Private Tutoring · Mathematics, English and Integrated Science
- Mathematics (S.1–S.3)
- HK$1,400
- Mathematics (S.4–S.6)
- HK$1,800
- Mathematics M1 / M2
- HK$2,200
Fee per four lessons
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Hong Kong Secondary (HKDSE and Junior Forms)
Junior secondary mathematics, plus the HKDSE Mathematics Compulsory Part (Paper 1, 105 marks; Paper 2, 45 multiple-choice questions) and the Extended Part — Module 1 (Calculus and Statistics) and Module 2 (Algebra and Calculus). One-to-one or a self-formed group, 75 minutes a lesson, Kwun Tong or online, with a free first trial lesson.
Looking for a secondary mathematics tutor? At PY Education the lessons are taught by Mr Wong — MSc in Financial Mathematics and Statistics, City University of Hong Kong (graduated with distinction); BBA, City University of Hong Kong (major in Finance). He is a full-time tutor with five years of one-to-one and small-group teaching experience, and is currently reading for an MSc in Computer Science at The Chinese University of Hong Kong.
This page covers three stages: junior secondary mathematics from S.1 to S.3, the HKDSE Mathematics Compulsory Part, and the Extended Part — Module 1 (Calculus and Statistics) and Module 2 (Algebra and Calculus). Lessons run 75 minutes, in Kwun Tong or online, billed every four lessons — one-to-one HK$1,400 for S.1–S.3, HK$1,800 for S.4–S.6, HK$2,200 for M1 or M2. A self-formed group is HK$200 less per student per four lessons. The first lesson can be a free trial.
Junior secondary mathematics runs along three lines. The topics below are grouped by those three lines, under the names the curriculum guide gives them.
Three practical things change between primary six and S.1. First, numbers become letters: x is no longer a blank to be filled in but a symbol standing for an unknown quantity, the rules of operation are the same as for numbers, but every step has to be set out. Second, in an English-medium school the topic names, the question instructions and the answering language all turn to English at once — equation, factorise, hence, correct to 3 significant figures are new words in the textbook. Third, answers begin to be marked on how they are written: on a school paper the same final number does not score the same with working shown and without.
The first few lessons take those three apart. We write an arithmetic question and the algebraic form of the same question side by side; we copy that term's English vocabulary into a bilingual list on the first page of the notes; and we go through the student's own papers, putting back the working that was left out, question by question.
Some students in Hong Kong are taught in Chinese and sit the paper in English, and others are taught in English but think in Cantonese. Both are handled the same way: the notes are written in both languages. 判別式 and discriminant, 餘式定理 and remainder theorem, 化至最簡 and express in the simplest form sit side by side on the same line in the notes.
When the school textbook and the exam paper word a thing differently — the textbook says 「解方程」, the paper says solve the equation, leaving your answer in surd form — we take the exam sentence apart word by word and point out which word is the one prescribing the form the answer has to take. Once that layer has been dealt with, a student can tell apart not being able to read the question and not knowing the topic.
Geometric proof is the first place a Hong Kong student's marks turn on how something is written. Every line needs a conclusion and a reason, and the reason has to use the name the paper accepts: ∠ABC = ∠DEF (corr. ∠s, AB // DE) — the phrase inside the brackets is the reason itself.
Which steps may be compressed also follows rules: vertically opposite angles and adjacent angles on a straight line can be carried by the reason alone; when congruence is used, the three corresponding conditions have to be listed one by one, with SAS, ASA or SSS stated, before the ≅ line is written. We take proofs the student has already done, put the missing reason back on each line, and then ask for the same question to be written out again.
Lessons one and two read the two most recent tests and quizzes, sort the wrong questions by topic, and work backwards from the wrong answer to find which year the break is really in. Lesson three deals with whatever that search turned up; at junior secondary the break is commonly in the laws of indices and in factorisation, then in operations with negative numbers and fractions. Lesson four changes the numbers on the same type of question and runs it again, to see whether the same place breaks or a different one does — the two are handled differently afterwards.
The Compulsory Part topics are set out below under the three strands of the curriculum guide, in the names that guide gives them.
