About AP Calculus AB
AP Calculus AB covers limits, derivatives and their applications, integrals, the Fundamental Theorem of Calculus and differential equations — roughly a first-semester university calculus course.
Advanced Placement · Mathematics · College Board (Advanced Placement Program)
AP Calculus AB Mock Tests, Syllabus & Complete Exam Guide
AP Calculus AB. Practise 20 full-length mock tests on the official pattern, drill every topic, and get the eligibility, syllabus, cut-off, rank and college details you need — all in one place.
AP Calculus AB at a glance
- Section I
- 45 MCQ · 1 h 45 min (50%)
- Section II
- 6 free response · 1 h 30 min (50%)
- Score
- 1–5
- Mocks here
- 20 full Section I tests
ModeSection I multiple choice + Section II free response
FrequencyOnce a year, in May
LanguagesEnglish
By the ExamguruX Editorial TeamReviewed for pattern accuracy against College Board (Advanced Placement Program)Last updated 13 October 2026
AP Calculus AB full-length mock tests
Attempt 20 full-length AP Calculus AB mock tests built on the official 45-question pattern. The first mock is free — every test comes with instant results and a step-by-step solution for each question.
AP Calculus AB Full Mock Test 01
Free45 Qs · 45 marks105 minEasy
AP Calculus AB Full Mock Test 02
45 Qs · 45 marks105 minModerate
AP Calculus AB Full Mock Test 03
45 Qs · 45 marks105 minHard
AP Calculus AB Full Mock Test 04
45 Qs · 45 marks105 minEasy
AP Calculus AB Full Mock Test 05
45 Qs · 45 marks105 minModerate
AP Calculus AB Full Mock Test 06
45 Qs · 45 marks105 minHard
AP Calculus AB Full Mock Test 07
45 Qs · 45 marks105 minEasy
AP Calculus AB Full Mock Test 08
45 Qs · 45 marks105 minModerate
AP Calculus AB Full Mock Test 09
45 Qs · 45 marks105 minHard
Unlock all AP Calculus AB tests
Try the first full-length mock free. Get the complete AP Calculus AB mock library, every topic test and all available languages for 3 months — a one-time ₹399 / 3 months.
AP Calculus AB — full access
₹399/ 3 months
- Every full-length mock test
- All topic-wise tests, every subject
- All available languages
- Step-by-step solution for every question
- Indicative marks-to-rank & cut-offs
Secure payment by Razorpay · one-time ₹399 for 3 months
AP Calculus AB topic-wise tests & syllabus
90 topic tests across 5 subjects — a focused set of 15 tests for every topic in the AP Calculus AB syllabus, tagged with approximate exam weightage so you practise where the marks are.
90 topic-wise tests · 15 per topic across 5 subjects. Pick a subject, expand a topic, and start drilling.
Limits & Continuity — Test 01
10 Qs · 10 marks10 minModerate
Limits & Continuity — Test 02
10 Qs · 10 marks10 minHard
Limits & Continuity — Test 03
10 Qs · 10 marks10 minEasy
Limits & Continuity — Test 04
10 Qs · 10 marks10 minModerate
Limits & Continuity — Test 05
10 Qs · 10 marks10 minHard
Limits & Continuity — Test 06
10 Qs · 10 marks10 minEasy
Limits & Continuity — Test 07
10 Qs · 10 marks10 minModerate
Limits & Continuity — Test 08
10 Qs · 10 marks10 minHard
Limits & Continuity — Test 09
10 Qs · 10 marks10 minEasy
Limits & Continuity — Test 10
10 Qs · 10 marks10 minModerate
Limits & Continuity — Test 11
10 Qs · 10 marks10 minHard
Limits & Continuity — Test 12
10 Qs · 10 marks10 minEasy
AP Calculus AB sample questions
A few real AP Calculus AB questions with answers and step-by-step solutions, in the exact style of the full mock tests.
Limits & ContinuitySample 1
What is lim (x → 2) of (x² − 4) / (x − 2)?
- A.2
- B.4
- C.1
- D.0
Solution: Factor: x² − 4 = (x − 2)(x + 2). After cancelling, the limit is 1(2 + 2) = 4.
DifferentiationSample 2
What is the derivative of sin(2x)?
