Private Tutoring (1:1) · Mathematics
60-minute lessons · billed every four lessons
- Further Mathematics
- HK$850 per hour
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GCE A-Level / IAL
GCE A-Level / IAL Further Mathematics tutoring: Edexcel's YFM01 is built from FP1 plus FP2 and/or FP3, covering complex numbers, matrices and linear transformations, further calculus, differential equations, mechanics and statistics. Taught by Tinnie, one-to-one only, 1 hour a lesson, Kwun Tong or online, with a free first trial lesson.
Need GCE A-Level or International A-Level Further Mathematics 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 subject is one-to-one private tutoring only, 1 hour a lesson, HK$850 per hour, billed every four lessons, in Kwun Tong or online, and the first lesson can be a free trial. Lessons follow the board the school has entered the student for: Edexcel IAL is modular and is taught to the combination of units already entered, while Cambridge International A Level Further Mathematics (9231) takes all four papers, with no choice of units. The content covers Further Pure, Mechanics and Statistics, and on the Edexcel side there is also a Decision Mathematics unit. The Pure core units of Mathematics, P1 to P4, are a separate subject with their own course page.
Further Mathematics is entered and graded separately from Mathematics; the two are separate qualifications. Take Edexcel IAL: Further Mathematics (YFM01) is built from six units — FP1 is compulsory, then one or both of FP2 and FP3, with the remaining units chosen from the Mechanics, Statistics and Decision Mathematics units. Every unit is externally assessed, 1 hour 30 minutes, 75 marks.
Resits and cashing in units: a unit can be resat, and the better result counts. But once a unit has been used in the cash-in for one qualification, it cannot be used again for another — so entering both Mathematics and Further Mathematics takes twelve units between them, with no overlap. Which two applied units go to Mathematics and which are kept for Further Mathematics is decided before entry.
The two boards are not structured the same way. Edexcel IAL is modular: Further Mathematics (YFM01) is built from six units, and they can be sat across more than one series. Cambridge International A Level Further Mathematics (9231) takes all four papers — Further Pure Mathematics 1, Further Pure Mathematics 2, Further Mechanics, Further Probability & Statistics — with no choice of units and no decision mathematics. The four can be sat in one series, or staged over two years: Paper 1 with Paper 3, or Paper 1 with Paper 4, in the first year as the AS, then the remaining two papers to complete the A Level, with the AS result carried forward under Cambridge's rules and time limits. Past papers from one board do not stand in for the other. When you enrol, tell us which board the school has entered the student for, and if it is Edexcel, which units have already been entered; we teach to that board's specification and that board's past papers, so that every paper practised runs in the same direction as the one to be sat.
If the board is Edexcel and the school has not yet settled the combination of units, or the student is still considering adding the subject, the trial lesson looks at the units already entered for Mathematics and at the sittings for the other subjects alongside them, and we weigh it up together. No enrolment decision is asked for at the trial lesson.
Further Pure is the spine of the subject, and most of the tools the other units use are built here.
These topics have a set way of being written out. A proof by induction has to set down the assumption, the working and the conclusion as three separate steps; a matrix question needs the matrix written out as well as the name of the transformation, and the method marks sit on the line the matrix is written on. When we teach these topics, we first work one through to the number of lines the mark scheme expects, then ask the student to redo a question in the same format.
Mechanics carries on from the kinematics and Newton's laws of the Mathematics mechanics units and puts the same methods to work on collisions and on motion that is not in a straight line. Edexcel splits it across three units, M1, M2 and M3; Cambridge gathers it into one paper, Paper 3 Further Mechanics.
For mechanics questions we ask for a force diagram first on every question, the positive direction marked, the equations written one direction at a time, and the numbers substituted last. That has a second use: if the final answer comes out wrong, those few lines show which step took the wrong direction or the wrong sign, without redoing the whole question.
Edexcel splits it across three units, S1, S2 and S3; Cambridge has one paper, Paper 4 Further Probability & Statistics.
In statistics the concluding sentence carries marks of its own. A hypothesis test is not finished at the test statistic — it needs the comparison with the critical value, whether the null hypothesis is rejected, and one sentence putting the conclusion back into the context of the question. When we mark, we look at those three lines separately, so the student can see which line the marks came off, rather than only that the question was wrong.
