AP CALC AB Cheat Sheet 2026

The 30 highest-yield AP CALC AB facts, distilled from real exam questions. Print it, save it as a PDF, or study it here — free, no sign-up.

1. Let f(x) = x⁴ − 4x³. Which statement about f at its critical points is correct? → f has a local minimum at x = 3 and no local extremum at x = 0.
2. If f(x) = x² sin x, what is f′(π)? → −π²
3. Evaluate lim (x→0) (e^(2x) − 1 − 2x) / x². → 2
4. Water flows into a tank at a rate of r(t) = 2t + 1 gallons per minute. If the tank holds 5 gallons at t = 0, how many gallons are in the tank at t = 3 minutes? → 17
5. What is lim(x→0) (√(x + 9) − 3)/x? → 1/6
6. A slope field is drawn for dy/dx = x − y. At which of the following points is the slope segment horizontal? → (2, 2)
7. A particle moves along a line with velocity v(t) = t² − 4t + 3 for 0 ≤ t ≤ 3. What is the total distance the particle travels on this interval? → 8/3
8. What is the value of ∫ from 0 to 2 of (3x² − 2x) dx? → 4
9. The point (1, 2) lies on the curve x² + xy + y² = 7. What is dy/dx at that point? → −4/5
10. What is lim(x→∞) (3x² + 5x)/(2x² − 1)? → 3/2
11. A particle moves along a line with position s(t) = t³ − 6t² + 9t for t ≥ 0. At which time is the particle speeding up? → t = 4
12. Which of the following functions is continuous at x = 0 but not differentiable at x = 0? → f(x) = x^(2/3)
13. If ∫ from 2 to 6 of f(x) dx = 10 and ∫ from 2 to 4 of f(x) dx = 3, what is ∫ from 6 to 4 of f(x) dx? → −7
14. If f(x) = x² / (x + 1), what is f′(1)? → 3/4
15. What is the average value of f(x) = sin x on the interval [0, π]? → 2/π
16. Let f(x) = x² for x ≠ 1 and f(1) = 3. Which statement is true? → lim(x→1) f(x) = 1, but f is not continuous at x = 1
17. What is lim(x→2) (x² − 4)/(x − 2)? → 4
18. Let f(x) = x³ + x + 1, which is one-to-one. If g is the inverse function of f, what is g′(3)? → 1/4
19. Suppose f(2) = 1 and f′(2) = 4. If h(x) = [f(x)]³, what is h′(2)? → 12
20. Which function is the solution to dy/dx = −x/y with initial condition y(0) = 2? → y = √(4 − x²)
21. A left Riemann sum with 4 subintervals of equal width is used to approximate ∫ from 0 to 4 of x² dx. What is the value of the sum? → 14
22. What is the value of ∫ from 0 to 1 of x/(x² + 1) dx? → (1/2)·ln 2
23. Let f(x) = (x² − x − 6)/((x − 3)(x + 1)). At which value of x does f have a removable discontinuity? → 3
24. If dy/dx = y² and y(0) = 1, what is y(1/2)? → 2
25. A slope field is drawn for dy/dx = sin x. Which statement about the field is true? → Slope segments are parallel along every vertical line.
26. What is the particular solution to dy/dx = x/y with initial condition y(0) = −2? → y = −√(x² + 4)
27. The function f is continuous on the closed interval [1, 4], with f(1) = −3 and f(4) = 6. Which statement must be true? → f(c) = 0 for some c in (1, 4)
28. Which function is the solution to dy/dx = y − 4 with y(0) = 1? → y = 4 − 3e^x
29. Let f(x) = x² on the interval [0, 3]. At what value of c in (0, 3) does f(c) equal the average value of f on [0, 3]? → √3
30. A function y = f(t) satisfies dy/dt = −3y with f(0) = 6. What is f(ln 2)? → 3/4