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Advanced Placement (AP)
AP Calculus AB and BC tutoring, covering Units 1 to 8 of AB, the parametric equations, polar coordinates and infinite series that BC adds, and how a free-response answer is written. One-to-one private tutoring, 60 minutes a lesson, Kwun Tong or online, with a free first trial lesson.
Need AP Calculus tutoring? At PY Education, this subject is taught by founder and principal tutor Tinnie. She holds an MSc in Finance and Economics from the London School of Economics (Distinction), first-class honours degrees in Accounting and Finance and in Data Science and Business Analytics from the University of London, and a BBA in Professional Accountancy from CUHK. She teaches mathematics for GCSE / IGCSE, GCE A-Level / IAL (including Further Mathematics), IBDP and AP.
This page covers AP Calculus AB and BC, taught to the College Board Course and Exam Description and the published scoring guidelines, with past free-response questions used for practice. One-to-one private tutoring, 60 minutes a lesson, HK$750 an hour, billed every four lessons, in Kwun Tong or online. The first lesson can be a free trial. Students whose school does not offer AP can enrol as self-study candidates.
AB and BC are taught from the same course framework; what differs is how many units are covered. AB takes Units 1 to 8:
BC takes those same eight units and adds the following two, along with the topics inside Units 6 to 8 that are BC only — integration by parts, linear partial fractions, improper integrals, Euler’s method, logistic models with differential equations, and arc length:
A BC score report carries an AB subscore alongside the BC score — a separate score calculated from the questions on the paper that fall within the AB range. Which one to take turns on which course the school offers, the teaching time available, the units already covered, and how fluent the student is in algebra and trigonometry; we look at where the student currently stands in the free trial lesson and weigh it up together.
Units 1 to 5, from the definition of a limit through to reading a derivative in context and using it to analyse a function.
Key topics: limits and continuity, the definition and rules of differentiation, rates of change, tangent lines, optimisation, related rates.
What a lesson usually stops on is not differentiating itself but Units 4 and 5: the question gives a situation or a graph, and the student has to decide which derivative to use, what the sign of it means, and what units the answer carries back. A question answered with the intermediate value theorem or the mean value theorem needs the conditions of that theorem written out one by one — the intermediate value theorem needs the function continuous on the closed interval, the mean value theorem also needs it differentiable on the open interval — before the conclusion is written.
Units 6 to 8, from Riemann sums and the definition of the definite integral through differential equations to integration applied to area, volume and accumulated quantities.
Key topics: definite and indefinite integrals, the fundamental theorem of calculus, area and volume, differential equations, slope fields.
Most of the marks here sit in the writing: a definite integral has to show the integrand, the variable and the limits; with u-substitution the limits are converted along with the variable; an area or a volume starts with the integral written out and the numbers substituted afterwards. A differential equation question needs the separation-of-variables step and the working for the constant C, not only the final solution.
Units 9 and 10, plus the topics inside Units 6 to 8 that are BC only: integration by parts, linear partial fractions, improper integrals, Euler’s method, logistic models with differential equations, and arc length.
Key topics: series and convergence tests, parametric equations, polar coordinates, vector-valued functions, integration by parts and improper integrals, Euler’s method, logistic models.
A series question asks for the test used to be named and the conditions that test checks to be written out: for the alternating series test, that the absolute values of the terms decrease and the limit is zero; for the ratio test, the value of the limit and the comparison with 1. A Taylor series question needs the centre of the expansion and the general term written out.
From May 2027: AB and BC take the same format — 3 hours 10 minutes in total, the two sections weighted 50% each.
AP Calculus is a hybrid digital exam: the multiple-choice section is answered inside College Board’s Bluebook application, while the free-response questions are read on screen and the answers are handwritten in the paper booklet.
Papers from 2017 to May 2026 follow a different format: 3 hours 15 minutes in total, 45 multiple-choice questions (Part A, 30 questions in 60 minutes without a calculator; Part B, 15 questions in 45 minutes with a graphing calculator) and 6 free-response questions. Papers older than that carry the same number of questions but divide them differently between Parts A and B. A past paper from 2026 or earlier will differ from the table above in question count and timing, but not in the topics it covers, so it is still usable for practice — we simply time it to the new limits.