Decision Mathematics appears on the Edexcel side only, as the D1 unit (WDM11); Cambridge 9231 has no decision mathematics. D1 covers algorithms, algorithms on graphs, critical path analysis and linear programming: shortest paths, minimum spanning trees, scheduling problems, and, once a question has been formulated as a linear program, graphical solution of two-variable problems by the ruler and vertex methods, together with problems whose solutions must have integer values. The answer to this kind of question is a process — each round's choice and the reason for it have to be written down, and that is where the marks are awarded. Whether D1 is taken depends on the combination of units on the Edexcel side, so tell us when you enrol.
The Further Mathematics units assume the Pure content of Mathematics is already in hand, so the two subjects have to be scheduled together. The usual prerequisites are these.
So for a student taking both subjects, we schedule the corresponding Mathematics topic ahead of the Further unit that draws on it; if the school has not yet reached one of those prerequisites, we spend a lesson or two picking it up first, then go back to the Further unit.
Every Edexcel unit's mark scheme sets out, question by question, which line the M marks (method) and the A marks (accuracy) fall on: an M mark is for using the right method and writing the working down, an A mark for the value or the form of that step being correct. So the working for every step needs to be written down — the M marks sit on those lines; and if the value in an earlier step comes out wrong, the M marks in the steps after it can still stand where the method is right.
When we mark, we go line by line against that same published mark scheme for the unit, and name which line was not written down, rather than marking the question right or wrong as a whole. How answers are to be presented — what to round to where the question does not say, degrees or radians, whether units are needed — is handled to that unit's mark scheme as well.
On the Edexcel side, Pearson runs three examination series a year — January, summer and October — but the Further Mathematics units are not in all three: FP1, FP2, FP3, M3, S3 and D1 run in January and June only, while October carries P1 to P4, M1, M2, S1 and S2. On the Cambridge side, 9231 runs in two series, June and November. So we do not schedule sittings from memory; we check them against the timetable for the year and the board the student is entered for.
Tell us at enrolment which unit is intended for which sitting, and we work the schedule back from it: the units for the nearest sitting are locked in first, and the rest follow. If a unit is to be resat, we get the previous paper and the mark breakdown back first and separate out whether the content was not understood, the time ran short, or marks went on how the answer was written — what to do about each of the three is different. Resit arrangements for Mathematics units are covered on the A-Level Mathematics course page.
On the Edexcel IAL side, entering both subjects takes twelve units between them with no overlap, so in the first lesson we lay both subjects' units and sittings out on one timeline. A common order is three units at the end of the first year — usually P1, P2 and one applied unit — then P3, P4 and the remaining units in the second year, with FP1 usually placed once the Pure content of Mathematics has come far enough along. That is a common arrangement rather than a rule; the actual order follows the units the school has entered and the student's own sittings.
The Mathematics units themselves, how the applied units pair up, and the overall planning of the modular structure are covered on the A-Level Mathematics course page, and are not repeated here.
Further Mathematics points towards mathematics, physics, engineering, actuarial science and quantitative economics — degree courses that use complex numbers, matrices, differential equations and vector work directly. Some university courses require or recommend it, and others ask only for Mathematics. The actual requirements are set by each institution and each programme and are revised from year to year, so check that programme's own admissions page; we list no grade requirements here.
Whether to add the subject is a question of the whole timetable as well as the degree direction: the other subjects being taken at the same time, the units already entered, and how far off the nearest sitting is. At the trial lesson we look at these together and weigh it up.
The first lesson confirms the board, the papers or units to be sat and the sittings, then works back from the papers the student has done most recently to see which question stops at which step. Within four lessons we finish one complete unit topic — a common starting point is complex numbers and matrices in FP1: getting the arithmetic of complex numbers and the Argand diagram representation solid first, then on to matrix multiplication, determinants and linear transformations, demonstrating along the way how mathematical induction is written out to the mark scheme.
After that comes a past paper for that unit, with the questions that went wrong redone with the numbers changed. The second attempt checks two things: whether the same type of question came out right, and whether the line that was missing last time has been put back in.