The Compulsory Part has been revised, and the 2026 HKDSE is the first sitting taken under the revised curriculum. The revision started in S.4 in September 2023, and it added the Theorem of three perpendiculars to the Compulsory Part and split the former learning unit "Equations of straight lines and circles" into two units, "Equations of straight lines" and "Equations of circles". The junior secondary curriculum for the same cohort has been revised too, and what the HKDSE assumes a candidate brings with them is the revised Foundation and Non-foundation Topics. The content deleted from it includes polar coordinates, the identities for the sum and difference of cubes (a³ ± b³), accumulated error in measurement calculated by formula, and scatter diagrams. The hexadecimal number system was not deleted but moved to the enrichment topics, which puts it outside what the HKDSE assumes as well. The Extended Part was revised earlier than the Compulsory Part: it started in S.4 in September 2019 and applied from the 2022 HKDSE.
This bears directly on how past papers are used. Pre-revision papers can still be worked, with the questions on deleted topics simply skipped, since the question types and the phrasing of the rest have not changed. The Theorem of three perpendiculars has no past-paper question to work on, so it is covered with textbook questions and school papers instead. If the student's textbook is a pre-revision edition, we mark in the book in the first lesson which chapters are no longer in scope.
The Compulsory Part has two written papers and no school-based assessment. Paper 1 runs 2 hours 15 minutes for 105 marks and carries 65% of the subject, in three parts: Section A(1) 35 marks, Section A(2) 35 marks, Section B 35 marks. Paper 2 runs 1 hour 15 minutes, 45 multiple-choice questions, and carries 35%.
Those 45 Paper 2 questions are spread over 75 minutes, which is about 100 seconds each on average. That is not an estimate, it is the division, and it settles how the paper is practised: we do Paper 2 in timed batches — 15 questions in 25 minutes first, then a look at which ones ran over, and whether it was slow calculation, slow reading, or starting to substitute the options the moment they came into view. Substituting the options is quicker than solving on some question types and slower on others, and the two have to be told apart.
The HKEAA marking scheme classifies marks in three categories: method marks (M marks, awarded for a correct method being used), accuracy marks (A marks, awarded for the accuracy of the answer), and marks carrying neither M nor A, awarded for correctly completing a proof or arriving at an answer the question has already given. Method marks follow the working and the derivation, so those intermediate lines are themselves marks. Unless otherwise specified, numerical answers should be exact or correct to 3 significant figures, and rounding early in the intermediate steps leaves the last figure out.
The two things students ask about most are both written in the marking scheme, and written question by question: where an earlier step has been miscalculated and the method of the steps after it is correct, the remaining method marks are usually still available; and on some questions the accuracy mark is still awarded for a correct answer with no working shown. Both depend on the question, so when we mark we open that year's HKEAA marking scheme and go through it question by question rather than applying a general rule — what the student sees is “this line does or does not carry a mark under the marking scheme”, not “it reads better written this way”.
On the grade boundaries: the HKEAA has never published the raw mark for any level, and the cut-off tables in circulation are put together by candidates themselves, so this page does not print a number.
There are three steps after a paper has been marked. First a review, sorting the wrong questions into three kinds — did not know it, knew it but miscalculated, knew it but missed a condition in the question — because the three are handled quite differently afterwards. Then the wrong question is set again with different numbers and done a few days later. On that second attempt we look at three things: whether the same type of question came out right the second time, whether marks are still going to knowing it but miscalculating, and whether the paper was finished.
Changing the numbers is deliberate. Redo the original question and what the student remembers may be the answer rather than the route; change the numbers and the step that has just been put back is the one that has to be used.
What the first four lessons contain follows from the topic audit, and in practice there are two common cases.
In one, the break is in an earlier topic: the wrong questions trace back and stop at quadratic equations or the laws of indices, so the first four lessons go on those two, and only once they are fluent do we return to what the school is teaching now, because the current topic is built on top of them. In the other, Section A is secure and the marks are going in Section B and to calculation slips: then the first four lessons are the Section B long questions — taking apart the relationship between the sub-parts, seeing whether the answer to one part is the way into the next — together with timed Paper 2 work and the review routine.
First, the thing families most often get wrong: only one Extended Part module can be entered. M1 and M2 cannot both be taken, and neither has to be taken. Which module a school offers is the school's decision, and the HKEAA does not require a student to take the Extended Part at all.
The difference between the two modules is in the content.
In choosing between them, two things to look at are which kind of mathematics the student's other electives draw on, and which module the school offers. We weigh both up together at the trial lesson.
The M1 curriculum is divided into the Foundation Knowledge Area, the Calculus Area and the Statistics Area, with a Further Learning Unit in addition.
The stem of a statistics question is a passage of context in English — a factory, a sampling survey, the defect rate of a batch of parts. The difficulty is often not in the calculation but in reading which sentence decides the distribution: “on average 3 an hour” points to the Poisson distribution, “how many out of 20” points to the binomial distribution, and the moment “sample mean” appears the work moves to the sampling distribution. We pull the stems out of past papers and do that one step only — read it, then write down which distribution and why, with no calculation. Once the distribution is right, the calculation is the mechanical part.
