The Free Response Questions (FRQs) on the AP Calculus AB exam are where strong math skills meet strategic problem solving. Worth 50% of your total exam score, these questions test your ability to apply calculus concepts to real-world problems, often combining multiple skills in a single prompt.
If you’re aiming for a top score, you need to know the format, master the scoring rubrics, and practice consistently — and that’s exactly what we’ll cover here.
AP Calc AB FRQ Format
- Section II of the Exam — 6 questions, 90 minutes total
- Part A: 2 questions, 30 minutes, calculator allowed
- Part B: 4 questions, 60 minutes, no calculator
Weight: FRQs make up 50% of your total AP Calc AB score.
Skills Tested in FRQs
The FRQs will challenge your ability to:
- Interpret and analyze functions from graphs, tables, and equations
- Apply derivatives to motion, optimization, and related rates problems
- Use integrals in area, volume, and accumulation contexts
- Work with differential equations and slope fields
- Justify solutions with clear mathematical reasoning
Example FRQ — Calculator-Allowed
Prompt:
The velocity of a particle moving along the x-axis is given by v(t)=t21+t3v(t) = \frac{t^2}{1 + t^3} meters per second for t≥0t \ge 0.
- Find the total distance traveled from t=0t = 0 to t=3t = 3.
High-Scoring Solution Outline:
- Recognize that distance = integral of ∣v(t)∣|v(t)|.
- Since v(t)v(t) is positive on [0, 3], integrate directly.
- Use your calculator to evaluate ∫03t21+t3 dt\int_0^3 \frac{t^2}{1 + t^3} \, dt.
- Answer with correct units: meters.
Example FRQ — No Calculator
Prompt:
A tank contains 50 liters of water at time t=0t = 0. Water flows in at a rate R(t)=10sin(πt4)R(t) = 10\sin(\frac{\pi t}{4}) liters/minute and drains at a constant rate of 3 liters/minute.
- Write an expression for the volume of water in the tank at t=5t = 5.
High-Scoring Solution Outline:
- Volume at time tt = initial volume + inflow – outflow.
- V(5)=50+∫0510sin(πt4)dt−3(5)V(5) = 50 + \int_0^5 10\sin\left(\frac{\pi t}{4}\right) dt - 3(5).
- Solve the definite integral without a calculator.
Top Strategies for AP Calc AB FRQs
- Write Everything Out — Even partial solutions can earn points.
- Label Units Clearly — Points are often awarded for correct units.
- Don’t Skip Justification Steps — “Because the derivative is positive…” matters.
- Time Management — ~15 minutes for each Part A question, ~15 for each Part B.
- Practice Without a Calculator — Especially for Part B questions.
Common FRQ Mistakes in AP Calc AB
- Forgetting to state units in the final answer
- Skipping verbal justification when required
- Making sign errors in definite integrals
- Using a calculator incorrectly for symbolic work
How RevisionDojo Helps You Master AP Calc AB FRQs
With RevisionDojo, you get:
- Past AP Calc AB FRQs with Solutions
- Step-by-Step Answer Walkthroughs
- Calculator & Non-Calculator Practice Sets
- Scoring Rubric Breakdowns so you know exactly how points are awarded
And when you finish the exam:
- University Match Quiz — Find out which schools give you credit for your AP Calc AB score.
- Universities Directory — Compare credit policies around the world.
FAQ – AP Calc AB FRQs
1. How much are FRQs worth on the AP Calc AB exam?
They make up 50% of your total score.
2. Are calculators allowed on all FRQs?
No — only on the first two in Part A.
3. Do I lose points for wrong answers?
No — points are only awarded, not deducted.
4. Should I box my final answer?
It’s not required but helps graders see it clearly.
5. What’s the best way to practice FRQs?
Work through official College Board FRQs and check your work against scoring guidelines.
6. Are there trick questions?
Not exactly — but many FRQs require applying multiple concepts in sequence.
Turn AP Calc AB FRQs into Your Strength
With consistent practice, FRQs can become your highest-scoring section.
🎯 Take the University Match Quiz to see where your AP score earns you credit.
🌍 Browse the Universities Directory for detailed AP credit policies.
