AP Calculus AB Practice Questions

5 free AP Calculus AB practice questions with worked answers. Tap an option to check your answer and read the explanation — then get a personalized study plan.

Question 1Finding Limits

What is $\lim_{x \to 3} \frac{x^2 - 9}{x - 3}$ ?

Question 2Continuity

A function $f$ is defined as $f(x) = \begin{cases} x^2 + 1 & x < 2 \\ 3x - 1 & x \geq 2 \end{cases}$ . Is $f$ continuous at $x = 2$ ?

Question 3Limits at Infinity and Asymptotes

What is $\lim_{x \to \infty} \frac{5x^3 + 2x}{3x^3 - 7}$ ?

Question 4Squeeze Theorem and Special Limits

What is $\lim_{x \to 0} \frac{\sin(5x)}{x}$ ?

Question 5Basic Differentiation Rules

If $f(x) = 4x^3 - 2x^2 + 7x - 5$ , what is $f'(x)$ ?

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