149 AP Calculus AB FRQs Categorized by Topic with Solutions (2006–2024)
Over the past 18 years—from 2006 to 2024, excluding 2020—I have carefully compiled and categorized AP Calculus Free Response Questions (FRQs) by topic to help students prepare more efficiently. During the earlier years (2006 to 2011), the AP Calculus exam featured two sets of papers per year, resulting in 6 additional exams.
Altogether, this compilation includes:
18 main exam papers (2006–2024, excluding 2020)
6 additional papers from 2006 to 2011
24 total papers, each containing 6 free response questions
That makes for a total of 144 FRQs. Additionally, I have included 5 BC questions that align closely with AB-level topics, bringing the grand total to 149 free response questions.
Each question in the PDF sets includes a detailed, step-by-step solution to help reinforce understanding. For clarity:
Questions 1 and 2 are calculator-allowed
Questions 3 through 6 are non-calculator
This resource is designed not just for practice—but for mastery. It gives students a clear structure to study topically, reinforces exam patterns, and provides full solutions for self-guided improvement.
The first topic is “Differentiation: Definition and Fundamental Properties.” This section includes 4 questions that focus on the foundational concepts of calculus. To master this topic, you should have a strong understanding of continuity and differentiability, which are essential for evaluating and interpreting derivatives at specific points. Keep in mind that while the focus is on fundamental differentiation, some questions may incorporate related ideas from other topics, reflecting the integrated nature of AP Calculus questions. Download PDF for Topic 1
The second topic is “Differentiation: Composite, Implicit, and Inverse Functions.” This section includes 6 questions that delve into more advanced differentiation techniques. To tackle these effectively, you should be confident with:
Finding the equation of a tangent line at a specific point
Implicit differentiation
The chain rule and its applications
These questions are designed to challenge your ability to apply differentiation rules in more complex and less direct scenarios. Additionally, you may encounter overlapping concepts from other areas of calculus, as AP questions often blend topics to test deeper understanding. Download PDF for Topic 2
The third topic is “Contextual Applications of Differentiation.” This section includes 2 FRQ questions. Key concepts you’ll need to master include:
L'Hôpital's Rule for resolving indeterminate limits
Approximating a function’s value using local linearity (tangent line approximations)
It’s worth noting that while this topic often overlaps with related areas like straight-line motion and related rates, those questions have been categorized separately for more focused practice. Still, some cross-topic elements may appear, as AP FRQs frequently blend multiple concepts in a single problem. Download PDF for Topic 3
The fourth topic is “Analytical Applications of Differentiation.” This section features 12 questions that dive deep into analyzing the behavior of functions using derivatives. To master this topic, you should be well-versed in:
Relative and absolute extrema
Concavity and points of inflection
Average rate of change
The Mean Value Theorem (MVT)
These questions often require a combination of graphical interpretation and algebraic manipulation, testing both your conceptual understanding and problem-solving skills. As with many AP FRQs, some problems may blend concepts from other topics to evaluate your ability to make connections across calculus principles. Download PDF for Topic 4
The fifth topic is “Related Rates.” This section includes 2 focused questions that test your ability to solve problems involving related rates—situations where two or more quantities are changing with respect to time. To excel in this topic, you should be comfortable with:
Setting up equations that relate multiple variables
Differentiating implicitly with respect to time
Applying geometric and real-world reasoning
Download PDF for Topic 5
The sixth topic is “Riemann Sums.” This section includes 22 questions collected from various years that focus on estimating area under a curve using different Riemann sum techniques. You'll need a solid understanding of:
Left-hand Riemann sums
Right-hand Riemann sums
Midpoint Riemann sums
Trapezoidal approximations
These problems often test your ability to approximate integrals and interpret numerical data from tables or graphs. While the primary focus is Riemann sums, many questions also incorporate ideas from other calculus topics, reflecting the integrated nature of the AP exam. Download PDF for Topic 6
The seventh topic is “Integration and Accumulation of Change.” With 42 questions, this is the largest section in the collection and covers a wide range of integral-based concepts central to the AP Calculus curriculum. To master this topic, you should be proficient in:
Recognizing and differentiating accumulation functions
Identifying relative and absolute extrema
Analyzing concavity and points of inflection
Applying properties of definite integrals
These questions often blend analytical reasoning with graphical and numerical interpretation, requiring a deep understanding of how accumulation relates to rate of change. Expect multi-step problems that may integrate concepts from earlier differentiation topics as well. Download PDF for Topic 7
The eighth topic is “Straight-Line Motion: Connecting Position.” This section features 16 questions that explore motion along a straight line using calculus. These problems require a solid understanding of the relationships between position, velocity, and acceleration. Key concepts include:
Interpreting and analyzing position, velocity, and acceleration functions
Understanding the difference between distance and displacement
Finding position using initial conditions and integrating velocity functions
These motion-based problems often appear in both conceptual and applied forms. Many questions also incorporate ideas from other calculus topics, making this a highly integrative section of the exam. Download PDF for Topic 8
The ninth topic is “Applications of Integration.” This section contains 25 questions that focus on applying definite integrals to geometric and physical problems. These are high-yield questions that frequently appear on both AP Calculus AB and BC exams. Key concepts covered include:
Finding the area between curves
Calculating volumes using cross-sectional areas
Volume of solids using the disk and washer methods
These problems require not only integration skills but also strong spatial reasoning and the ability to interpret graphical data. Many of these questions are multi-step and may connect with other topics, reinforcing the importance of a comprehensive understanding of integration. Download PDF for Topic 9
The tenth topic is “Differential Equations.” This section includes 18 questions that explore the theory and application of differential equations. To excel in this topic, you’ll need to understand:
Interpreting slope fields and visualizing solution curves
Solving differential equations through separation of variables
Working with both general and particular solutions
These questions test your ability to connect graphical representations, algebraic manipulation, and conceptual understanding. As with many AP FRQs, differential equations often appear in multi-concept problems, integrating ideas from across the calculus spectrum. Download PDF for Topic 10
