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AP Calculus AB Tutoring & Prep Course

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

Since 2008, TestPrep Europe has taught AP Calculus AB 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 AB: what it covers and who it suits

AP Calculus AB tutoring at TestPrep Europe is a one-to-one online programme that walks through the eight College Board units — Limits & Continuity through Applications of Integration — in the exact MCQ + FRQ format used on the May exam. Calculator-active and no-calculator sections are practised separately so the student is fluent in both.

  • All 8 units covered in order, Unit 1: Limits and Continuity through Unit 8: Applications of Integration
  • MCQ + FRQ practice and error analysis after every unit
  • Calculator-active and no-calculator strategy drilled separately
Read more

AP Calculus AB is the foundation for university success in engineering, physics, economics and computer science. Students who score a 4 or 5 typically place out of first-semester calculus, saving tuition and fast-tracking into upper-division STEM coursework. Beyond the credit, the limit, derivative and integral concepts that anchor the course are the working language of optimisation, motion analysis and area/volume modelling across every quantitative discipline.

AP Calculus AB covers roughly the first semester of college-level calculus and is administered by the College Board every May. The course progresses from limits and continuity to differentiation as a tool for analysing rate of change, and finally to integration as a tool for accumulating change. The Fundamental Theorem of Calculus ties differentiation and integration together and is one of the most heavily tested ideas on the exam. Beyond formula recall, the AP exam tests conceptual understanding and problem-solving: Free Response questions ask students to interpret graphs, draw conclusions from tabular data and construct mathematical arguments. Our AP Calculus AB programme builds a personalised study plan against the College Board CED around each student's weakest sub-units, and dedicates significant time to FRQ-writing strategy, aiming at the full 9 points on each free-response problem.

One-to-one AP Calculus AB 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 AB 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 AB exam format

The College Board runs the AP Calculus AB 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). Question count and timing were updated effective with the May 2027 exam.

  • 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 questions are answered in the Bluebook app; free-response questions are viewed in Bluebook and answered by hand 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 AB 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 AB

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 AB 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 (1/5)
30 Sep 2026 (done)Wed · 19:00–20:30Unit 1: Limits and Continuity (2/5)
5 Oct 2026Mon · 19:00–20:30Unit 1: Limits and Continuity (3/5)
7 Oct 2026Wed · 19:00–20:30Unit 1: Limits and Continuity (4/5)
12 Oct 2026Mon · 19:00–20:30Unit 1: Limits and Continuity (5/5)
14 Oct 2026Wed · 19:00–20:30Unit 2: Differentiation: Definition and Fundamental Properties (1/5)
19 Oct 2026Mon · 19:00–20:30Unit 2: Differentiation: Definition and Fundamental Properties (2/5)
21 Oct 2026Wed · 19:00–20:30Unit 2: Differentiation: Definition and Fundamental Properties (3/5)
26 Oct 2026Mon · 19:00–20:30Unit 2: Differentiation: Definition and Fundamental Properties (4/5)
28 Oct 2026Wed · 19:00–20:30Unit 2: Differentiation: Definition and Fundamental Properties (5/5)

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 AB course: Units 5 and 6 carry the most weight (15–20%), Units 3 and 7 the least (5–10%).

  • 100% First-Lesson Money-Back Guarantee

    Not satisfied? Full refund, no questions asked.

  • Secure Payments

    Powered by Stripe with 256-bit encryption.

    Stripe

  • 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 AB on your own

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

  • AP Calculus AB 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 AB 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 AB 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

10–15%
  • 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

10–15%
  • 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

10–15%
  • 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

15–20%
  • 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 using Riemann Sums
  • Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals
  • Antiderivatives and indefinite integrals
  • Properties of integrals and integration techniques
7

Unit 7: Differential Equations

5–10%
  • Interpreting verbal descriptions of change as separable differential equations
  • Sketching slope fields and families of solution curves
  • Solving separable differential equations to find general and particular solutions
  • Deriving and applying a model for exponential growth and decay
8

Unit 8: Applications of Integration

10–15%
  • 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

Approach

How we teach AP Calculus AB

Study plan

  1. 1

    Phase 1 — Foundation (Units 1–3)

    Limits, continuity, definition of the derivative

    • Algebraic, graphical and one-sided limits
    • Continuity and the Intermediate Value Theorem
    • Derivative definition and rules, the chain rule and implicit differentiation
  2. 2

