3 Most Common Mistakes Students Make in AP Calculus

AP Calculus is challenging not just because of the content, but because small, avoidable mistakes often cost students more points than they expect. Whether you’re preparing for the AB or BC exam, mastering the big ideas isn’t enough — you need to be sharp on details too. 

The most important thing to remember throughout the year is that if you’re not doing it in your homework, you won’t remember to do it on the test. In your homework, always force yourself to:

1. Use correct notation

2. Write answers out in full

3. Give answers with units in word problems

4. Pay attention to details, organization and presentation

Here are three recurring mistakes students make, why they matter, and what you can do to avoid them.

Mistake #1: Forgetting the “+ C” in Indefinite Integrals

• What it is: Whenever you integrate a function without bounds (indefinite integral), you must include the constant of integration, “+ C.”

• Why it hurts: On free-response questions, missing “+ C” means losing a point even if the rest of the work is correct. Graders expect this.  

• How to avoid it: Treat every “∫ … dx (no bounds)” as a mental flag — before writing your answer, double check: did I write + C? Build the habit in practice.

Mistake #2: Algebra & Arithmetic Errors

• What it is: Small mistakes in algebra (factoring, expanding, simplifying) or arithmetic (signs, fractions, distributing negatives) that derail otherwise correct methods. Many students have trouble simplifying derivatives, combining like terms, or managing fractions.  

• Why it hurts: These errors lose points easily and are often preventable. They not only reduce accuracy but hurt confidence under timed conditions.

• How to avoid it: Slow down at each step. After getting a result, re-review algebraic manipulation. Use simpler sub-problems inside larger problems. Practice with timed drills emphasising clean algebra.

Mistake #3: Not Understanding the Exam Format / Not Managing Time Well

• What it is: Underestimating the structure of the exam (multiple choice + free response), how many questions, how many parts, how strict time per section is; also mismanaging pauses, checking, or moving through parts inefficiently.

• Why it hurts: Students spend too long on one free-response part, then rush others; or they don’t plan time to check their answers. Also, because free-response grading is partial, clear, well-structured answers help.

• How to avoid it: Practice full timed exams. Break down sample free response questions under exam-like constraints. Learn how many minutes you can (~allocate per question). Also practise how to write partial credit even when uncertain; show work clearly.

Conclusion:

Your homework is where you practice skills to use on the day. Demand precision and thoroughness from yourself when doing your homework. On the day of the test, these will be habits that you’ve already formed. 

Want more detailed walkthroughs & worked-examples on each of these? Keep an eye out for my full guide coming next Tuesday, October 7th, on the Learn Locus blog — I’ll walk through sample problems, timing strategies, and checklists to catch common errors.

— Doug