Practice Exam AP Calculus AB 2026

1.  Let \(f'(x)=x^2-4\). Which statement is true?

2. If \(f'(x)\) changes from positive to negative at \(x=c\), then:

3. Evaluate: \(\lim_{x\to0}\frac{\sin x – x}{x^3}\)

4. If \(f”(x)>0\) and \(f'(x)=0\) at \(x=c\), then:

5. The graph of \(f'(x)\) is shown below. It crosses the \(x\)-axis at \(x=-1\) and \(x=3\). Which is correct?

6. If \(f(x)=e^x\sin x\), then \(f'(x)\) is:

7. Evaluate: \(\lim_{x\to\infty}\frac{\ln x}{x}\)

8. If \(f'(x)=\frac{1}{x-2}\), where is \(f\) decreasing?

9. Which function grows fastest?

10. If \(f'(x)=0\) but \(f”(x)=0\), then:

11. \(\lim_{x\to0}\frac{e^x-1}{x}\) equals:

12. If \(f”(x)<0\), then \(f\) is:

13. A particle has velocity \(v(t)=t^2-4t+3\). When is it at rest?

14. If \(f'(x)>0\) and \(f”(x)>0\), then:

15. Evaluate: \(\int_0^1 \frac{1}{1+x^2} dx\)

16. If \(f(x)=x^3-3x\), number of critical points:

17. If \(f'(x)=\cos x\), then \(f(x)\) is:

18. \(\lim_{x\to0}\frac{\tan x}{x}\) equals:

19. If \(f'(x)=x-2\), then \(f\) is increasing when:

20. If \(f'(x)=x^2-1$\), then \(f\) has:

21. If \(f”(x)=6x\), inflection point at:

22. \(\int e^{3x}dx\) equals:

23. \(\lim_{x\to\infty}\frac{3x^2+1}{x^2}\) equals:

24. If \(f(x)=|x|\), then \(f'(0)\) is:

25. If \(f”(x)>0\), graph is:

26. If \(f(x)=x^2+1\), slope at \(x=1\):

27. If \(f'(x)=0\) and changes from + to -, then:

28. \(\lim_{x\to0}\frac{\sin x}{x}\) equals:

29. Evaluate: \(\lim_{x\to0}\frac{e^{2x}-1-2x}{x^2}\)

30. If \(f'(x)=x^3-3x^2\), at how many points does \(f\) have a local maximum?

31. A function satisfies \(f'(x)>0\) and \(f”(x)<0\) for all \(x\). Which is true?

32. The graph of \(f'(x)\) is shown:

Where does \(f\) have a local minimum?

33. If \(f(x)=\int_0^x (t^2-1)dt\), where is \(f\) decreasing?

34. Evaluate: \(\int_0^1 xe^{x^2}dx\)

35. If \(f'(x)=\sin x + x\), how many critical points does \(f\) have on \([-2,2]\)?

36. \(\lim_{x\to0}\frac{\ln(1+2x)-2x}{x^2}\)

37. If \(f'(x)=e^{-x^2}\), which is true?

38. If \(f(x)=x^x\), then \(f'(x)=\)

39. The graph of \(f(x)\) is shown:

How many inflection points does \(f\) have?

40. Evaluate: \(\int \frac{x}{x^2+1}dx\)

41. A particle has acceleration \(a(t)=2t\). If \(v(0)=1\), then \(v(t)=\)

42. If \(f”(x)=x(x-1)\), where is \(f\) concave up?

43. \(\lim_{x\to\infty}\left(x-\ln x\right)\)

44. If \(f'(x)=\frac{x}{x^2+1}\), where is \(f\) increasing?

45. The graph of \(f'(x)\) is shown:

Where is \(f\) concave down?

46. Evaluate: \(\int_0^1 \ln(1+x)dx\)

47. If \(f(x)=\frac{x}{x+1}\), then horizontal asymptote is:

48. Evaluate: \(\lim_{x\to1} \frac{\ln x}{x-1}\)

49. Which function has horizontal asymptote \(y=2$\)

50. If \(f”(x)<0\) for all \(x\), then \(f\) is: