AP Calculus BC Tutoring for the May Exam
AP Calculus BC covers the whole of AB and then adds sequences and series, parametric, polar and vector-valued functions and further integration techniques, so the difficulty lies as much in the pace as in the mathematics. Infinite series, the unit least like anything students have met before, carries one of the largest shares of the multiple-choice section and comes last in the course order, when time is shortest.
Short answer
AP Calculus BC 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 BC.
- 2 scored components, from AP Central
- Live online lessons of 90 minutes
- From USD 65 per lesson
How AP Calculus BC 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 BC · 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 BC syllabus
Topic names are left in English, as they appear on the paper and in the mark scheme.
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
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
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 (5–10%)
Applying understandings of differentiation to problems involving motion · Solving related rates problems · Local linearity and approximation · L’Hospital’s rule
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
Unit 6: Integration and Accumulation of Change (15–20%)
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
Unit 7: Differential Equations (5–10%)
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
Unit 8: Applications of Integration (5–10%)
Determining the average value of a function using definite integrals · Modeling particle motion · 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
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
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
Where AP Calculus BC marks are usually lost
Convergence tests applied without their conditions
Each convergence test has conditions: the alternating series test needs terms that decrease towards zero, a comparison needs terms of the right sign, and the ratio test says nothing when its limit equals one. The exam directions state that justifications must verify the conditions of any test used, so a correct conclusion reached without checking them loses the point.
Two error bounds confused
BC asks for error estimates in two forms: the alternating series error bound and the Lagrange error bound for a Taylor polynomial. Students mix up which one applies, use the wrong term or derivative, or give a bound without saying what it bounds. A complete answer names the bound, shows the expression and states that the error is less than that value.
Parametric and polar set-ups half remembered
Questions on a particle moving in the plane ask for its speed, the distance it travels or its position at a later time; polar questions ask for the area of a region or the slope of a curve. Students who confuse speed with velocity, forget the factor of one half in the polar area integral or integrate over the wrong interval lose points on otherwise routine questions.
How we teach AP Calculus BC
The tutor first checks the AB foundations, because BC covers limits, derivatives and integrals faster than AB does and leaves little time to repair gaps later. The BC-only topics — integration by parts and partial fractions, improper integrals, Euler’s method, logistic models, arc length, and parametric, polar and vector-valued functions — are then taught with released free-response questions scored against College Board’s guidelines. Series is started early enough to be revisited several times before May rather than crammed at the end: each convergence test is learned with its conditions and a counter-example, and every Taylor polynomial is paired with an error bound. Calculator questions are practised on the Desmos graphing calculator in Bluebook as well as on a handheld one, and the no-calculator parts are drilled separately.
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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