- A.−2cos(2x)
- B.2cos(2x)
- C.2sin(2x)
- D.cos(2x)
Solution: By the chain rule, d/dx sin(2x) = 2cos(2x).
Applications of DerivativesSample 3
For f(x) = 3x² on [1, 3], what value of c satisfies the Mean Value Theorem?
- A.3
- B.8
- C.2
- D.1
Solution: f′(c) = 6c must equal (f(3) − f(1))/(3 − 1) = 3(1 + 3) = 12, so c = 2.
Integration & AccumulationSample 4
What is ∫ from -1 to 2 of (2x² − 6x − 6) dx?
- A.21
- B.-20
- C.-12
- D.-21
Solution: Antiderivative: 2x³/3 − 6x²/2 − 6x. Evaluating from -1 to 2 gives -21.
Applications of IntegrationSample 5
The region under y = x² from x = 0 to x = 7 is revolved about the x-axis. What is the volume of the solid?
- A.343π/2
- B.49π
- C.16807π/5
- D.49π/3
Solution: Disc method: V = π∫₀^7 (x²)² dx = 16807π/5.
About the AP Calculus AB exam
College-level differential and integral calculus for high-school students; may earn university credit.
AP Calculus AB eligibility & exam pattern
Check whether you meet the AP Calculus AB eligibility criteria and understand exactly how the paper is structured and marked before you plan your preparation.
Eligibility criteria
- Who can take it
- Any student; you do not need to have taken the AP course.
- Where
- Through a school or authorised AP test centre.
Exam pattern & marking
| Subject | Questions | Marks |
|---|---|---|
| Section I — Part A60 minutes, no calculator | 30 | 33.3% |
| Section I — Part B45 minutes, graphing calculator | 15 | 16.7% |
| Section II — Free response90 minutes (not included in these mocks) | 6 | 50% |
| Total | 51 | 100 |
Section I has 45 multiple-choice questions in 1 hour 45 minutes: Part A, 30 questions in 60 minutes without a calculator, and Part B, 15 questions in 45 minutes with a graphing calculator. Section II has 6 free-response questions in 90 minutes. Each section is 50% of the score. These mocks cover the full multiple-choice section (Section I); free-response questions are not included. Questions are computed exactly and set to be answerable without a calculator.
Duration: 1 hour 45 minutes (Section I).
How to prepare for AP Calculus AB
A proven, focused AP Calculus AB preparation method — from building strong fundamentals to peaking with full-length mocks.
- 1
Know the derivative rules cold
Product, quotient, chain and implicit differentiation appear throughout.
- 2
Link derivatives to meaning
Motion, rates of change and optimisation questions test interpretation.
- 3
Practise accumulation
Riemann sums, the FTC and average value are reliable points.
AP Calculus AB scores explained
AP exams are scored 1–5. The multiple-choice section is 50% of the score; the free-response section is the other 50%.
AP Calculus AB marks vs. rank
| Score range | Score | What it means |
|---|---|---|
| 5 | Extremely well qualified | Often earns credit at selective universities |
| 4 | Very well qualified | Commonly earns credit |
| 3 | Qualified | Earns credit at many universities |
Scores at a glance
Section I50%
Indicative marks: Multiple choice
Section II50%
Indicative marks: Free response
Format follows College Board's AP Calculus AB exam description. Confirm dates on apstudents.collegeboard.org.
How AP scores are used
Many universities award credit or advanced placement for scores of 3, 4 or 5; policies vary by university.
| Use | Where | Notes | Typical use |
|---|---|---|---|
| College credit / placement | USA, Canada and many other countries | Score of 3–5 | University-specific |
| Admissions | Global | Evidence of advanced coursework | — |
A representative set of institutes that admit through AP Calculus AB. Many more universitys participate in the counselling process.
AP Calculus AB important dates
The typical AP Calculus AB timeline, from notification to counselling. Dates are tentative until the official notification is released.
Registration
Usually by mid-November through your school or an authorised centre
Exams
First two weeks of May
Scores
Early July
AP Calculus AB — frequently asked questions
Quick, reliable answers to the questions AP Calculus AB aspirants ask most.
How many multiple-choice questions are on AP Calculus AB?
45: 30 without a calculator and 15 with a graphing calculator.
Start your AP Calculus AB preparation today
Take your first full-length mock free, see your predicted rank, and let the analysis show you exactly what to fix next.