Each AP subject is examined on its own and reported on a 1 to 5 scale, so AP Calculus by itself produces a score rather than a diploma. The College Board does award an AP International Diploma, but it takes scores of 3 or higher on five or more AP Exams across four content areas. Credit and placement arrangements are set by each university individually rather than uniformly worldwide, so check that university’s own admissions or credit page directly.
AP free-response questions are marked line by line: the theorem used, the calculation, and the conclusion put back into the context of the question all have to be written down. We mark question by question against the College Board’s published scoring guidelines, checking line by line whether the theorem, the calculation and the conclusion are all there.
Take an intermediate value theorem question: a complete line of answer states that the function is continuous on that closed interval and that the values at the two ends bracket the target value, and only then gives the conclusion. A question set in context also needs the conclusion written back in the original quantity and units — for example, “at t = 3 minutes the water depth is falling at 0.4 cm per minute” — and the published scoring guidelines list the units and the context as requirements of that line.
The first four lessons start from the student’s most recent paper or a single free-response question: first we establish whether it is AB or BC, how far through the units the school has taught, and how many lesson hours remain before the May examination, then we look at which line the writing stops on. The four to eight lessons after that usually concentrate on one group of units — Units 1 to 3, limits and the rules of differentiation, say, or Unit 6, integration and accumulation of change — doing one type of question once, then again with the numbers changed. Every four lessons we check three things: whether the same type of question came out right the second time, whether the free-response answers contain every line that earns a mark, and how much of a paper gets done within the time limit. We do not promise a particular score.
Students whose school does not offer AP can enrol. The schedule is planned from the beginning and worked backwards from the May examination date, and we go through the registration arrangements as well.
Working backwards means counting the lesson hours left before the examination and then fitting the units into them in order: AB runs from Unit 1 to Unit 8, BC to Unit 10, with series and parametric equations usually in the second half and past free-response papers in the final few lessons. Registration is handled by the candidate directly with a school or test centre that hosts AP examinations, the closing date is whatever that centre announces, and we do not register candidates on their behalf.
AP, IB and A-Level mathematics are all taught by the same tutor, so students switching systems or taking two of them often ask how the three compare. AP Calculus is calculus and nothing else — eight units for AB, ten for BC. In IB Analysis and Approaches (AA) or Applications and Interpretation (AI), calculus is one topic among several, and the same subject also examines number and algebra, functions, geometry and trigonometry, and statistics and probability. The calculator rules differ too: each of the two AP sections has a part where a calculator is allowed and a part where it is not, AA Paper 1 (at both SL and HL) allows no calculator at all, and every AI paper assumes a graphic display calculator is in hand.
The content of AP Calculus AB is spread across P1 to P4 of Edexcel IAL Mathematics: P1 and P2 hold differentiation of polynomials and definite integration; the chain, product and quotient rules and the derivatives of exponential, logarithmic and trigonometric functions are in P3; implicit differentiation, related rates, integration by substitution and by parts, and differential equations are in P4. IAL splits the whole subject into six units sat separately, each a 1 hour 30 minute, 75-mark paper, whereas AP Calculus is examined in a single sitting. The overlapping content can be prepared together, but the two mark schemes ask for different things from the written answer, so we hold the student to the requirements of the paper they are actually sitting.
Lessons are 60 minutes, one-to-one private tutoring; there is no group option for AP. Charging is by the hour at HK$750, billed every four lessons — HK$3,000 for four. In Kwun Tong or online, whether the student is in Hong Kong or overseas. The first lesson can be a free trial: we confirm whether it is AB or BC, how far the school has taught, and the May examination date, then discuss which unit to start from. There is no obligation to enrol on the day.
