---
title: "AP Calculus AB/BC Guided Practice"
description: "Fiveable has 16,707 AP Calculus AB/BC multiple-choice practice questions across 10 units. Practice one unit or topic at a time."
canonical: "https://fiveable.me/ap-calc/guided-practice"
type: "guided-practice"
subject: "AP Calculus AB/BC"
---

# AP Calculus AB/BC Guided Practice

## Overview

Fiveable has 16,707 AP Calculus AB/BC multiple-choice practice questions across 10 units. Practice one unit or topic at a time.

## Practice Questions by Unit

- Unit 1 – Limits and Continuity: 2,259 multiple-choice questions
- Unit 2 – Fundamentals of Differentiation: 1,325 multiple-choice questions
- Unit 3 – Composite, Implicit, and Inverse Functions: 737 multiple-choice questions
- Unit 4 – Contextual Applications of Differentiation: 1,042 multiple-choice questions
- Unit 5 – Analytical Applications of Differentiation: 2,161 multiple-choice questions
- Unit 6 – Integration and Accumulation of Change: 2,239 multiple-choice questions
- Unit 7 – Differential Equations: 1,688 multiple-choice questions
- Unit 8 – Applications of Integration: 1,805 multiple-choice questions
- Unit 9 – Parametric Equations, Polar Coordinates, and Vector–Valued Functions (BC Only): 1,317 multiple-choice questions
- Unit 10 – Infinite Sequences and Series (BC Only): 2,134 multiple-choice questions

## Sample Question

Consider $\lim_{x \to 0} \frac{\sqrt{x + 4} - 2}{x}$. Substituting $x = 0$ yields $\frac{0}{0}$. Which algebraic technique transforms this expression into an equivalent form that allows direct limit evaluation?

- (A) Multiplying by the conjugate $\frac{\sqrt{x+4}+2}{\sqrt{x+4}+2}$ yields $\frac{x}{x(\sqrt{x+4}+2)} = \frac{1}{\sqrt{x+4}+2}$
- (B) Factoring out $\sqrt{x}$ from the numerator simplifies to $\frac{\sqrt{x}(\sqrt{1+4/x}-2/\sqrt{x})}{x}$
- (C) Dividing numerator and denominator by $\sqrt{x}$ yields $\frac{\sqrt{1+4/x}-2/\sqrt{x}}{1}$, which approaches $-\infty$
- (D) Using the identity $\sqrt{a} - b = \frac{a - b^2}{\sqrt{a}+b}$ directly gives $\frac{x}{\sqrt{x+4}+2}$ without further simplification

**Answer: (A)** Rationalizing the numerator by multiplying by the conjugate eliminates the radical. The numerator becomes $(x+4) - 4 = x$, which cancels the denominator's $x$. The resulting equivalent form $\frac{1}{\sqrt{x+4}+2}$ is continuous at $x = 0$, yielding limit $\frac{1}{4}$.

## Related Practice

- [Calculator FRQ practice: Calculator-Required FRQ questions scored by part](/ap-calc/frqs/calculator)
- [No-Calculator FRQ practice: No-Calculator FRQ questions scored by part](/ap-calc/frqs/no-calculator)
- [AP Calculus AB unit tests: a timed practice test for every unit](/ap-calc-ab/unit-test)
- [AP Calculus BC unit tests: a timed practice test for every unit](/ap-calc-bc/unit-test)
- [AP Calculus AB full-length practice exams](/ap-calc-ab/practice-exams)
- [AP Calculus BC full-length practice exams](/ap-calc-bc/practice-exams)
- [AP Calculus AB/BC subject hub](/ap-calc)

## About This Document

Canonical Fiveable pages are available as Markdown at the same path plus `.md`.

- [llms.txt](https://fiveable.me/llms.txt): index of Fiveable's sections and URL patterns
- [llms-full.txt](https://fiveable.me/llms-full.txt): complete subject and unit listing
- [MCP server](https://fiveable.me/mcp): call Fiveable as tools instead of fetching pages (`https://fiveable.me/api/mcp`)
- [MCP server for AP teachers](https://fiveable.me/mcp/teachers): a teacher's classes, assignments and AP-rubric grading (`https://fiveable.me/api/mcp/teacher`)