — 20 Qs
  • 7.4 Reasoning with Slope Fields — 20 Qs
  • 7.6 General Solutions via Separation — 20 Qs
  • 7.7 Particular Solutions with Initial Conditions — 40 Qs
  • 7.8 Exponential Models — 20 Qs

Unit 8 | Applications of Integration

  • 8.1 Average Value of a Function — 20 Qs
  • 8.2 Position, Velocity, Acceleration via Integrals — 40 Qs
  • 8.3 Accumulation Functions in Context — 20 Qs
  • 8.4 Area Between Curves (as functions of x) — 30 Qs
  • 8.5 Area Between Curves (as functions of y) — 20 Qs
  • 8.6 Areas with >2 Intersections — 20 Qs
  • 8.7 Volumes: Cross-Sections (Squares/Rectangles) — 20 Qs
  • 8.8 Volumes: Cross-Sections (Triangles/Semicircles) — 20 Qs
  • 8.9 Volume: Disc Method about x- or y-Axis — 20 Qs
  • 8.10 Volume: Disc Method about Other Axes — 20 Qs
  • 8.11 Volume: Washer Method about x- or y-Axis — 20 Qs
  • 8.12 Volume: Washer Method about Other Axes — 20 Qs

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