    Phase 2 — Applications of the derivative (Units 4–5)

    Optimization, related rates, MVT

    • Related rates, local linearity and L'Hospital's rule
    • Motion problems
    • Mean Value Theorem, Extreme Value Theorem and curve analysis
    • Optimization in FRQ format
  3. 3

    Phase 3 — Integrals (Units 6–7)

    Antiderivatives, definite integrals, FTC

    • u-substitution
    • Riemann sums and the definite integral
    • FTC Parts 1 and 2
    • Separable differential equations + slope fields
  4. 4

    Phase 4 — Applications + mock exam (Unit 8 + review)

    Area, volume, FRQ technique

    • Area between curves; volumes by cross-sections, discs and washers
    • Timed released FRQ sets
    • Calculator-active vs no-calculator practice
    • Full-length mock with score estimate

How lessons work

  • Calculator-active and no-calculator drilled apart

    Most students under-prepare the no-calculator half. Each unit closes with separate sessions for both formats so timing reflexes match the real paper.

  • FRQ rubric coaching

    Released FRQs are scored against the official rubric so the student sees exactly which step earns which point — and never falls into the 'right answer, missing justification' trap.

  • Notational discipline

    Leibniz, Lagrange and Newton notation are taught explicitly; consistency inside a single response is treated as a habit, not a stylistic choice.

Advice

AP Calculus AB: common mistakes and study tips

  • MistakeMixing notation (dy/dx, f′(x), Df) inside the same FRQ.

    FixPick one notation per question and keep it consistent — the FRQ rubric rewards notational discipline.

  • MistakeForgetting the inner derivative when applying the chain rule, especially inside ln, sin or e^u.

    FixAlways rewrite as u = …, then d/dx = (outer derivative)·(du/dx) so the chain step is explicit.

  • MistakeJustifying with 'because it is increasing' instead of citing the sign of f′.

    FixTie every justification to a derivative sign: 'f′(x) > 0 on (a,b), so f is increasing on (a,b).'

  • MistakeDropping units in applied integral problems.

    FixDecide whether the question gives a rate or an amount before setting up the integral, and write units before integrating.

  • MistakeConfusing the graphs of f, f′ and f″.

    FixIf the graph isn't labelled, annotate first: extrema → f′ = 0; inflection points → f″ = 0.

  • MistakeRounding to two decimals on calculator-active questions.

    FixAP rubrics demand three decimals or more on calculator-active items; rounding too early loses the point.

Study tips

  • Show every step on FRQs — the AP rubric awards points for the solution path, not just the final answer.
  • Master the calculator for numerical integration, root finding and graph analysis; Part B questions assume calculator fluency.
  • After each unit, attempt the released College Board FRQs and self-grade against the official scoring guidelines.
  • Build conceptual links between limit, derivative and integral instead of memorising rules in isolation.

Ready to raise your AP Calculus AB score?

You can start one-to-one AP Calculus AB 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 AB Prep — Frequently Asked Questions

The questions students ask most about AP Calculus AB preparation.

AB covers the first half of calculus (one semester); BC covers all of AB plus sequences, series, parametric equations and polar coordinates. The BC exam also reports an AB sub-score.

Yes. A graphing calculator (TI-84 or TI-Nspire CX) is required for Section I Part B and Section II Part A. The other halves are calculator-free.

Roughly 60-70% of total points typically earns a 5, but the curve shifts each year based on overall cohort performance.

AB covers roughly the first semester of college calculus; BC covers AB plus a second semester (series, parametric, polar). BC is broader, not deeper — students who plan a STEM degree in the US usually take BC.

The College Board allows the TI-84 family, the TI-Nspire CX (non-CAS) and the Casio fx-CG50 among others. We teach both TI and Casio workflows so the student can use whichever they own.

Students starting from a solid Algebra II / Pre-Calculus base usually book 40–60 hours across the year; students starting from scratch or aiming for a 5 from a 3 baseline often book more.

No — and we would be wary of anyone who does. An AP score depends on the student's starting point, the hours they put in and exam-day performance, so no tutor can promise a number. What we do guarantee is simple: if you are not satisfied after your first lesson, you get a full refund. Beyond that we commit to a written study plan and honest progress reporting against it.

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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