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AP Calculus BC Tutoring & Prep Course

One-to-one AP Calculus BC tutoring, with full past-paper practice and a personalised study plan built around your target grade.

Since 2008, TestPrep Europe has taught AP Calculus BC through one-to-one tutoring and small-group courses on its own online learning platform. The programme combines the AP syllabus with subject teaching, problem solving and past-paper practice.

One-to-one and small groups · Live online · College Board curriculum

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About the subject

AP Calculus BC: what it covers and who it suits

AP Calculus BC tutoring at TestPrep Europe covers everything in AB plus the two BC-only units — Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions and Unit 10: Infinite Sequences and Series — and the extra BC topics inside Units 6–8, such as integration by parts, partial fractions, improper integrals and logistic models. The exam returns both an AB subscore and a BC score, so the AB foundation has to be airtight before BC topics layer on top.

  • All 10 BC units covered, AB material reviewed first as the foundation
  • Series convergence tests practised as a flowchart, not as memorisation
  • Parametric, polar and vector calculus drilled with timed FRQs
Read more

AP Calculus BC suits students targeting mathematics, physics and engineering. It covers everything in AB plus infinite sequences and series, Taylor and Maclaurin series, parametric equations and polar coordinates. A successful score typically places students out of two semesters of university calculus, a major advantage for STEM applicants and a meaningful tuition saving at private universities.

AP Calculus BC covers the equivalent of two semesters of university calculus. It includes all of AB (limits, derivatives, integrals, differential equations) and adds parametric, polar and vector functions, plus infinite sequences and series. Taylor and Maclaurin series are particularly important: they let students approximate transcendental functions with polynomials and underpin huge swathes of physics and engineering. On exam day students receive both a BC score and an AB sub-score, giving universities flexibility in awarding credit. Our BC programme tailors the pacing to each student's incoming background — students arriving from IB Math AA HL, for instance, already have most of the parametric and series content, so we focus tutoring time on AP-specific FRQ formatting and the alternating series error bound.

One-to-one AP Calculus BC tutoring

Our one-to-one AP tutoring is built entirely around the student's current level and target score. Each lesson works on your specific weak topics, drills exam-format questions and teaches free-response and essay technique with the College Board's scoring guidelines in front of us. Our tutors follow every revision of the Course and Exam Description, so the work you put in matches what is rewarded in May.

AP Calculus BC small-group course

Our small-group AP courses (no more than 6 students per class) give you a structured weekly programme alongside students aiming for the same score. The syllabus follows the College Board's Course and Exam Description unit by unit, and every lesson is taught live online.

Exam

AP Calculus BC exam format

The College Board runs the AP Calculus BC exam every May. Sections, timing and weighting:

  • Section I: Multiple Choice

    50%

    42 questions in 1 hour 40 minutes. Part A (29 questions, 62 minutes, no calculator) and Part B (13 questions, 38 minutes, graphing calculator). AB and BC share the same multiple-choice structure.

  • Section II: Free Response

    50%

    6 questions in 1 hour 30 minutes. Part A (2 questions, 30 minutes, calculator) and Part B (4 questions, 60 minutes, no calculator).

  • Exam delivery

    Hybrid digital

    Multiple choice is answered in Bluebook; free-response answers are handwritten in a paper booklet.

How do I register for the exam?
  • You can take AP Exams without taking the AP course at your school, but you can't register on your own.
  • Find a school that runs AP Exams and ask its AP coordinator to place you in an "exam only" section; enter the join code in My AP as soon as you get it. In some countries, College Board also lists authorized AP test centers you can register with directly.
  • Schools place their exam orders by mid-November; late additions, up to about mid-March, cost extra. Contact schools by the end of October at the latest.
  • College Board's AP Course Ledger lists the schools that offer AP; search it by country and city.

AP Course LedgerAuthorized AP test centers outside the U.S.

One-to-one AP tutoring

AP Calculus BC Private Tutoring

Private AP lessons planned around you: the units you find hardest, your school's pace and the score you are aiming for. Every lesson is live and online, with a tutor who teaches this subject.

