Step-by-Step Solutions to 2024 AP Calculus FRQs
The Free Response Questions (FRQs) are one of the most important—and challenging—parts of the AP Calculus AB and BC exams. They test not only your ability to compute but also your ability to explain reasoning, show steps clearly, and apply calculus to real-world problems.
In 2024, the FRQs followed the typical format: six questions, including problems on differential equations, integrals, series, and applied modeling. Each FRQ requires careful justification, logical structure, and mastery of concepts across the AP Calculus curriculum.
This guide will break down the 2024 AP Calculus FRQs step by step, highlight common pitfalls, and show you how to approach them strategically. By the end, you’ll know how to maximize points and develop exam-ready skills.
And remember—if you want guided practice, the best resource is RevisionDojo, where you’ll find step-by-step solutions, practice questions, and study plans tailored specifically for AP Calculus AB & BC.
Why FRQs Matter on the AP Calculus Exam
- FRQs count for 50% of your total AP score.
- There are 6 questions total: 4 in Part A (no calculator, 30 minutes) and 2 in Part B (graphing calculator allowed, 60 minutes).
- Each question typically has multiple parts (a–d or a–e), testing both computation and justification.
- FRQs are where many students lose points due to incomplete explanations or small algebra mistakes.
Takeaway: Mastering FRQs is the single best way to boost your AP Calculus score from a 3 or 4 to a 5.
2024 AP Calculus AB FRQs: Step-by-Step Walkthroughs
Let’s start with the AB exam. These are not just about “getting the right answer”—they’re about showing correct reasoning at every step.
FRQ 1: Differential Equation Modeling
- The Question: You were given a differential equation representing population growth, with an initial condition. Parts asked you to sketch a slope field, solve the differential equation, and interpret the solution in context.
- Step-by-Step Solution:
- Slope field: Plot slopes by substituting points into the derivative. Even if you can’t draw perfectly, showing correct direction patterns is worth partial credit.
- Solve the DE: Use separation of variables → integrate both sides → apply the initial condition to find the particular solution.
- Interpretation: Explain in words what the solution means (e.g., population leveling off, growth rate decreasing).
- Common Mistakes: Forgetting +C, misapplying ln properties, or skipping interpretation.
FRQ 2: Area & Volume with Integrals
- The Question: A region bounded by two curves was given, and you needed to find the area and then compute the volume of the solid generated when rotated.
- Step-by-Step Solution:
- Set up area: Identify left/right (for dy integrals) or top/bottom (for dx integrals). Show ∫(top - bottom) dx.
- Volume with rotation: Use π∫[(outer radius)^2 - (inner radius)^2] dx (washer method).
- Justify: Write the integral setup even if you don’t compute fully.
- Common Mistakes: Forgetting π, mixing up bounds, or not stating the method (disk/washer).
FRQ 3: Tabular & Graphical Interpretation
- The Question: A table of function values was provided. You had to estimate derivatives, evaluate Riemann sums, and use the Mean Value Theorem.
- Step-by-Step Solution:
- Approx derivative: Use difference quotient f(b)-f(a) / (b-a).
- Riemann sum: Multiply function values by width, sum carefully.
- Mean Value Theorem: Check continuity/differentiability, then find c where f’(c) matches average rate of change.
- Common Mistakes: Forgetting units, not stating MVT conditions, arithmetic slips.
FRQ 4: Applications of Derivatives
- The Question: A function’s derivative was given, and you had to analyze intervals of increase/decrease, concavity, and local extrema.
- Step-by-Step Solution:
- Critical points: Solve f’(x) = 0.
- Test intervals: Sign chart for f’(x) → increasing/decreasing.
- Concavity: Use f’’(x) or derivative test from f’(x).
- Answer in complete sentences.
- Common Mistakes: Writing just “max/min at x=2” without justification. Always explain using f’ or f’’.
2024 AP Calculus BC FRQs: Step-by-Step Walkthroughs
The BC exam includes everything from AB plus advanced topics like series, parametric equations, and polar curves.
FRQ 5: Series & Convergence
- The Question: A power series was given. You had to determine radius/interval of convergence and approximate a function value.
- Step-by-Step Solution:
- Ratio Test: Limit of |a(n+1)/an| < 1 → radius.
- Endpoints: Test separately for convergence.
- Approximation: Use partial sums or Taylor series expansion.
- Common Mistakes: Forgetting endpoints, misusing convergence tests.
FRQ 6: Parametric & Polar
- The Question: A curve given in parametric or polar form. You had to find arc length, slope dy/dx, and area.
- Step-by-Step Solution:
- Slope: dy/dx = (dy/dt) / (dx/dt).
- Arc length: ∫√((dx/dt)² + (dy/dt)²) dt.
- Polar area: ½∫(r(θ))² dθ.
- Common Mistakes: Dropping ½, misidentifying bounds, or forgetting dx/dt ≠ 0.
Common Mistakes Students Made in 2024
- Not labeling integrals clearly.
- Forgetting to justify with theorems (IVT, MVT, FTC).
- Skipping units in applied problems.
- Relying too much on calculator answers without proper setup.
Strategies for Tackling FRQs
- Always show work: Even partial setups earn points.
- Label graphs clearly when sketching.
- State conditions for theorems before applying them.
- Write in complete sentences for interpretation questions.
- Practice timed FRQs regularly—RevisionDojo provides simulations with grading rubrics.
Why RevisionDojo is the Best FRQ Prep Resource
Most students fail not because they don’t know calculus, but because they don’t practice writing AP-style justifications. RevisionDojo fixes this by:
- Offering step-by-step worked solutions to past AP FRQs.
- Providing interactive practice problems with instant feedback.
- Teaching you exactly how AP readers award points.
- Supplying study schedules (like 30 Days to a 5) tailored to your exam date.
Instead of wasting time hopping between different apps, RevisionDojo is your all-in-one AP Calculus prep platform.
Frequently Asked Questions
Q: How many points are the FRQs worth on the AP Calculus Exam?
A: FRQs make up 50% of your total score, with each question worth about 9 points.
Q: Do I need to get every part of an FRQ correct to earn points?
A: No—scoring is part-by-part. Even if you miss part (a), you can still earn full credit on (b) and (c).
Q: Can I use my calculator on all FRQs?
A: No. Only Part B (last 2 FRQs, 60 minutes) allows a calculator.
Q: What is the best way to study for AP Calculus FRQs?
A: The best strategy is to practice with step-by-step solutions and compare your work to official rubrics. RevisionDojo is the best platform for this.
Q: Should I memorize theorems or just rely on intuition?
A: You must state conditions for theorems like the Mean Value Theorem or Fundamental Theorem of Calculus to earn credit.
Conclusion
The 2024 AP Calculus FRQs tested the full range of skills: differential equations, applications of integrals, series, and parametric/polar analysis. Success comes from more than just getting the right answer—it’s about clear justifications, correct setups, and structured explanations.
If you’re serious about scoring a 5, the smartest prep move you can make is practicing FRQs with step-by-step breakdowns. That’s exactly what you’ll find on RevisionDojo, the ultimate AP Calculus prep resource.
