Practice Dojo

AP Calculus AB practice

Free, original practice questions for the AP Calculus AB exam, written to the College Board Course and Exam Description.

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How the practice works

Each unit has three multiple-choice sets. White belt covers core terms and foundational ideas. Regular is set at exam level, with concept checks and applications. Black belt has harder, multi-step questions. After each answer you get an explanation, plus a "Still don't get it?" walkthrough with the key idea, a worked solution, a short practice problem and the most common wrong answer.

The exam mix draws questions from every unit in proportion to the exam's unit weights, so you can practice the whole course in one sitting.

Free-response questions come with point-by-point scoring rubrics in the style of College Board scoring guidelines, model answers that earn every point, and walkthroughs for each part.

No account is needed. Your progress is saved in your own browser.

Units and topics

Unit 1: Limits and Continuity

10 to 15% of the exam · 180 multiple-choice questions · 5 free-response questions

• 1.1 Introducing Calculus
• 1.2 Defining Limits and Limit Notation
• 1.3 Limits from Graphs
• 1.4 Limits from Tables
• 1.5 Limit Laws
• 1.6 Algebraic Manipulation of Limits
• 1.7 Selecting Limit Procedures
• 1.8 Squeeze Theorem
• 1.9 Connecting Limit Representations
• 1.10 Types of Discontinuities
• 1.11 Continuity at a Point
• 1.12 Continuity over an Interval
• 1.13 Removing Discontinuities
• 1.14 Infinite Limits and Vertical Asymptotes
• 1.15 Limits at Infinity
• 1.16 Intermediate Value Theorem

Unit 2: Differentiation: Definition and Fundamental Properties

10 to 15% of the exam · 180 multiple-choice questions · 5 free-response questions

• 2.1 Average and Instantaneous Rates of Change
• 2.2 Derivative Definition and Notation
• 2.3 Estimating Derivatives
• 2.4 Differentiability and Continuity
• 2.5 Power Rule
• 2.6 Constant, Sum, and Difference Rules
• 2.7 Derivatives of Sine, Cosine, Exponential, and Logarithm
• 2.8 Product Rule
• 2.9 Quotient Rule
• 2.10 Derivatives of Other Trigonometric Functions

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

5 to 10% of the exam · 180 multiple-choice questions · 5 free-response questions

• 3.1 Chain Rule
• 3.2 Implicit Differentiation
• 3.3 Derivatives of Inverse Functions
• 3.4 Inverse Trigonometric Derivatives
• 3.5 Selecting Differentiation Procedures
• 3.6 Higher-Order Derivatives

Unit 4: Contextual Applications of Differentiation

10 to 15% of the exam · 180 multiple-choice questions · 5 free-response questions

• 4.1 Interpreting Derivatives in Context
• 4.2 Position, Velocity, and Acceleration
• 4.3 Rates of Change in Context
• 4.4 Introduction to Related Rates
• 4.5 Solving Related Rates
• 4.6 Local Linearity and Linearization
• 4.7 L’Hospital’s Rule

Unit 5: Analytical Applications of Differentiation

15 to 20% of the exam · 180 multiple-choice questions · 5 free-response questions

• 5.1 Mean Value Theorem
• 5.2 Extreme Value Theorem and Critical Points
• 5.3 Increasing and Decreasing Functions
• 5.4 First Derivative Test
• 5.5 Absolute Extrema
• 5.6 Concavity
• 5.7 Second Derivative Test
• 5.8 Graphs of Functions and Derivatives
• 5.9 Connecting Functions and Derivatives
• 5.10 Introduction to Optimization
• 5.11 Solving Optimization Problems
• 5.12 Implicit Relations

Unit 6: Integration and Accumulation of Change

15 to 20% of the exam · 180 multiple-choice questions · 5 free-response questions

• 6.1 Accumulation of Change
• 6.2 Riemann Sums
• 6.3 Riemann Sums and Definite Integral Notation
• 6.4 FTC and Accumulation Functions
• 6.5 Behavior of Accumulation Functions
• 6.6 Properties of Definite Integrals
• 6.7 FTC and Definite Integrals
• 6.8 Basic Antiderivatives
• 6.9 Integration by Substitution
• 6.10 Long Division and Completing the Square
• 6.14 Selecting Antidifferentiation Techniques

Unit 7: Differential Equations

5 to 10% of the exam · 180 multiple-choice questions · 5 free-response questions

• 7.1 Modeling with Differential Equations
• 7.2 Verifying Differential Equation Solutions
• 7.3 Slope Fields
• 7.4 Reasoning with Slope Fields
• 7.6 Separation of Variables
• 7.7 Initial-Value Problems
• 7.8 Exponential Models

Unit 8: Applications of Integration

10 to 15% of the exam · 180 multiple-choice questions · 5 free-response questions

• 8.1 Average Value
• 8.2 Motion Using Integrals
• 8.3 Accumulation in Context
• 8.4 Area Between Curves in x
• 8.5 Area Between Curves in y
• 8.6 Multiple Intersections
• 8.7 Square and Rectangular Cross Sections
• 8.8 Triangle and Semicircle Cross Sections
• 8.9 Disk Method about Coordinate Axes
• 8.10 Disk Method about Other Axes
• 8.11 Washer Method about Coordinate Axes
• 8.12 Washer Method about Other Axes

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