The free response section (FRQ) of the AP Calculus AB & BC exams is where top scorers pull ahead. Unlike multiple choice, you must show all steps, justify answers, and present solutions in a clear, logical format.
The good news? The FRQ section is predictable in structure — and with the right process, you can consistently earn points even on challenging problems.
In this RevisionDojo guide, we’ll break down a 7-step method to tackle any AP Calculus FRQ with confidence.
1️⃣ Read the Entire Question First
Why: AP FRQs often have multiple parts (a), (b), (c), and later parts may give hints for earlier steps.
RevisionDojo Tip:
- Circle key words: “rate of change,” “maximum,” “accumulated,” “area,” “justify.”
- Identify whether it’s a derivative, integral, limits, or application problem before diving in.
2️⃣ Identify the Topic and Formula Needed
Look for clues:
- Rate of change: Related rates or derivatives
- Area/volume: Definite integrals or solids of revolution
- Growth/decay: Differential equations or exponential models
- Series/approximations: BC-only topics like Taylor polynomials
3️⃣ Organize Given Information
Make a quick summary of:
- Functions, graphs, or tables provided
- Given values and units
- What’s being asked in each part
Example:
Given: f′(x)=3x2−4x+1f'(x) = 3x^2 - 4x + 1, f(2)=5f(2) = 5
Asked: Find f(0)f(0)
4️⃣ Write Down the General Method Before Calculating
This helps you earn method points even if you make an arithmetic mistake later.
Example:
If finding the slope of a tangent line:
- Find f′(x)f'(x)
- Substitute x-value into f′(x)f'(x) to find slope
- Use point-slope form to write equation
5️⃣ Solve Step-by-Step (Show All Work)
- Write each substitution clearly
- Don’t skip algebra steps
- Label intermediate results (e.g., “Slope = 7”)
Even partial solutions can earn significant points if your reasoning is clear.
6️⃣ Justify Your Answers Where Required
The College Board loves the word justify — meaning you must provide reasoning, not just the final value.
Example:
If asked whether a function has a maximum, justify with:
- f′(x)=0f'(x) = 0 and sign change from positive to negative
- or by citing the Extreme Value Theorem on a closed interval
7️⃣ Check Units and Answer in Context
- If the question involves rates, include units like “m/s” or “gallons/min”
- If the question is about a real-world situation, interpret your answer in words
Example:
Instead of just “5.2,” write “The population increases by 5.2 thousand fish per year.”
⚠️ Common FRQ Mistakes to Avoid
- Leaving answers without units in applied problems
- Using decimals when exact values (like π) are preferred
- Forgetting to write the general solution before substituting values
- Ignoring later parts that give hints for earlier work
📊 Practice Strategy from RevisionDojo
- Weekly: Do at least 1 full FRQ under timed conditions
- Review: Grade yourself with the College Board scoring guidelines
- Track: Keep a log of mistakes and how to fix them
🧭 Final Advice from RevisionDojo
The FRQ section isn’t about perfection — it’s about earning every possible point through clear work, correct methods, and proper justification. Even if you can’t finish a part, write down your approach.
Remember: On the AP Calculus exam, partial credit can turn a 3 into a 5.
