Even strong math students lose points on the AP Calculus AB & BC exams because of avoidable mistakes. From misusing formulas to forgetting units, these errors can add up — and sometimes cost an entire problem’s worth of points.
In this RevisionDojo guide, we’ll go through the top 10 most common AP Calculus mistakes and how to prevent them, so you can walk into the exam confident and ready.
1️⃣ Forgetting + C in Indefinite Integrals
The Mistake: Writing
∫x2dx=x33\int x^2 dx = \frac{x^3}{3}
without + C in an indefinite integral.
Why It Hurts: On free-response questions, this can lose you an accuracy point.
How to Avoid It: Create a mental trigger — whenever you see “∫” with no limits, automatically add “+ C” at the end.
2️⃣ Misapplying the Chain Rule
The Mistake: Forgetting to multiply by the derivative of the inner function when differentiating composite functions.
Example: ddxsin(3x)=cos(3x)\frac{d}{dx} \sin(3x) = \cos(3x) (incorrect) — should be 3cos(3x)3\cos(3x).
How to Avoid It: Always identify the “outer” and “inner” function first before differentiating.
3️⃣ Ignoring Domain Restrictions
The Mistake: Giving answers that include values outside the domain of the original function (e.g., taking ln(x)\ln(x) and including x≤0x \le 0 in your solution).
How to Avoid It: Check domain at the start and after solving.
4️⃣ Using Calculator Incorrectly
The Mistake:
- Typing functions incorrectly (missing parentheses)
- Using degree mode instead of radians
- Rounding too early in calculations
How to Avoid It:
- Always double-check calculator mode before the exam
- Use full precision until the final step
5️⃣ Mixing Up Integration and Differentiation Rules
The Mistake: Applying derivative rules when integrating, or vice versa.
Example: Thinking ∫exdx=xex\int e^x dx = xe^x (incorrect).
How to Avoid It: Spend time drilling each process separately, then in mixed practice sets.
6️⃣ Not Labeling Units in Applied Problems
The Mistake: Writing “3.5” instead of “3.5 meters/second” in a rate problem.
How to Avoid It: Always check if the question involves rates, area, or volume — these require units for full credit.
7️⃣ Misinterpreting Graphs and Tables
The Mistake:
- Assuming a function is linear between table points
- Reading wrong coordinate values from a graph
How to Avoid It: Use points given, avoid assumptions unless stated, and label axes mentally before solving.
8️⃣ Not Showing Work on Free-Response Questions
The Mistake: Writing only the final answer without demonstrating steps.
How to Avoid It: Even if you can do it in your head, write enough to earn method points.
9️⃣ Forgetting The Fundamental Theorem of Calculus Applications
The Mistake: Missing that
ddx∫axf(t)dt=f(x)\frac{d}{dx} \int_a^x f(t) dt = f(x)
and its variations are key in many problems.
How to Avoid It: Practice with problems where the upper limit is a function of x.
🔟 Rushing and Misreading the Question
The Mistake: Answering “find the derivative” when the question actually asks for the slope at a specific point.
How to Avoid It: Underline what the question is really asking before solving.
🧭 Final Advice from RevisionDojo
Most AP Calculus mistakes come from carelessness, not lack of knowledge. Slow down enough to:
- Read the question fully
- Double-check units, domains, and conditions
- Show complete work
With consistent practice and error tracking, you can avoid these pitfalls and earn every possible point on exam day.