  • A lesson plan built around your target score
  • Every unit of the College Board course, in the order you need it
  • Multiple-choice and free-response technique, checked against College Board scoring guidelines
  • Lesson times that fit around your school week

How it works

  1. 1

    Tell us your goal

    We start from your school syllabus, your exam date and the result you are aiming for.

  2. 2

    Your own plan

    We map out the lessons you need, unit by unit.

  3. 3

    Live one-to-one lessons

    Meet your tutor online at times that suit your week.

  4. 4

    Regular progress checks

    Homework and a short check after each lesson show how you are getting on.

Start one-to-one AP Calculus BC

Per lesson in a package, from

€54

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Right for you if you want a plan built entirely around you, flexible lesson times and a tutor's full attention.

Book one-to-one lessons

No package needed — you can book a single lesson.

Even our newest AP tutor has been teaching AP prep since 2016.

Group course calendar

AP Calculus BC Group Course Calendar

50 lessons in total (40 topic lessons + 10 past-paper lessons). Topic lessons on Monday and Wednesday, 19:00–20:30; past-paper lessons on Monday, 19:00–20:30 (Türkiye time). Lessons are taught in English.

2026-27 intake

Full

First lesson

28 September 2026

Last lesson

26 April 2027

Enrolment deadline

25 September 2026

AP exam

10 May 2027

Course fee

€1,566single payment

or 3 instalments of €522

  • 50 lessons in total
  • 40 topic lessons
  • 10 past-paper lessons
  • Lesson recordings available for 14 days

Every one of our 2026-27 AP group courses is full — thank you for the interest. The 2027-28 start dates are published on 1 November, and you can enrol now.

If three or more of you enrol together, you can have a group of your own at the same group course price. Each of you can buy a place online now, and we let you know as soon as your group is ready.

Buy a private group place

Lesson-by-lesson calendar

Topic lessonPast-paper lesson
Lesson-by-lesson calendar
DateTopic
28 Sep 2026 (done)Mon · 19:00–20:30Unit 1: Limits and Continuity (1/3)
30 Sep 2026 (done)Wed · 19:00–20:30Unit 1: Limits and Continuity (2/3)
5 Oct 2026Mon · 19:00–20:30Unit 1: Limits and Continuity (3/3)
7 Oct 2026Wed · 19:00–20:30Unit 2: Differentiation: Definition and Fundamental Properties (1/3)
12 Oct 2026Mon · 19:00–20:30Unit 2: Differentiation: Definition and Fundamental Properties (2/3)
14 Oct 2026Wed · 19:00–20:30Unit 2: Differentiation: Definition and Fundamental Properties (3/3)
19 Oct 2026Mon · 19:00–20:30Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (1/3)
21 Oct 2026Wed · 19:00–20:30Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (2/3)
26 Oct 2026Mon · 19:00–20:30Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (3/3)
28 Oct 2026Wed · 19:00–20:30Unit 4: Contextual Applications of Differentiation (1/3)

Good to know

  • 50 lessons in total: 40 teaching lessons and 10 exam walkthroughs.
  • Teaching phase: two lessons a week (Monday and Wednesday), 19:00–20:30.
  • Walkthrough phase: one lesson a week (Monday), 19:00–20:30.
  • There is no lesson in the week of 8 March 2027.
  • Past exams are worked through from 2026 back to 2017. The 2020 exam was a shortened, free-response-only online exam, so a TestPrep practice test takes its place.
  • Lessons per unit follow the exam weighting in the College Board AP Calculus BC course.

  • 100% First-Lesson Money-Back Guarantee

    Not satisfied? Full refund, no questions asked.

  • Secure Payments

    Powered by Stripe with 256-bit encryption.

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  • Flexible Billing

    Pay in EUR — local cards welcome, instalments available.

Lessons cancelled less than 3 hours before the start count as taken. Full terms

Practice test · Question bank · AI Tutor

Practise AP Calculus BC on your own

Three ways to practise between lessons. Each one is a separate product.