The M2 curriculum is divided into the Foundation Knowledge Area, the Algebra Area and the Calculus Area, with a Further Learning Unit in addition.
More about trigonometric functions is not a chapter that is read once and finished with in M2; it keeps coming back. Mathematical induction proofs are frequently trigonometric identities; through differentiation and integration, composite trigonometric functions and the half-angle and double-angle formulae recur; and applications of definite integration are often simplified by a trigonometric substitution. So we put it before calculus and make it solid first, and then each time it is used afterwards we name which identity that step is using.
The following topics are outside the M2 curriculum, and students working on their own frequently read into them: complex numbers, L'Hôpital's rule, arc length, diagonalisation of matrices, inverse trigonometric functions. Students catching up from a university-level reference book or from overseas material most often read extra into L'Hôpital's rule and inverse trigonometric functions, so we mark out the scope once in the first lesson.
One distinction to keep straight: complex numbers are not in M2, but complex numbers are in the Compulsory Part — the section on the nature of the roots of a quadratic equation is exactly the case where the discriminant is less than zero. So “M2 does not examine complex numbers” is right and “DSE Mathematics has no complex numbers” is wrong; what separates the two sentences is the scope.
M1 and M2 have the same paper structure: one paper per module, 2 hours 30 minutes, 100 marks, Section A 50 marks (eight to twelve short questions; elementary short questions from the 2027 HKDSE) and Section B 50 marks (three to five long questions), all questions to be attempted, calculators permitted.
The Section B long questions are divided into sub-parts, and the answer to one part is usually the way into the next — which shows most plainly on the M2 derivation questions: (a) asks you to prove an identity and (b) asks you to use it. If (a) does not come out, the result of (a) can still be quoted to do (b), and the method marks are awarded on the derivation as written. When we drill Section B, we read the question first and mark the relationship between the sub-parts before any calculation starts.
When a few months of M2 have gone by and the student cannot keep up, the place it most often stops is differentiation: the chain rule and implicit differentiation carry on down the page, and then the application questions do not connect. This is not a case for reading the whole thing again from the beginning.
The approach is to step back two stages. First, check whether the definition of a limit and the section on differentiation from first principles were actually done — learning differentiation from the table of formulae, having never derived one, leaves nothing to work from when an unfamiliar function turns up. Then check whether the basic derivatives of the trigonometric and logarithmic functions were memorised or derived. The first four lessons usually run like this: lesson one is the audit, working questions from different topics to see at which step it stops; lessons two and three rebuild the basic rules of differentiation and apply them on the spot to what the school is teaching now; lesson four is a timed Section A paper, to see whether the speed has come up.
When the decision has to be made is set by the school, not by the HKEAA. When a school starts teaching the Extended Part, and when it closes the window for dropping it, differ from school to school, so ask the panel head of mathematics or the class teacher. A school offering one module only is common; that is the school's timetabling.
On university admission: each university and each programme sets its own requirement for M1 or M2, and the requirements change, so this page does not print a table and does not print a grade. Read the entrance requirements page of the programme itself, and distinguish what it states as an entrance requirement from what it says will be counted in the score.
Taking neither module is a real option, and putting the time the Extended Part would have taken back into the Compulsory Part is one way to arrange it. At the trial lesson we look together at where the student stands in the Compulsory Part, which module the school offers, and how much time the timetable can actually produce.
Lessons run 75 minutes, in Kwun Tong or online, billed every four lessons. One-to-one: HK$1,400 for S.1–S.3, HK$1,800 for S.4–S.6, HK$2,200 for Extended Part M1 or M2. A self-formed group is put together by the students themselves and is HK$200 less per student per four lessons, that is HK$1,200, HK$1,600 and HK$2,000.
The first lesson can be a free trial — tick the box on the enrolment form. The trial lesson looks first at where the student stands and where the weak points are, then talks through which topic to start from, with no enrolment asked for on the spot. For a student in the Extended Part, the same lesson confirms which module the school offers and whether the entry decision has been made.
Kwun Tong
Online
75 minutes
It is not the same — the fee is tiered by level, billed every four lessons, 75 minutes a lesson. One-to-one: HK$1,400 for S.1–S.3, HK$1,800 for S.4–S.6, HK$2,200 for Extended Part M1 or M2. A self-formed group is HK$200 less per student per four lessons, that is HK$1,200, HK$1,600 and HK$2,000. In Kwun Tong or online, and the first lesson can be a free trial.
