AP Calculus AB Tutoring for the May Exam
AP Calculus AB tests calculus that students can often do mechanically but cannot yet justify in words: many free-response points are for stating the reason, the theorem or the units that make an answer complete. The exam has parts without a calculator and parts that require a graphing calculator, so both habits need to be strong.
Short answer
AP Calculus AB is offered online, one-to-one or in a group class.
A private lesson runs 90 minutes and starts at USD 65 per lesson; the group course runs 50 lessons of 90 minutes for USD 1,755, and a class never takes more than 6 students.
Group classes next begin on 27 September 2027.
From USD 65 per lesson
Your lessons are taught by Gökhan İnce, who teaches AP Calculus AB.
- 2 scored components, from AP Central
- Live online lessons of 90 minutes
- From USD 65 per lesson
How AP Calculus AB is assessed
Set and scored by College Board and reported on the 1–5 AP scale. Each university sets its own rule on which scores earn credit or placement. Component names are as College Board prints them.
College Board
AP Calculus AB · AP Central exam page
| Component | Share of score | Length | What it involves |
|---|---|---|---|
| Section I: Multiple Choice | 50% | 1 hour 40 min | 42 questions in 1 hour 40 minutes (from May 2027; previously 45 in 1 hour 45). Part A: 29 questions in 62 minutes with no calculator; Part B: 13 questions in 38 minutes with a graphing calculator required (handheld, or the Desmos graphing calculator in Bluebook). |
| Section II: Free Response | 50% | 1 hour 30 min | 6 questions in 1 hour 30 minutes. Part A: 2 questions in 30 minutes with a graphing calculator required; Part B: 4 questions in 60 minutes with no calculator. Procedural and conceptual tasks are roughly balanced and at least 2 questions are set in a real-world context; answers are handwritten in a paper booklet. |
- Hybrid exam: answers are entered in Bluebook for multiple choice and handwritten in a paper booklet for free response.
- 2027 exam date: 10 May 2027.
Checked on 8 October 2026
College Board revises individual exams between years. The exam page linked above is the authority for your sitting.
The AP Calculus AB syllabus
Topic names are left in English, as they appear on the paper and in the mark scheme.
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
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
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
Unit 4: Contextual Applications of Differentiation (10–15%)
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
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
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
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
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
Where AP Calculus AB marks are usually lost
Justifications that give no reason
When a question asks the student to justify an answer — that a function has a relative maximum, or that the Mean Value Theorem applies — the point depends on stating the condition: the sign change of the derivative, or continuity and differentiability on the interval. A correct answer with no justification loses the point.
Answers with no meaning in context
Free-response questions built on a real situation, such as water flowing into a tank, ask what a derivative or an integral means. The answer needs the value, the units and a sentence that interprets them. A bare number is incomplete: the reader wants to know how much of what, per unit of what, and at what time.
Calculator work shown badly
In the calculator parts, the setup must be written in standard mathematical notation — the integral or the equation — not in calculator syntax, followed by the answer to the accuracy the exam asks for. Students who write only a number, or who round intermediate values too early, drop points on work that is otherwise correct.
How we teach AP Calculus AB
The tutor builds understanding first — the derivative as a rate of change, the integral as accumulation — because most AP Calculus questions reward knowing what a quantity means, not only how to compute it. Each unit then moves to released free-response questions, marked against College Board’s scoring guidelines, so the student learns the exact form a justification needs. No-calculator fluency (algebra, derivative rules, standard integrals, reading values from a graph or table) is drilled separately from calculator skills, and the student practises with the Desmos graphing calculator built into Bluebook as well as a handheld one. For students who learned mathematics in French or Arabic before moving to an American-curriculum school, the tutor pays attention to the English wording of justifications, where marks slip even when the mathematics is right.
There is no separate diagnostic, because there is no single test that stands in for two years of a school syllabus. The first lesson is the assessment: the tutor works through your recent marked work, past-paper questions from your own specification, and the units your school has already covered, and reads current level, gaps, exam technique and where school work stands. It is a normal paid lesson and it teaches as it assesses.
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