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With so many topics-limits, derivatives, integrals, and more—preparing for the AP Calculus AB exam can seem overwhelming. It is even more difficult to find practice questions that correspond with the actual exam.
For this reason, we put together a small set of more than 500 AP Calculus AB practice problems with complete answers, arranged by subject, and complete practice exams. It is free to download, exam-level, and simple to use. Ideal for last-minute review or early preparation for the 2025 test.
| Resource | Description | Download Link |
|---|---|---|
| Practice Problems Set 1 | 200+ problems covering Units 1-4 with complete solutions | Download PDF |
| Practice Problems Set 2 | 200+ problems covering Units 5-8 with detailed explanations | Download PDF |
| Full-Length Practice Test | 2 complete exams (45 MC + 6 FRQ each) with answer keys | Download PDF |
| Topic-Wise Workbook | Organized problems by difficulty level (Easy/Medium/Hard) | Download PDF |
| Calculator Practice Set | 100+ problems designed for calculator section preparation | Download PDF |
Pro tip: Avoid attempting to do everything at once! Use the practice sets to improve in those particular areas after using the topic workbook to identify your areas of difficulty. When you’re feeling confident and want to replicate the actual exam experience, save the full-length exams.
We’ve broken down every single topic you’ll see on the AP Calculus AB exam. Here’s what you’ll find inside:
| Unit | Topic | Total Problems | Easy | Medium | Hard | Key Concepts Covered |
|---|---|---|---|---|---|---|
| Unit 1 | Limits & Continuity | 50 | 15 | 25 | 10 | Evaluating limits algebraically & graphically, one-sided limits, infinite limits, continuity, IVT, Squeeze Theorem |
| Unit 2 | Differentiation Basics | 60 | 20 | 30 | 10 | Power rule, product rule, quotient rule, chain rule, exponential/logarithmic/trig derivatives, higher-order derivatives |
| Unit 3 | Advanced Differentiation | 50 | 10 | 25 | 15 | Implicit differentiation, inverse function derivatives, logarithmic differentiation, related rates problems |
| Unit 4 | Applications of Derivatives | 80 | 20 | 40 | 20 | Critical points, First/Second Derivative Tests, curve sketching, optimization, related rates, linear approximation, MVT |
| Unit 5 | Integration Fundamentals | 70 | 25 | 30 | 15 | Basic antiderivatives, u-substitution, definite/indefinite integrals, integral properties, FTC Parts 1 & 2, Riemann sums |
| Unit 6 | Applications of Integration | 80 | 15 | 40 | 25 | Area between curves, volume (disk/washer method), average value, position/velocity/acceleration, accumulation functions |
| Unit 7 | Differential Equations | 40 | 15 | 20 | 5 | Slope fields, separation of variables, exponential/logistic growth models, initial value problems |
| Unit 8 | Mixed Review & Challenge | 70 | 10 | 30 | 30 | Multi-concept problems, exam-level difficulty, trap questions, calculator/non-calculator sections |
| TOTAL | All Topics | 500 | 130 | 240 | 130 | Complete AP Calculus AB Exam Coverage |
| Problem Type | Questions | Format | Calculator | Solutions Include | Best For |
| MCQs | 300+ | 4 options | 50% no-calc, 50% calc | Correct answers + explanations | Speed & concept checks |
| FRQs | 24 (4 sets) | Multi-part | Mixed | Step-by-step work + scoring rubric | Show-your-work mastery |
| Topic Mini Tests | 16 tests | Mixed | Varies | Focused practice + feedback | Topic mastery |
| Full Practice Exams | 2 exams | 45 MC + 6 FRQ | Real exam format | Full explanations + score chart | Exam simulation |
| Diagnostic Test | 1 test | Mixed | Both | Gap analysis + study plan | Starting point evaluation |
| Strategy | Why It Helps | Suggested Frequency |
| Diagnostic Practice | Identifies weak topics early | Once at the start |
| Topic-by-Topic Practice | Builds focused mastery | 20–30 questions per topic |
| Timed Practice | Improves speed & exam readiness | 2–3 times per week |
| Full-Length Tests | Simulates real exam conditions | 1 week before exam |
| Error Analysis | Helps learn from mistakes | After every session |
| Mixed Review | Reinforces all topics | Final 2 weeks before exam |
Download Multiple choice practice test
| S.No | Common Mistake | How to Avoid It | Points at Risk |
| 1 | Sign errors in derivatives (especially chain rule) | Double-check every step, circle all negative signs | 3-5 points |
| 2 | Incorrect u-substitution (not substituting dx) | Always write “du = ___ dx” explicitly | 4-6 points |
| 3 | Forgetting +C in indefinite integrals | Add +C immediately after integrating | 1-2 points |
| 4 | Misapplying chain rule | Identify f(g(x)) composition before differentiating | 3-5 points |
| 5 | Related rates setup errors | Draw diagram first, label all variables with (t) | 8-10 points |
| 6 | Volume method confusion (disk vs washer) | Always draw cross-section first | 4-6 points |
| 7 | Not showing work on FRQs | Write every step with proper notation | 6-9 points |
| 8 | Using calculator on non-calculator section | Practice both sections separately | Disqualification risk |
| 9 | Poor time management | Skip hard problems, return later (2-min rule) | 5-12 points |
| 10 | Direct substitution on indeterminate limits | Check for 0/0 or ∞/∞ first, then factor | 2-4 points |
Pro Tip: The top 3 mistakes alone cost students an average of 15-20 points per exam. Master these and you’re already ahead.
