About AP Calculus BC
AP Calculus BC includes all AB content plus infinite series, Taylor polynomials, parametric, polar and vector functions, Euler's method, logistic growth and integration by parts.
Advanced Placement · Mathematics · College Board (Advanced Placement Program)
AP Calculus BC Mock Tests, Syllabus & Complete Exam Guide
AP Calculus BC. 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 BC 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 BC full-length mock tests
Attempt 20 full-length AP Calculus BC 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 BC Full Mock Test 01
Free45 Qs · 45 marks105 minEasy
AP Calculus BC Full Mock Test 02
45 Qs · 45 marks105 minModerate
AP Calculus BC Full Mock Test 03
45 Qs · 45 marks105 minHard
AP Calculus BC Full Mock Test 04
45 Qs · 45 marks105 minEasy
AP Calculus BC Full Mock Test 05
45 Qs · 45 marks105 minModerate
AP Calculus BC Full Mock Test 06
45 Qs · 45 marks105 minHard
AP Calculus BC Full Mock Test 07
45 Qs · 45 marks105 minEasy
AP Calculus BC Full Mock Test 08
45 Qs · 45 marks105 minModerate
AP Calculus BC Full Mock Test 09
45 Qs · 45 marks105 minHard
Unlock all AP Calculus BC tests
Try the first full-length mock free. Get the complete AP Calculus BC mock library, every topic test and all available languages for 3 months — a one-time ₹399 / 3 months.
AP Calculus BC — 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 BC topic-wise tests & syllabus
90 topic tests across 8 subjects — a focused set of 15 tests for every topic in the AP Calculus BC syllabus, tagged with approximate exam weightage so you practise where the marks are.
90 topic-wise tests · 15 per topic across 8 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
AP Calculus BC sample questions
A few real AP Calculus BC questions with answers and step-by-step solutions, in the exact style of the full mock tests.
Limits & ContinuitySample 1
What is lim (x → 0) of sin(1x) / (9x)?
- A.0
- B.1/9
- C.9
- D.1
Solution: sin(1x)/(9x) = (1/9) · sin(1x)/(1x) → 1/9 × 1 = 1/9.
DifferentiationSample 2
What is the derivative of ln(4x)?
- A.1/(4x)
- B.ln(4)/x
- C.4/x
- D.1/x
Solution: d/dx ln(4x) = 4/(4x) = 1/x.
Applications of DerivativesSample 3
For f(x) = 3x² on [0, 2], what value of c satisfies the Mean Value Theorem?
- A.2
- B.1
- C.4
- D.5
Solution: f′(c) = 6c must equal (f(2) − f(0))/(2 − 0) = 3(0 + 2) = 6, so c = 1.
Integration & AccumulationSample 4
What is ∫ from -2 to -1 of (4x² − 3x − 2) dx?
- A.-15
- B.-71/6
- C.77/6
- D.71/6
Solution: Antiderivative: 4x³/3 − 3x²/2 − 2x. Evaluating from -2 to -1 gives 71/6.
Applications of IntegrationSample 5
What is the area of the region enclosed by y = x and y = x²?
- A.1/2
- B.1/6
- C.1/3
- D.1/12
Solution: The curves meet at x = 0 and x = 1. Area = ∫₀^1 (1x − x²) dx = 1³/2 − 1³/3 = 1/6.
SeriesSample 6
What is the sum of the infinite series 4 + 4(1/6) + 4(1/6)² + …?
- A.The series diverges
- B.4/5
- C.24/5
- D.24/7
Solution: Geometric series with first term 4 and ratio 1/6: sum = 4 / (1 − 1/6) = 24/5.
About the AP Calculus BC exam
Full-year university calculus (AB topics plus series, parametric, polar and vector functions); may earn university credit.
AP Calculus BC eligibility & exam pattern
Check whether you meet the AP Calculus BC 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 |
AP Calculus BC has the same structure as AB — 45 multiple-choice questions (30 without a calculator, 15 with) in 1 hour 45 minutes, then 6 free-response questions in 90 minutes — and adds series, parametric, polar and vector functions and further integration techniques. Students also receive an AB subscore. These mocks cover the full multiple-choice section (Section I); free-response questions are not included.
Duration: 1 hour 45 minutes (Section I).
How to prepare for AP Calculus BC
A proven, focused AP Calculus BC preparation method — from building strong fundamentals to peaking with full-length mocks.
- 1
Series are high-yield
Know geometric, p-series, ratio test and Taylor coefficients.
- 2
Parametric and polar
dy/dx, speed and polar area follow standard formulas — practise them until automatic.
- 3
Do not neglect AB topics
About 60% of the exam is shared with AB.
AP Calculus BC 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 BC 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 BC 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 BC. Many more universitys participate in the counselling process.
AP Calculus BC important dates
The typical AP Calculus BC 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 BC — frequently asked questions
Quick, reliable answers to the questions AP Calculus BC aspirants ask most.
Does AP Calculus BC include AB topics?
Yes. About 60% of the exam covers AB content, and BC students receive an AB subscore.
Start your AP Calculus BC preparation today
Take your first full-length mock free, see your predicted rank, and let the analysis show you exactly what to fix next.