  • AP Calculus BC Question Bank

    College Board-style questions unit by unit, with an explanation for every question. The first 30 questions are free.

    Try it free

  • AP Calculus BC Practice Test

    A full-length test in the real exam format, with a detailed score report. Two attempts per test, and 12 months to use them.

    Go to the practice test

  • AI Tutor

    Talks you through the questions you got wrong on a practice test, out loud. Your first 2 mistakes are free.

    Meet the AI Tutor

Syllabus

AP Calculus BC topics

Unit and topic names are the College Board's own. Percentages are each unit's share of the exam score, as the College Board publishes them.

1

Unit 1: Limits and Continuity

5–10%
  • How limits help us to handle change at an instant
  • Definition and properties of limits in various representations
  • Definitions of continuity of a function at a point and over a domain
  • Asymptotes and limits at infinity
  • Reasoning using the Squeeze theorem and the Intermediate Value Theorem
2

Unit 2: Differentiation: Definition and Fundamental Properties

5–10%
  • Defining the derivative of a function at a point and as a function
  • Connecting differentiability and continuity
  • Determining derivatives for elementary functions
  • Applying differentiation rules
3

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

5–10%
  • The chain rule for differentiating composite functions
  • Implicit differentiation
  • Differentiation of general and particular inverse functions
  • Determining higher-order derivatives of functions
4

Unit 4: Contextual Applications of Differentiation

5–10%
  • Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change
  • Applying understandings of differentiation to problems involving motion
  • Generalizing understandings of motion problems to other situations involving rates of change
  • Solving related rates problems
  • Local linearity and approximation
  • L'Hospital's rule
5

Unit 5: Analytical Applications of Differentiation

10–15%
  • Mean Value Theorem and Extreme Value Theorem
  • Derivatives and properties of functions
  • How to use the first derivative test, second derivative test, and candidates test
  • Sketching graphs of functions and their derivatives
  • How to solve optimization problems
  • Behaviors of Implicit relations
6

Unit 6: Integration and Accumulation of Change

15–20%
  • Using definite integrals to determine accumulated change over an interval
  • Approximating integrals with Riemann Sums
  • Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals
  • Antiderivatives and indefinite integrals
  • Properties of integrals and integration techniques, extended
  • Determining improper integrals
7

Unit 7: Differential Equations

5–10%
  • Interpreting verbal descriptions of change as separable differential equations
  • Sketching slope fields and families of solution curves
  • Using Euler's method to approximate values on a particular solution curve
  • Solving separable differential equations to find general and particular solutions
  • Deriving and applying exponential and logistic models
8

Unit 8: Applications of Integration

5–10%
  • Determining the average value of a function using definite integrals
  • Modeling particle motion
  • Solving accumulation problems
  • Finding the area between curves
  • Determining volume with cross-sections, the disc method, and the washer method
  • Determining the length of a planar curve using a definite integral
9

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions

10–15%
  • Finding derivatives of parametric functions and vector-valued functions
  • Calculating the accumulation of change in length over an interval using a definite integral
  • Determining the position of a particle moving in a plane
  • Calculating velocity, speed, and acceleration of a particle moving along a curve
  • Finding derivatives of functions written in polar coordinates
  • Finding the area of regions bounded by polar curves
10

Unit 10: Infinite Sequences and Series

15–20%
  • Applying limits to understand convergence of infinite series
  • Types of series: Geometric, harmonic, and p-series
  • A test for divergence and several tests for convergence
  • Approximating sums of convergent infinite series and associated error bounds
  • Determining the radius and interval of convergence for a series
  • Representing a function as a Taylor series or a Maclaurin series on an appropriate interval

Approach

How we teach AP Calculus BC

Study plan

  1. 1

    Phase 1 — AB foundation review

    Limits, derivatives, integrals

    • Tighten AB rules
    • Calculator-active reflexes
  2. 2

    Phase 2 — Integration techniques

    BC-only integration

    • Integration by parts
    • Partial fractions
    • Improper integrals
  3. 3

    Phase 3 — Parametric, polar, vector

    Unit 9

    • Parametric derivatives + arc length
    • Polar area
    • Vector-valued functions
  4. 4

    Phase 4 — Series + mock

    Unit 10 + full exam

    • Convergence test flowchart
    • Power series + radius of convergence
    • Taylor/Maclaurin
    • Released full-length papers

How lessons work

  • Series as a decision tree

    Convergence tests are taught as a routing problem — given the form of the series, which test runs fastest. Students stop guessing and start matching pattern to test.