Yes. Kwun Tong and online are both available, at the same fee, 75 minutes a lesson either way. Online lessons use screen sharing with a digital whiteboard, so the student's working is visible as it is written and a missing line can be circled as we mark. Those two are the options; there is no home tuition.
Yes. You put the group together yourselves, and it is HK$200 less per student per four lessons. It works when the two students are at a similar stage, because the group works through the same paper and the same review; if the two breaks are two years apart, separate lessons are more practical.
No enrolment is asked for on the spot. The first lesson can be a free trial — tick the box on the enrolment form. It looks first at where the student stands and where the weak points are, then talks through which topic to start from. For a student already in the Extended Part, the same lesson confirms which module the school offers and whether the entry decision has been made.
Because three things change at once: numbers become letters, the whole subject turns to English in an English-medium school, and answers start to be marked on how they are written rather than on the final number alone. The three are handled differently, so the first few lessons take them apart — an arithmetic question written beside its algebraic form, that term's English vocabulary copied into a bilingual list on the first page of the notes, and the student's own papers gone through to put back the working that was left out.
The notes are written in both languages. 判別式 and discriminant, 餘式定理 and remainder theorem, 化至最簡 and express in the simplest form sit side by side on the same line. When the textbook and the paper word a thing differently — the textbook says 「解方程」, the paper says solve the equation, leaving your answer in surd form — we take the exam sentence apart word by word and point out which word is prescribing the form the answer has to take.
Yes. Every line of a proof needs a conclusion and a reason, and the reason has to be in the form the paper accepts — ∠ABC = ∠DEF (corr. ∠s, AB // DE), where the phrase in brackets is the reason. Which steps may be shortened also follows rules: vertically opposite angles and adjacent angles on a straight line can be carried by the reason alone; when congruence is used, the three corresponding conditions are listed one by one and SAS, ASA or SSS is stated. We take proofs the student has already done, put the missing reason back on each line, and ask for the same question again.
Yes. There is no need to walk back through S.1 chapter one. We work backwards from the questions that came out wrong to find which year the break is really in, and pick it up from there. At junior secondary the break is commonly in the laws of indices and in factorisation.
Either — say which when you enrol. Following the school's pace is the common arrangement, because school tests and homework follow it. If the school is moving slowly and the student wants to move ahead, one lesson in every four can go on the ahead-of-school material and the rest stays with the school.
Not necessarily. What S.3 can usefully do is find out what is in the two modules — M1 is calculus alongside statistics, M2 is algebra alongside calculus — and check which one the school offers. The topic list for both modules is on this page, to read through as a family. If you do want to prepare, the laws of indices, factorisation and trigonometric ratios are used in both modules.
45 questions in 75 minutes is about 100 seconds each. We practise in timed batches: 15 questions in 25 minutes, then a look at which ones ran over, and whether it was slow calculation, slow reading, or starting to substitute the options the moment they came into view. Substituting is quicker than solving on some question types and slower on others, and the student needs to be able to tell which is which.
Often not. The marking scheme sorts marks into three categories: method marks (M marks), accuracy marks (A marks), and marks with neither M nor A, awarded for completing a proof or arriving at an answer the question has already given. Where an earlier step is miscalculated and the method after it is correct, the method marks that follow are usually still available. This is written question by question in the marking scheme rather than as a general rule, so when we mark we open that year's marking scheme and go through it question by question.
Unless the question specifies otherwise, answers should be exact or correct to 3 significant figures. Do not round early in the intermediate steps, or the last figure will not match — that is one of the ways marks go on questions the student can do.
The Compulsory Part has changed, and the 2026 HKDSE is the first sitting under the revised curriculum. The revision started in S.4 in September 2023 and added the Theorem of three perpendiculars to the Compulsory Part. The junior secondary curriculum for the same cohort was revised too, and what the HKDSE assumes is the revised Foundation and Non-foundation Topics. Deleted from it: polar coordinates, the identities for the sum and difference of cubes (a³ ± b³), accumulated error in measurement calculated by formula, and scatter diagrams. The hexadecimal number system was not deleted but moved to the enrichment topics, which puts it outside what the HKDSE assumes as well. If the textbook is a pre-revision edition, we mark in the book in the first lesson which chapters are out of scope. The Extended Part was revised earlier — September 2019, applying from the 2022 HKDSE.
