AP Calculus AB Study Guide: The Topics That Score Most

AP Calculus AB rewards depth on a small number of topics. Here are the six that dominate the exam, ranked by how often they show up.

1. Derivatives (40% of the exam)

Drill the rules: power, product, quotient, chain. Memorise the derivatives of trig, exponential, and log functions. Use Math Solver for worked examples.

Common question types:

• Find the derivative of a complex function
• Implicit differentiation
• Related rates problems

2. Integrals (35% of the exam)

Antiderivatives, definite integrals, the fundamental theorem of calculus. Drill u-substitution and integration by parts.

Common question types:

• Definite integrals
• Area between curves
• Volumes of revolution

3. Limits and continuity (10% of the exam)

Often combined with derivatives. Know the standard limits, especially limit as x approaches infinity.

4. Applications of derivatives (10% of the exam)

• Optimisation problems
• Mean value theorem
• Critical points and inflection points

5. Differential equations (5% of the exam)

Separable equations only. Slope fields appear sometimes.

6. Series (NOT on AB)

Series are on Calculus BC, not AB. Skip them if you're only taking AB.

Calculator vs no-calculator

The exam has both sections. Practice both. Calculator section lets you use TI-84. No-calculator section requires you to compute by hand. Most students underprepare for the no-calculator section.

Three-week plan before the exam

• Week 1: drill derivatives and integrals. One Mock Exam at the end.
• Week 2: applications. Optimisation, related rates, area/volume problems.
• Week 3: full mock exams under timed conditions.

What examiners reward

• Showing work (free response is 50% of the exam)
• Stating units in answers
• Using calculus notation correctly

Common pitfalls

• Forgetting +C on indefinite integrals
• Wrong sign on the chain rule
• Not labeling units in physics-style problems
• Treating the calculator as a crutch instead of a tool

Try AP-style calculus problems →