AP Calculus BC
Our AP Calculus BC course covers all the AB content plus the BC-only topics: further integration techniques, logistic models and Euler's method, parametric equations, polar coordinates and vector-valued functions, and infinite sequences and series, including Taylor and Maclaurin series. You practise both calculator and non-calculator sections and earn an AB subscore along the way. Lessons are live and one-to-one with a verified tutor, who uses College Board style multiple-choice and free-response questions and scores practice answers against the published rubrics. Suitable for students in the US and at international schools sitting the May exams.
Reviewed by M. Wazid, Master's in Mathematics, Jamia Millia IslamiaLast updated
$14 – $42
per hour
Free demo class · pay only if you continue
What you will learn
Learning outcomes
- Evaluate limits and continuity
- Apply advanced differentiation techniques
- Analyze functions using derivatives
- Solve optimization and related rates problems
- Evaluate definite and indefinite integrals
- Apply integration techniques
- Use the Fundamental Theorem of Calculus
- Solve differential equations
- Analyze parametric equations
- Analyze polar functions
- Work with vector-valued functions
- Determine convergence of infinite series
- Apply convergence tests
- Work with Taylor and Maclaurin series
- Solve AP-style multiple-choice and free-response problems
Prerequisites
- Algebra
- Geometry
- Trigonometry
- Precalculus
- Functions and graphs
- Exponential and logarithmic functions
- Polynomial and rational functions
- Basic limits
- Strong algebraic manipulation skills
Tags
Course structure
Syllabus(10 modules)
- Defining Limits and Limit Notation
- Estimating Limits from Graphs and Tables
- Determining Limits Using Limit Laws
- Algebraic Techniques for Limits
- Squeeze Theorem
- Types of Discontinuities
- Continuity at a Point
- Continuity over an Interval
- Removing Discontinuities
- Infinite Limits and Vertical Asymptotes
- Limits at Infinity and Horizontal Asymptotes
- Intermediate Value Theorem
What is AP Calculus BC?
In short: this course gives one-to-one online tutoring for AP Calculus BC. A verified maths tutor teaches all AB content plus series, parametric, polar and vector-valued functions, and free-response justification, using College Board-style practice.
AP Calculus BC is a College Board Advanced Placement course equivalent to first- and second-semester college calculus. It covers everything in AP Calculus AB plus parametric, polar and vector functions and infinite sequences and series. The exam is taken in May, scored 1 to 5, and also reports an AB subscore.
This course covers all ten BC units one to one with a verified calculus tutor.
Official specification: AP Calculus BC exam (College Board).
For wider support, see our maths tutoring page, or start with the AP Calculus AB course if calculus is new to you.
What is the AP Calculus BC exam format?
The AP Calculus BC exam is a hybrid digital exam lasting 3 hours 10 minutes: you answer multiple-choice questions in the Bluebook app and handwrite free-response answers in a paper booklet. Calculators are permitted. You can't take both AP Calculus AB and BC in the same year.
| Section | Questions | Time | Weighting |
|---|---|---|---|
| I: Multiple choice | 42 | 1 hour 40 minutes | 50% |
| II: Free response | 6 | 1 hour 30 minutes | 50% |
AP exams are scored on a 1 to 5 scale. Exam details from AP Students (College Board).
Which units does AP Calculus BC cover?
| Unit | Topic |
|---|---|
| 1 | Limits and continuity |
| 2 | Differentiation: definition and fundamental properties |
| 3 | Differentiation: composite, implicit and inverse functions |
| 4 | Contextual applications of differentiation |
| 5 | Analytical applications of differentiation |
| 6 | Integration and accumulation of change |
| 7 | Differential equations |
| 8 | Applications of integration |
| 9 | Parametric equations, polar coordinates and vector-valued functions |
| 10 | Infinite sequences and series |
How do you master series in AP Calculus BC?
Unit 10 is the largest BC-only unit.
- Learn when to use each convergence test: nth term, integral, comparison, ratio and alternating series.
- Build Taylor and Maclaurin polynomials for standard functions.
- Find the interval and radius of convergence.
- Use the alternating series and Lagrange error bounds.
- Practise free-response series questions from past exams.
How do you answer AP Calculus free-response questions?
Free-response questions reward clear reasoning as much as the answer.
- Show the set-up: the derivative or integral you are evaluating.
- Use correct notation, including units in context.
- Justify conclusions with theorems such as the Mean Value Theorem or the first derivative test.
- Write answers in context, such as rate of change per hour.
- Don't round intermediate values; give three decimal places where required.
What does a worked BC series question look like?
Here is a typical series question: find the sum of the geometric series 1 + 1/2 + 1/4 + 1/8 + …
| Step | Working | ||
|---|---|---|---|
| First term and ratio | a = 1, r = 1/2 | ||
| Convergence | r | < 1, so the series converges | |
| Sum formula | S = a ÷ (1 − r) | ||
| Answer | 1 ÷ (1 − 1/2) = 2 |
Where do students lose marks in AP Calculus BC?