Kwun Tong
Online
60 minutes (1 hour)
60-minute lessons · billed every four lessons
Further Mathematics is HK$850 per hour, lessons are 1 hour, billed every four lessons, so HK$3,400 for four. Mathematics is a separate subject, at HK$800 per hour. This subject is one-to-one only; there is no group rate. Lessons run in Kwun Tong or online, and the first lesson can be a free trial.
We teach both. Tell us which board the school has entered the student for, and if it is Edexcel IAL, which units have already been entered. The two are not structured the same way — Edexcel is modular, while Cambridge International A Level Further Mathematics (9231) takes all four papers with no choice of units — and the paper structure and the specification both differ, so past papers from one board cannot stand in for the other. Once that is settled, every paper practised runs in the same direction as the one to be sat.
Structurally it needs the Pure content of Mathematics underneath it. The Further units assume differentiation, integration, trigonometric identities and vectors, so the two subjects are usually scheduled together. If Mathematics has already been sat, taking Further on its own is fine.
Edexcel IAL's Further Mathematics (YFM01) takes six units: FP1 is compulsory, then one or both of FP2 and FP3, with the rest chosen from the Mechanics, Statistics and Decision Mathematics units. Which combinations are actually open depends on that board's specification and on the units the school has already entered, and we go through them one by one at enrolment. Every unit is externally assessed, 1 hour 30 minutes, 75 marks. Cambridge 9231 has no such choice — the A Level takes all four papers.
On the Edexcel IAL side, twelve, and they cannot overlap. Once a unit has been used in the cash-in for one qualification, it cannot be used again for the other. So which two applied units are kept for Mathematics and which for Further is decided before entry, and we go through it with you in the first lesson.
On the Edexcel IAL side, yes, and the better result counts. Cambridge 9231 works differently: there is no resitting a single paper on its own, though a whole AS or a whole A Level can be retaken. The four A Level papers can be sat in one series, or staged over two years — Paper 1 with Paper 3, or Paper 1 with Paper 4, in the first year as the AS, then the remaining two papers to complete the A Level, with the AS result carried forward under Cambridge's rules and time limits. Before a resit we get the previous paper and the mark breakdown back and look at them properly: whether the content was not understood, the time ran short, or marks went on how the answer was written. What each of the three calls for is entirely different.
On the Edexcel IAL side, yes — the modular structure lets units be handled separately, so tell us which unit and when the sitting is, and we work the schedule back from the sitting. Cambridge 9231 is not modular, and no single paper can be taken apart on its own, so there we work by paper instead — concentrating on the content of Further Pure Mathematics 2, for example, which on the staged route is one of the two papers sat in the second year.
On the Edexcel IAL side, Pearson runs three examination series a year — January, summer and October — but the Further Mathematics units are not in all three: FP1, FP2, FP3, M3, S3 and D1 run in January and June only, while October carries P1 to P4, M1, M2, S1 and S2. For Cambridge 9231, the examinations run in two series, June and November. So rather than going from memory, we check the timetable for the year and the board the student is entered for, and schedule from that.
The order is Mathematics P1 and P2 first, because the Further units assume A-Level Pure content. A student who has taken 0606 Additional Mathematics or 4PM1 Further Pure has already met differentiation, integration and factorisation, which overlap with the first few topics of P1, so that part does not start from nothing. For a summer bridge we start by looking at how fluent the laws of indices and factorisation are.
There are online lessons; we do not teach at students' homes. Lessons can be in person in Kwun Tong or online, and both are 1 hour a lesson, billed every four lessons. Students studying abroad can take lessons too.
We are a tutorial centre, in Kwun Tong; mathematics is one-to-one private tutoring only, and there is no group for this subject. Mathematics is taught by Tinnie alone — the same person handles the trial lesson, the scheduling of sittings and the marking.
No. This page is GCE A-Level / IAL Further Mathematics only. A-Level Mathematics — P1 to P4 and the applied units — is on the A-Level Mathematics page, and IB, AP, IGCSE and the DSE each have their own course page. Note that the lesson lengths differ: IGCSE, IAL, IB Diploma and AP lessons are 1 hour and charged by the hour, while DSE and primary lessons are 75 minutes.