AP Calculus AB
AP Calculus AB FRQ Tips: How to Write Answers That Actually Score
days until your Calc AB exam
Mon, May 11 · Morning session
How the 9 points per FRQ are scored
Each FRQ is worth 9 points. Two FRQs allow a calculator (30 minutes); four are no-calc (60 minutes). Readers award credit for correct setup, correct antiderivative or derivative, correct boundary values, and a final answer with units. Setup is often worth more than the final number.
Points per FRQ · 9
Suggested time budget · 90 min
Calc-allowed FRQs (×2)
18 pt · 30 minGraphical or numerical problems; calculator allowed. Store decimals - round only at the final step.
No-calc FRQs (×4)
36 pt · 60 minSymbolic manipulation, antiderivatives, derivatives by definition, and related rates. Show every step.
Exam composite weighting
6 FRQs carry the same weight as 45 MCQs
Decode the task word before you write
Every AP FRQ begins with a task word. It tells you the minimum sentence type required for the point. Writing too much costs time; writing the wrong kind costs the point outright.
Want to know if you're actually doing this?
Write one Calc FRQ. Get your setup, work, and final answer scored line by line.
Weak vs. strong: accumulation with calculator
Calculator FRQs reward setup + stored values. Writing the integral FIRST, evaluating with the calculator second, wins points even if the final number is off.
Prompt
Water flows into a tank at a rate R(t) = 3 + 5sin(t) gallons per hour for 0 ≤ t ≤ 6. Find the total water that flows into the tank over the 6-hour period.
Weak answer
"Total = 18 + 5(−cos(6) + cos(0)) = 18 + 5(1 − 0.96) ≈ 18.2 gallons"
Why it lost points
- Doesn't write the integral explicitly - reader can't award the setup point.
- No units shown on intermediate steps.
- Arithmetic error: cos(6) ≈ 0.960, but 1 − 0.960 = 0.040, so 5·0.040 = 0.20, giving 18.2 - the answer is close but the logic jumped.
Strong answer
"Total water = ∫₀⁶ R(t) dt = ∫₀⁶ (3 + 5sin(t)) dt. Evaluating, [3t − 5cos(t)]₀⁶ = (18 − 5cos(6)) − (0 − 5cos(0)) = 18 − 5(0.9602) + 5 = 18.199 gallons. Total water ≈ 18.20 gallons."
Why it scores full marks
- Writes the integral with correct limits before computing - earns the setup point.
- Shows the antiderivative before substituting.
- Includes units (gallons) on the final answer.
Weak vs. strong: related rates
No-calc related-rates prompts reward showing the relationship equation + implicit differentiation step-by-step. Readers want every step, not a memorized result.
Prompt
A spherical balloon is being inflated such that its volume increases at 12 cm³/s. Find the rate at which the radius is increasing when the radius is 2 cm.
Weak answer
"dr/dt = 12 / (4π(2)²) = 12 / 16π ≈ 0.239 cm/s"
Why it lost points
- Jumps to the formula without writing V = (4/3)πr³ first.
- No implicit differentiation shown.
- No units explicitly stated on intermediate values.
Strong answer
"Volume of a sphere: V = (4/3)πr³. Differentiating both sides with respect to t: dV/dt = 4πr² · dr/dt. Given dV/dt = 12 cm³/s and r = 2 cm: 12 = 4π(4) · dr/dt, so dr/dt = 12/(16π) = 3/(4π) ≈ 0.239 cm/s."
Why it scores full marks
- Writes the volume relationship before differentiating - earns the setup point.
- Shows implicit differentiation explicitly (dV/dt = 4πr² · dr/dt).
- Final answer in exact form (3/(4π)) plus decimal, with units.
What you see in GradGPT
This is what your feedback looks like
Every Calc FRQ you write gets scored against the same rubric AP readers use. Strengths, improvements, and notes are highlighted inline - on your work, not in a generic rubric summary.
Your response
V = (4/3)πr³. dV/dt = 12. Plugging in, dr/dt = 12/(4π(2)²) ≈ 0.24 cm/s. So the radius grows fast.
Inline feedback
Rubric breakdown
You scored higher than 69% of students on this prompt
Setup (formula stated)
1/1
Volume formula cited
Implicit differentiation
0/1
Chain-rule step skipped
Final answer with units
1/1
cm/s included
Get this on your own answer.
The 5 FRQ patterns that cover Calc AB
Every Calc AB FRQ fits one of these five patterns. Learn the setup for each; the rest is algebra.
Accumulation / rate × time
A rate function r(t) and an initial value. Integrate, interpret, compare.
- Write the integral with limits BEFORE computing.
- Interpret answers in context ('gallons', 'meters', 'people').
Related rates
Geometry + chain rule. Volume-radius, ladder-wall, shadow-person.
- Write the relating equation first.
- Differentiate implicitly before plugging in values.
Graphical analysis of f'
Given f'(x)'s graph, reason about f: critical points, concavity, absolute max.
- Use sign of f' for increasing/decreasing.
- Use sign change of f' for local max/min.
Particle motion
Position, velocity, acceleration. Interpret sign, find total distance, solve for when velocity is zero.
- Total distance ≠ displacement: use the absolute value of velocity.
- Cite the time of a critical event with units.
Area / volume of revolution
Region between curves; revolve about x- or y-axis; disk/washer.
- Sketch the region and label the axis of revolution.
- Choose disk, washer, or shell BEFORE writing the integral.
The mistakes that quietly cost points
These show up every year. Each one is a single habit - fix the habit and you bank points you were already close to earning.
Skipping the integral setup on calculator FRQs. The setup is often worth more than the final number - writing '∫₀⁶ R(t) dt' before evaluating banks the point even if arithmetic is off.
Dropping units. Every context-based FRQ expects units on the final answer: gallons, meters per second, degrees.
Using the equals sign as an arrow ('=...'). Each equals sign should be mathematically true.
Writing 'by FTC' instead of using the FTC. Readers want you to DO the computation, not cite a theorem name.
Forgetting the +C on indefinite integrals when it matters (rarely on AP, but sign-error-prone).
Not storing decimals on the calculator. Rounding mid-calculation leads to wrong final answers on multi-step FRQs.
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Your first FRQ scored against the real AP Calc AB rubric.
Frequently Asked Questions
Six. Two with a calculator (30 minutes) and four without (60 minutes). Each FRQ is worth 9 points - 54 points total on the FRQ section.
Yes - arguably more than on no-calc FRQs. Readers want the integral or derivative written out BEFORE you use the calculator. A correct decimal with no setup earns partial credit at best.
Yes, and this is where most students leave points on the table. Setup, formula, and intermediate steps are each worth credit. Write them all out.
Jumping to the answer without writing the setup. 'dr/dt = 12/16π' earns 1 point. Writing V = (4/3)πr³, differentiating implicitly, then solving earns all 3.
50/50. Six FRQs carry the same weight as 45 multiple-choice questions. FRQs are where most students have the most room to grow, making them the highest-leverage prep.
Fill the space that the math requires and no more. Clear setup, clean work, boxed final answer with units. Readers value brevity with structure.
Write one Calc FRQ. See exactly where you lost points.
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