Introduction
One of the biggest challenges AP Calculus students face is remembering the huge list of formulas needed on test day. While the AP Exam provides a formula sheet, it’s limited — meaning you need to memorize and understand many more formulas to succeed.
This guide lays out the essential AP Calculus AB and BC formulas you need to know, explains when to use them, and shows how RevisionDojo can help you practice them until they become second nature.
Limits and Continuity
- limx→0sinxx=1\lim_{x \to 0} \frac{\sin x}{x} = 1
- limx→∞(1+1x)x=e\lim_{x \to \infty} \Big(1 + \frac{1}{x}\Big)^x = e
- Continuity: f(x)f(x) is continuous at cc if:
- limx→c−f(x)=limx→c+f(x)\lim_{x \to c^-} f(x) = \lim_{x \to c^+} f(x)
- f(c)f(c) is defined
Derivative Rules
- Power Rule: ddx[xn]=nxn−1\frac{d}{dx} \big[x^n\big] = nx^{n-1}
- Product Rule: (fg)’=f’g+fg’(fg)’ = f’g + fg’
- Quotient Rule: (fg)’=f’g−fg’g2\Big(\frac{f}{g}\Big)’ = \frac{f’g - fg’}{g^2}
- Chain Rule: (f(g(x)))’=f’(g(x))⋅g’(x)(f(g(x)))’ = f’(g(x)) \cdot g’(x)
- Derivatives of trig functions:
- (sinx)’=cosx(\sin x)’ = \cos x
- (cosx)’=−sinx(\cos x)’ = -\sin x
- (tanx)’=sec2x(\tan x)’ = \sec^2 x
Integrals (AB Must-Know)
- Power Rule for Integration: ∫xndx=xn+1n+1+C, n≠−1\int x^n dx = \frac{x^{n+1}}{n+1} + C, \ n \neq -1
- ∫1xdx=ln∣x∣+C\int \frac{1}{x} dx = \ln |x| + C
- Trigonometric Integrals:
- ∫sinxdx=−cosx+C\int \sin x dx = -\cos x + C
