AP Calculus AB · Key concepts
The Calc AB cheat sheet: every concept the exam keeps coming back to.
Limits & derivatives · Integrals · Reasoning across f, f', f'' — plus the FRQ habits that earn the setup points.
days until your Calc AB exam
Mon, May 11 · Morning session
Foundations
Limits & Derivatives
Limits & continuity
Algebraic, graphical, and end-behavior limits — plus where IVT applies.
Chain, product, quotient rules
Fluency matters. Most derivative MCQs hinge on a clean chain rule.
Implicit differentiation
Treat y as a function of x and chain-rule every y term.
Related rates & linearization
Set up the equation first. Differentiate. Substitute last.
Integration
Integrals & accumulation
Riemann sums & FTC
Net change = ∫ rate. The FTC is half the FRQ section.
U-substitution
Pick u where du shows up in the integrand. The most-tested integration technique.
Area between curves
Top minus bottom, integrated over the interval. Watch for sign changes.
Differential equations
Separable, slope fields, exponential growth/decay. Always include +C.
Reasoning
Across f, f', f''
Critical points & extrema
Sign of f' tells you increasing/decreasing — say so explicitly.
Concavity & inflection
Sign change of f''. Justify with a calculus reason, not a graph.
Particle motion
Position, velocity, acceleration — same function, different derivatives.
MVT & IVT justification
State the conditions, then the conclusion. Theorem language earns the point.
Exam at a glance · 3 hours 15 minutes
MCQ Part A · 60 min
30 no-calculator questions.
MCQ Part B · 45 min
15 with calculator.
FRQ Part A · 30 min
2 calculator questions.
FRQ Part B · 60 min
4 no-calculator questions.
What AP Calc readers actually reward
Three FRQ habits that separate students who 'know calculus' from students who score it.
Rubric move
Show the setup before solving
Half the FRQ points come from the integral or derivative expression itself. Skipping the setup forfeits them even with a correct final answer.
Weak
Volume = 12.4
Scoring-ready
Volume = ∫₀² π[f(x)]² dx = 12.4
Rubric move
Justify with theorem language
Saying 'increasing' isn't enough. Say WHY using the calculus reason — sign of f', critical points, MVT conditions.
Weak
f is increasing on [1, 3].
Scoring-ready
f is increasing on [1, 3] because f'(x) > 0 throughout the interval.
Rubric move
Interpret with units
Application FRQs reward translating the math back into the real-world quantity, with units.
Weak
f'(5) = 3.
Scoring-ready
At t = 5 seconds, the particle's velocity is 3 m/s and increasing.
Want to see exactly which FRQ row you're losing points on?
Spot the concept
These are the concepts behind a real Calc AB stem.
Three mini MCQs from the exam's most common skill areas. Tap to reveal the answer.
If f(x) = sin(3x²), then f'(x) = ?
- Acos(3x²)
- B6x cos(3x²)
- C3x² cos(3x²)
- D6x sin(3x²)
How fast is the volume increasing when the radius is 5 cm?
- A40π cm³/s
- B100π cm³/s
- C200π cm³/s
- D400π cm³/s
If g(x) = ∫₂ˣ √(1 + t³) dt, then g'(x) = ?
- A√(1 + x³) − √9
- B√(1 + x³)
- C(1/2)(1 + x³)^(−1/2)
- D3x² · √(1 + x³)
Will you score the 5?
Write one timed FRQ. See exactly where rubric points would slip — while there's still time to fix it.
Quick questions
Analytical applications of derivatives (Unit 5) and integration (Unit 6) together carry over a third of the exam. They also feed almost every FRQ. Drill those before anything else.
Write the integral or derivative expression on its own line before doing any computation. Most readers award the setup point even if the arithmetic that follows is wrong.
No — the calculator section rewards interpretation more than computation. The no-calc section rewards algebraic fluency. Most students lose more points on no-calc than they expect.
45 MCQs. 6 FRQs. The 5 lives in the FRQ setup.
Or if you want a schedule.