  • Dual-track AB protection

    Because BC also yields an AB subscore, every BC session keeps a small AB review block so the AB material doesn't decay.

  • Released FRQ scoring

    Recent BC FRQs are scored against the official rubric in session; the student sees exactly where partial credit is gained or lost.

Advice

AP Calculus BC: common mistakes and study tips

  • MistakePicking the wrong convergence test under time pressure.

    FixStart every series question with the divergence test, then route through ratio / integral / comparison / alternating-series tests via a fixed flowchart (the root test is not part of the AP course).

  • MistakeTreating polar area as Cartesian area.

    FixPolar area is (1/2)∫r²dθ, never ∫y dx. Re-derive it once and the formula sticks.

  • MistakeConfusing parametric speed with parametric arc length.

    FixSpeed is √((dx/dt)² + (dy/dt)²); arc length is the integral of speed over t. Different objects, different units.

  • MistakeDropping the +C in indefinite integrals on FRQs.

    FixIndefinite integrals always carry +C — losing it costs the answer-mark and can cascade into later parts.

  • MistakeUsing a Taylor series centred at 0 when the question asks for a different centre.

    FixRead the centre carefully; a Taylor series at x = a uses (x − a)^n, not x^n.

Study tips

  • Learn the convergence tests as a systematic decision tree — know which test applies to which series shape.
  • Memorise the Taylor/Maclaurin expansions for sin(x), cos(x), e^x, 1/(1-x) and ln(1+x).
  • BC reports an AB sub-score, so build rock-solid AB fluency first, then layer the BC-only material on top.
  • On parametric and polar problems, sketch the curve first to ground your intuition before doing the analytic work.

Student results

AP success stories

Results our AP students shared in their own reviews.

  • AP Calculus BC: 5
    “I went from zero in trigonometry and algebra to top-tier results.”
    Mert T.AP Calculus BC student

Ready to raise your AP Calculus BC score?

You can start one-to-one AP Calculus BC lessons with a single lesson. Every package and price is on one page.

  • Live one-to-one lessons online
  • No package needed — book a single lesson
  • Lesson times that fit your school week
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FAQ

AP Calculus BC Prep — Frequently Asked Questions

The questions students ask most about AP Calculus BC preparation.

BC includes an AB subscore. Most US universities grant credit based on the BC score for second-semester calculus and the AB subscore for first-semester calculus, but the policy varies — check the target university's AP credit chart.

No. Many strong students go straight to BC. We typically front-load 4–6 weeks of AB review at the start of the BC programme.

Unit 10: Infinite Sequences and Series carries 15–20% of the BC exam — the largest single BC-only block. Plan at least 6–8 dedicated weeks.

Pairing it with Physics C (Mechanics or E&M) suits STEM applicants.

A cohort takes 24 students, taught in classes of at most 6 because the cohort is split by level. Lessons are live and online, and every lesson is recorded; each recording stays available for 14 days from the lesson date.

The money-back guarantee covers live lessons. If you are not satisfied after your first private lesson, we refund your payment in full. On a group course, the same applies to the lessons held in the first week. The question bank and practice tests are not part of it.

No. They are digital products that open the moment you buy them, so they are not refundable. The one exception is the EU right of withdrawal: within 14 days of purchase, as long as you have not started a test or opened the question bank.

Lessons cancelled less than 3 hours before the start count as taken and are not refunded. A lesson that has not been paid for 3 hours before it starts is cancelled automatically.

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