Free · Rubric Scoring · No card required
AP Calculus AB Formula Reference — What You Must Know
AP Calculus AB formula reference. No formula sheet is provided on the AP Calc exam — learn which derivatives, integrals, and theorems you must know from memory.
Grade an essay right now
Paste your prompt and your response. You get a point-by-point rubric breakdown in about 20 seconds — no account, nothing to install.
Scored against the standard published point categories for this format. Because it is your own prompt there is no official scoring guide behind it, so treat this as practice feedback rather than a predicted score. How we tested the grader.
Unlike AP Chemistry or Physics, AP Calculus AB provides no formula sheet. Every derivative, integral, theorem, and limit definition must come from memory. This makes concept mastery non-negotiable.
Essential Derivatives to Know
- d/dx[xⁿ] = nxⁿ⁻¹, d/dx[eˣ] = eˣ, d/dx[ln x] = 1/x
- d/dx[sin x] = cos x, d/dx[cos x] = −sin x, d/dx[tan x] = sec²x
- d/dx[arcsin x] = 1/√(1−x²), d/dx[arctan x] = 1/(1+x²)
- Chain rule, product rule, quotient rule — must apply fluently without hesitation
Essential Integrals to Know
- ∫xⁿ dx = xⁿ⁺¹/(n+1) + C, ∫eˣ dx = eˣ + C, ∫1/x dx = ln|x| + C
- ∫sin x dx = −cos x + C, ∫cos x dx = sin x + C, ∫sec²x dx = tan x + C
- Fundamental Theorem of Calculus (both parts) — appears on virtually every exam
Key Theorems to Know
Mean Value Theorem, Intermediate Value Theorem, Extreme Value Theorem, and L'Hôpital's Rule. For each, know the hypotheses (what conditions must be satisfied) and the conclusion (what it guarantees). FRQ justifications require stating the theorem, not just applying it.
AP Calc AB Practice · AP Calc AB FRQ Guide · AP Calc AB Study Guide
AP and Advanced Placement are trademarks of College Board. AimFive is not affiliated with or endorsed by College Board.