AP Calculus AB Practice Quiz — 20 Free Sample Questions
AP Calculus AB covers limits, derivatives, and integrals through the Fundamental Theorem of Calculus. Equivalent to a first-semester college calculus course, the exam is taken by high school students seeking college credit in mathematics. Our quiz tests the core concepts and problem-solving techniques you need for the exam.
What this AP Calculus AB quiz helps you figure out
Use this page as a readiness check, not just a question bank. The point is to identify which concepts you can explain under pressure and which ones still fall apart when the wording changes.
Certificate exams usually punish shallow familiarity. A short diagnostic tells you whether your problem is domain coverage, scenario judgment, or weak retention across the most tested workflows.
Study path
This page works best as a three-step loop: quiz, focused review, then targeted follow-up in the coach and guide cluster.
Scenario judgment
Test whether you can choose the best next action, not just recall terms.
Tool familiarity
Measure whether you actually understand the platforms or workflows being tested.
Domain balance
See which major exam domain deserves your next study block.
Topic-specific study sequence
Baseline your readiness
Take the quiz before studying so you know which domain needs attention first.
Review by workflow
Cluster misses by process, tool, or scenario type.
Turn misses into a plan
Use the coach and guide cluster to reinforce the same concepts from different angles.
How to read your score
0-9 correct
You are still in the learn-the-framework stage. Focus on the core blueprint first.
10-15 correct
You have useful coverage, but one or two domains are still holding the score down.
16-20 correct
You are close to readiness. Study the misses as decision-making patterns, not isolated facts.
Build your study cluster before you start
The strongest SimpuTech path is not quiz-only. Pair the result with the matching coach, the best supporting guide, and one article that drills the exact topic family you miss most.
Coach
AP Calculus AB AI Study Coach
Use the coach for targeted follow-up once you know which concept family needs reinforcement.
Guide
AP Calculus AB 2026–27: Calculator Rules Change Four Times, and 68.3% Is No-Calculator
Open the guide when you need the broader exam roadmap, official facts, and next-step links in one place.
Articles
Best next reads for this quiz
Use the quiz explanations and AI coach together while the supporting article cluster is still growing for this topic.
Question styles you will see on this page
Sample angle 1
What is lim(x→2) of (x² - 4)/(x - 2)?
Factor: (x-2)(x+2)/(x-2) = x+2. As x→2, the limit = 4.
Sample angle 2
If f(x) = 3x⁴ - 2x² + 5, what is f'(x)?
Using the power rule: d/dx(3x⁴) = 12x³ and d/dx(-2x²) = -4x. Constants differentiate to 0.
Sample angle 3
What is the derivative of sin(x²) using the chain rule?
Chain rule: d/dx[sin(u)] = cos(u)·u', where u = x², u' = 2x. So the result is 2x·cos(x²).
What is lim(x→2) of (x² - 4)/(x - 2)?
About the AP Calculus AB and what to do after this result
The AP Calculus AB exam covers roughly a semester of college calculus, focusing on limits, derivatives, and integrals with applications. The exam is 3 hours and 15 minutes long and consists of two sections. Section I has 45 multiple-choice questions (30 without calculator, 15 with) worth 50% of the score. Section II has 6 free-response questions (2 with calculator, 4 without) worth the remaining 50%. Key topics include limits and continuity, differentiation rules (power, product, quotient, chain), implicit differentiation, related rates, curve sketching, optimization, Riemann sums, definite integrals, the Fundamental Theorem of Calculus (both parts), and basic differential equations including slope fields. Applications of derivatives and integrals — area between curves, accumulation, average value — are heavily tested. The national pass rate is approximately 60%, with a mean score around 3. Students who succeed typically develop strong algebraic fluency, practice with and without calculators, and work through past free-response questions from College Board. Common pitfalls include sign errors in chain rule applications, forgetting the constant of integration, and confusing Part 1 and Part 2 of the FTC. About 300,000 students take AP Calculus AB annually, making it one of the most common AP exams.
Next best steps
- Use the coach for targeted follow-up: AP Calculus AB AI Study Coach
- Use the authoritative guide: Exam guide hub
- Browse matching guides in Study Tips
Frequently Asked Questions
What is the format of the AP Calculus AB exam?
45 multiple-choice questions and 6 free-response questions. Total time is 3 hours 15 minutes. A graphing calculator is required for part of the exam.
What topics are on AP Calculus AB?
Limits and continuity, derivatives (rules, implicit, related rates), applications of derivatives, integration, Fundamental Theorem of Calculus, and basic differential equations.
What is the difference between AP Calculus AB and BC?
Calculus AB covers roughly one semester of college calc. BC covers both semesters, adding series, polar coordinates, parametric equations, and more integration techniques.
What score do I need for college credit?
Most colleges accept a 3 or higher. Selective colleges often require a 4 or 5 for credit or placement.