Students most often lose free-response points by not answering exactly what the task verb asks, skipping units or justification, leaving work unlabelled and running out of time on long questions.
| Mark-loser | What to do instead |
|---|---|
| Ignoring the task verb | Answer exactly what "justify", "explain" or "calculate" asks |
| Missing units or justification | Show units and reasoning for every answer |
| Unlabelled work | Label graphs, diagrams and steps |
| Time pressure | Practise timed free-response sets |
| Guessing patterns in multiple choice | Eliminate options using reasoning |
How the lessons work
Lessons are live and one to one on video with a shared whiteboard. Your tutor uses released College Board free-response questions and scoring guidelines. See also AP Calculus AB, AP Physics and our Mathematics subject page.
AP Calculus BC tutor online: who this course is for, prerequisites and study plan
An AP Calculus BC tutor online gives you live 1-to-1 lessons on series, parametric and polar functions and integration techniques, with free-response practice.
This course suits high school students taking AP Calculus BC at school or self-studying, in the US and abroad.
Prerequisites: algebra, trigonometry, precalculus and basic limits.
Course length: 40 one-hour lessons across 10 units.
| Stage | Topics | What you can do afterwards |
|---|---|---|
| 1 | Limits and continuity; differentiation | Differentiate any standard function |
| 2 | Applications of differentiation | Solve rates and optimisation problems |
| 3 | Integration; differential equations; applications of integration | Integrate and find areas and volumes |
| 4 | Parametric, polar and vector functions; infinite sequences and series | Test series and find Taylor polynomials |
Where it leads: see the AP Calculus AB course to build the base, or our maths tutoring page.
AP Calculus BC: frequently asked questions
What is the difference between AP Calculus AB and BC?
BC covers all AB content plus parametric, polar and vector functions and infinite series.
How long is the AP Calculus BC exam?
3 hours 10 minutes: 42 multiple-choice and 6 free-response questions.
Does BC give an AB subscore?
Yes. The BC exam reports an AB subscore based on the AB content.
Is a calculator allowed?
Calculators are permitted for the exam; check the College Board AP Calculus exam page and calculator policy for exactly where they can be used.
What is the hardest part of AP Calculus BC?
Infinite series, especially convergence tests and error bounds.
Can I take BC without taking AB first?
Yes, if you have a strong precalculus background. Many students go straight to BC.
How do I get a 5 in AP Calculus BC?
Master series and polar, practise released free-response questions and learn from scoring guidelines.
Do you use College Board materials?
Yes. Tutors use released free-response questions and scoring guidelines. FLN Tutors is not affiliated with the College Board.
How much does an AP Calculus tutor cost?
The price depends on the tutor and session length. You see the hourly rate before booking, with no subscription.
Can I study online from any country?
Yes. Lessons are online and scheduled around your time zone.
How many multiple-choice questions are on the AP Calculus BC exam?
42 questions, worth 50% of the score.
How many free-response questions are there?
6 questions, worth 50% of the score.
Is the AP Calculus BC exam digital?
It is a hybrid digital exam: multiple choice in the Bluebook app and handwritten free-response answers in a paper booklet.
Is AP Calculus BC hard?
AP Calculus BC is one of the more demanding AP exams because it covers all of AB plus series, parametric and polar functions and extra integration techniques at a fast pace. Students with strong algebra and steady practice do well. Series and convergence tests usually need the most practice, so a tutor focuses there.
Is AP Calculus BC worth taking?
AP Calculus BC is worth taking if you are strong in maths and plan to study engineering, physics, maths, economics or computer science, because a high score can earn more college credit than AB. If calculus is new to you or your schedule is heavy, AB may be the better choice. Discuss it with your school counsellor.
Do you offer lessons in my time zone?
Yes. Lessons are online, so you can book times that suit your time zone.
Can I take AP Calculus AB and BC in the same year?
No. College Board does not allow both exams in the same year.
How do I find the sum of a geometric series?
If |r| < 1, the sum is a ÷ (1 − r). For 1 + 1/2 + 1/4 + …, the sum is 2.
Which BC topics are not in AB?
Series, parametric, polar and vector-valued functions, plus some extra integration and differential equation techniques.
Where can I find AP Calculus BC past exam questions?
College Board publishes past AP Calculus BC free-response questions with scoring guidelines on its AP Central website. Work through them under timed conditions, then mark your answers with the guidelines. Your tutor uses the results to choose which units to revisit before the exam.
Can I get an AP Calculus BC tutor online?
Yes. You can learn with a 1-to-1 AP Calculus BC tutor online through live video lessons from any country. Your tutor explains series and parametric topics step by step, shows you how to justify free-response answers and practises under exam timing.
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