Yes, with selection. On pre-revision papers the questions on deleted topics are skipped, and the question types and phrasing of the rest have not changed. The Theorem of three perpendiculars has no past-paper question to work on, so that part is covered with textbook questions and school papers.
There is no answer to give. The HKEAA has never published the raw cut-off for any level, and the tables in circulation are assembled by candidates themselves, so we do not print a number here. What we do instead is look at where the marks are going on the paper, rather than work towards a mark target.
Yes, and in most cases that is what should happen. We work backwards from the questions that came out wrong to find which year the break is really in, and pick it up from there. The break is dealt with before we go back to what the school is teaching now, because the new topic is built on top of it.
Yes. For that student the first four lessons are usually not more practice on questions they can already do, but two things: how the answer to one sub-part becomes the way into the next in the Section B long questions, and the marks lost to knowing it but miscalculating. We do not promise a particular grade. What we do is sort every lost mark after each paper into three kinds — did not know it, knew it but miscalculated, missed a condition — and set the next four lessons by whichever kind is largest.
No. Only one Extended Part module can be entered, M1 or M2. Taking neither is allowed; taking both is not. Which module a school offers is the school's decision, and the HKEAA does not require a student to take the Extended Part.
This page will not say which is easier: the two modules examine different content, they are not graded off the same raw mark, and the HKEAA has not published the cut-offs. What can be answered is the content. M1 is calculus alongside statistics, and most questions are a passage of context in English that the figure then has to be interpreted back into. M2 is algebra alongside calculus; mathematical induction, matrices and vectors are the parts M1 does not have, and the answer is usually a derivation rather than a value. Which one fits your situation, we weigh up together at the trial lesson.
Neither. M2 does not examine complex numbers, L'Hôpital's rule, arc length, diagonalisation of matrices or inverse trigonometric functions. Worth noting: complex numbers are in the Compulsory Part — the section on the nature of the roots of a quadratic equation is the case where the discriminant is less than zero. So “M2 does not examine complex numbers” is right, and “DSE Mathematics has no complex numbers” is wrong.
A good deal of it is. The stem of a statistics question is a passage of context in English, and the difficulty is often not the calculation but reading which sentence decides the distribution — “on average 3 an hour” points to the Poisson distribution, “how many out of 20” points to the binomial distribution, and the moment “sample mean” appears the work moves to the sampling distribution. We pull the stems out of past papers and do that step only: read it, write down which distribution and why, no calculation.
For entry, yes — which module the school offers and which module a student enters are two different things. In practice it means studying the whole module independently with no class to follow, so it has to be settled with the school's panel head of mathematics, both the entry and the lesson arrangements. We can teach either module, and at the trial lesson we can look at whether the timetable works.
Not necessarily. When a few months of M2 have gone by and it stops working, the place it most often stops is differentiation. The approach is not to read the whole thing again from the beginning but to step back two stages: check whether the definition of a limit and differentiation from first principles were actually done, then whether the basic derivatives of the trigonometric and logarithmic functions were memorised or derived. The deadline for dropping the module is set by the school, so that has to be asked at the school.
That needs the timetable on the table rather than a yes or no. Three things to look at together: which Compulsory Part topics the student is currently stuck on, how many hours a week they can actually produce, and when the school starts teaching the Extended Part. We weigh it up together at the trial lesson.
Taking neither is a real option. Putting the time the Extended Part would have taken back into the Compulsory Part is a practical arrangement. On university admission, each institution and each programme sets its own requirement and the requirements change, so we do not print a figure here — read the entrance requirements page of the programme itself.
That has to be read off each programme's own published entrance requirements. Every university and every programme sets its own, and they change from year to year, so we do not print a table or a grade. What we can do is take the entrance requirements page for your target programme and read it together, distinguishing what it states as an entrance requirement from what it says will be counted in the score.
The school sets that. When a school starts teaching the Extended Part, and when it closes the window for dropping it, differ from school to school, so ask the panel head of mathematics or the class teacher. Entry dates are published by the HKEAA each year.
There is no single answer, and we do not promise a particular grade. What we actually look at is three things: whether the same type of question came out right the second time, whether marks are still going to knowing it but miscalculating, and whether the paper gets finished. Whichever of the three moves first sets where the next four lessons go.
No. IGCSE Mathematics is on the GCSE / IGCSE page, A-Level Mathematics on the GCE A-Level / IAL page, IB Mathematics on the IBDP page, and AP Calculus and AP Statistics on the Advanced Placement page. Those four run 60-minute lessons, one-to-one only, charged by the hour; this page's lessons run 75 minutes, one-to-one or in a self-formed group.