Kwun Tong
Online
60 minutes (1 hour)
60-minute lessons · billed every four lessons
HK$750 per hour
HK$750 an hour one-to-one, 60 minutes a lesson, billed every four lessons (HK$3,000 for four). AP is offered as one-to-one private tutoring only, and AP Calculus and AP Statistics are charged at the same rate. The first lesson can be a free trial.
Both are taught. BC covers the eight units of AB plus Unit 9 (parametric equations, polar coordinates and vector-valued functions) and Unit 10 (infinite sequences and series), together with the topics inside Units 6 to 8 that are BC only: integration by parts, linear partial fractions, improper integrals, Euler’s method, logistic models with differential equations, and arc length. Which one to take mainly depends on which course the school offers, whether there is enough teaching time, and how fluent you are in algebra and trigonometry. In the trial lesson we look at which unit you are currently on and weigh it up together.
No. The ten units of BC already contain the eight of AB, so teaching from Unit 1, Limits and Continuity, is already the first half of BC. A BC score report also carries a separate AB subscore, calculated from the questions on the paper that fall within the AB range.
Yes, the format has changed. From May 2027 the paper runs 3 hours 10 minutes: 42 multiple-choice questions (Part A, 29 questions in 62 minutes without a calculator; Part B, 13 questions in 38 minutes with a graphing calculator) and 6 free-response questions (Part A, 2 questions in 30 minutes with a graphing calculator; Part B, 4 questions in 60 minutes without). May 2026 and earlier follow the older format of 3 hours 15 minutes with 45 multiple-choice questions, so the question count and timings on your old papers will differ. The topics covered have not changed, so old papers are still worth working through, and we time them to the new limits. Separately, AP Calculus is a hybrid digital exam: the multiple-choice section is answered inside College Board’s Bluebook application, while the free-response questions are read on screen and the answers are handwritten in the paper booklet.
Usually it is not a calculation error but an incomplete answer. AP free-response questions are marked line by line: which theorem was used, how the calculation goes, and how the conclusion is placed back into the context of the question all have to be written down. We mark question by question against the official scoring guidelines.
Yes. Registration and scheduling are handled by the candidate directly with a school or test centre that hosts AP examinations — we do not register candidates on their behalf, but we go through what needs preparing in the trial lesson, and the closing date is whatever that centre announces. The schedule is planned from the beginning and worked backwards from the May examination date, with the order of units and the timing of past-paper practice set out in advance.
AP reports a score from 1 to 5 for each subject, so a single subject produces a score rather than a diploma. There is an AP International Diploma, awarded for scores of 3 or higher on five or more AP Exams across four content areas. How credit and admissions are calculated is set by each university individually and varies from one to another, so read that university’s own admissions or credit page before applying. We do not quote a threshold score.
Both the scope and the examination differ. AP Calculus is calculus throughout — eight units for AB, ten for BC. In IB AA, calculus is one topic among several, and the same subject also examines number and algebra, functions, geometry and trigonometry, and statistics and probability. The calculator rules differ too: each of the two AP sections has a part where a calculator is allowed and a part where it is not, while AA Paper 1 allows no calculator at all.
Yes — they are separate examinations, registered separately. Both are taught here, though a lesson usually covers one subject only, so taking both means the lessons for each, charged at the same HK$750 an hour.
Online lessons are available at the same rate as face-to-face lessons in Kwun Tong, and students overseas can attend as long as the time difference works. AP is one-to-one only, with no group option, so the pace follows whichever unit you have reached.
We start by confirming whether you are taking AB or BC, how far through the units your school has taught, and how many lessons remain before the May examination, then look at your most recent paper or a single free-response question to see which line the writing stops on, and discuss which unit to start from. The first trial lesson is free, and there is no obligation to enrol on the day.
No — each has its own course page. This page is AP Calculus only; AP Statistics, IB Mathematics (AA / AI), Edexcel IAL Mathematics, IGCSE Mathematics and DSE Mathematics (M1 and M2 included) each have a page of their own. The lesson arrangements differ: AP, IGCSE, IAL and IBDP lessons are 60 minutes and charged by the hour, while primary and DSE lessons are 75 minutes.