Understanding what’s heavily tested helps you prioritize your study time:
| Unit | Topics Covered | Exam Weightage | Number of Practice Problems |
| Unit 1 | Limits & Continuity | 10-12% | 50 problems |
| Unit 2 | Differentiation: Definition & Basic Rules | 10-12% | 60 problems |
| Unit 3 | Differentiation: Composite, Implicit, Inverse | 9-13% | 50 problems |
| Unit 4 | Applications of Differentiation | 15-18% | 80 problems |
| Unit 5 | Analytical Applications of Differentiation | 15-18% | 70 problems |
| Unit 6 | Integration & Accumulation | 17-20% | 70 problems |
| Unit 7 | Differential Equations | 6-12% | 40 problems |
| Unit 8 | Applications of Integration | 10-15% | 80 problems |
Have you noticed that over 60% of the test consists of Units 4, 5, 6, and 8? The majority of your practice time should be spent there!
Weeks 1-2: Build Your Foundation – Start with thirty problems from Units 1-3 each day. Make an effort to fully comprehend limits and fundamental derivatives. To reinforce what you learned, go over the formula sheet after every practice session.
Weeks 3-4: Master Applications – Increase the number of problems from Units 4-5 to 40 per day. This is where calculus really comes into play—related rates, curve sketching, and optimization. To assess your progress, take one mini-test per topic every week.
Weeks 5-6: Integration Deep Dive – Proceed with 40 problems from Units 6–8 every day. Practice FRQs (aim for two each week). During this time, make sure you’re becoming accustomed to using calculator functions.
Week 7: Full-Length Practice Mode – Take two full practice tests in authentic testing settings (timed, phone-free, appropriate breaks). This is very important! Examine each error in detail and identify your mistakes.
Week 8: Final Polish – Do 20 mixed review problems daily. Go back through all your FRQ solutions. This is also when you should ease up a bit—don’t burn out right before the exam!
4-Week Intensive Plan (Crunch Time)
Week 1: Every day, tackle 50 problems that cover every unit. To find out where you stand, take one complete practice test.
Week 2: Every day, concentrate on 60 problems, particularly the high-weightage items in Units 4, 6, and 8. Practice all kinds of FRQ.
Week 3: Take two lengthy practice exams. Next, use 40 targeted problems to focus on your weakest areas.
Week 4: Mixed review with 30 problems daily. Take your final practice test 3 days before the actual exam, then just relax and trust your preparation.
| Calculator Function | When to Use | How to Use | Common Mistakes to Avoid |
| nDeriv (Numerical Derivative) | Finding derivative at a specific point | nDeriv(function, x, value) | Don’t use for symbolic derivatives; only for numerical values |
| fnInt (Definite Integral) | Computing definite integrals with messy functions | fnInt(function, x, lower, upper) | Remember to write the setup first before using calculator |
| Solve Function | Finding intersection points, zeros, solving equations | Solve(equation, x, guess) | Need a reasonable guess value; may miss multiple solutions |
| Graph Function | Visualizing problems, checking work | Y= menu, then GRAPH | Make sure window settings show relevant portion |
| Calc Menu (Max/Min) | Finding maximum/minimum values | 2nd CALC → 3 (minimum) or 4 (maximum) | Must set appropriate left/right bounds |
| Table Function | Evaluating function at multiple points | 2nd TABLE after defining Y= | Make sure table settings (TblStart, ΔTbl) are appropriate |
| Intersection | Finding where two curves meet | 2nd CALC → 5 (intersect) | Calculator needs both functions graphed first |
| Strategy | Description | When to Apply |
| ✓ DO use calculator for: | Numerical derivatives, definite integrals, graphical equation solving, checking algebra, complex evaluations | Calculator-allowed sections (1B & 2B) |
| ✗ DON’T use calculator for: | Symbolic derivatives/integrals, justification problems, showing algebra, finding exact values, “show that/prove” questions | Non-calculator sections (1A & 2A) |
AP Calculus AB is easier to learn when you have the correct Study Resources. To help students improve their comprehension and test performance, TestprepKart provides a number of free downloadable e-books that cover every essential idea and formula required to succeed in AP AP Calculus AB and other AP science courses.
1. In the USA, where can I find practice problems and solutions for AP Calculus AB?
The College Board, academic platforms, and tutoring websites all provide solved AP Calculus AB practice PDFs. For FRQs, MCQs, and step-by-step solutions to enhance exam performance, students prefer downloadable PDFs.
2. Do completed AP Calculus AB PDFs qualify for a score of 4 or 5?
High scorers use timed practice, official FRQs, mock exams, and concept review in addition to solved PDFs, which aid in concept revision. Students require real exam-style questions and regular problem-solving in order to consistently score 4–5.
3. What kinds of practice questions work best for AP Calculus AB?
Differential equations, integrals, limits, derivatives, and area-volume applications are examples of mixed sets. Calculator vs. non-calculator practice, MCQs with reasoning, and FRQs with complete answers are the most beneficial for students.
4. Are practice PDFs for AP Calculus AB sufficient to receive a 5?
Top scorers combine PDFs with College Board past papers, AP Classroom progress checks, and guided practice through review books or tutoring to help with concept revision and problem-solving.
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