Written and reviewed by Theon Teo, Founder · editorial policy
What H2 Further Mathematics (9649) involves for the 2027 A-Level: the two papers, the pure and statistics topics, some JCs that offer it, how it counts in the University Admission Score, a self-check list, a marked worked example and a two-year plan.
Further Maths adds new areas, such as matrices and recurrence relations, and pushes familiar ones further. The full H2 Maths syllabus is in our JC2 H2 Mathematics guide, so this table shows only the differences.
| Point | H2 Mathematics 9758 | H2 Further Mathematics 9649 |
|---|---|---|
| Taken with | Any subject combination | Only alongside H2 Mathematics |
| Assumed knowledge | O-Level Maths, with Additional Maths topics listed | All of H2 Mathematics |
| Paper 2 split | 40 marks pure, 60 marks statistics | 50 marks pure, 50 marks statistics |
| Complex numbers | Cartesian form and Argand diagrams only | Polar and exponential form, de Moivre's theorem, nth roots, loci |
| Differential equations | Separable equations, dy/dx = f(x)g(y) | Integrating factor, second order linear equations, logistic growth and harvesting |
| Calculus extras | Area and volume of revolution | Arc length, surface area, shells, functions of two variables, partial derivatives |
| Matrices and linear algebra | Not in the syllabus | 3 by 3 matrices, eigenvalues, diagonalisation, linear spaces, rank |
| Discrete and numerical | Sequences and series | Recurrence relations, Newton-Raphson, Simpson's rule, Euler's method |
| Statistics | Binomial, normal, sampling, z-tests, correlation and regression | Poisson, geometric, continuous variables, t-tests, chi-square tests, confidence intervals, sign and Wilcoxon tests |
| Assessment objectives | 30% techniques, 60% problem solving, 10% reasoning | The same 30%, 60% and 10% |
The pure half has two strands: algebra and calculus, then discrete mathematics, matrices and numerical methods. The statistics half sits entirely in Paper 2 Section B.
The assessment objectives, in plain words: about 30% of marks reward carrying out a known method correctly, about 60% reward choosing the right tool and turning a situation into equations, and the last 10% reward explaining and proving. A graphing calculator without computer algebra is expected, and a formula list (MF27) is provided.
SEAB lists application contexts such as electrical circuits, population growth, cooling, cryptography, genetics and polling. The question supplies everything about the context, so the skill is turning words into a model, not knowing the science.
Five or more honest yes answers is a good sign. Two or fewer suggests the time is better spent on H2 Maths.
For students who sat the A-Level in 2025 or later, the University Admission Score is out of 70. NUS counts GP and three H2 content subjects from the same sitting. A fourth H1 or H2 content subject is added only if it improves the score, and the total is then rebased from 80 to 70. Our UAS explainer has the full method.
Further Maths has its own grade, so it can be one of those three H2 subjects. Take a double maths student with H2 Physics and a contrasting H1 Economics.
| Subject | Grade | Points |
|---|---|---|
| H2 Mathematics | A | 20 |
| H2 Further Mathematics | B | 17.5 |
| H2 Physics | A | 20 |
| GP | B | 8.75 |
| Base score | 66.25 out of 70 | |
| H1 Economics | B | 8.75, tested as a fourth subject |
Adding H1 Economics gives (66.25 + 8.75) ÷ 80 × 70 = 65.63, which is lower, so the university keeps 66.25. If Further Maths had been a C, the base would fall to 63.75. That is the real risk: Further Maths is not a bonus subject. If a student offers four H2 subjects and no H1 content subject, ASRJC's UAS guide says the weakest H2 is computed at the H1 weighting of 10 points when tested as the fourth subject.
We wrote this question for the differential equations topic (1.5). The integrating factor method is not in H2 Maths. The marks show how we would split credit, not an official scheme.
The question. A tank holds 50 litres of pure water. Salt solution with 0.2 kg of salt per litre flows in at 3 litres per minute. The mixture is kept well stirred and flows out at 2 litres per minute. The tank holds 100 litres when full. Let S kg be the salt in the tank after t minutes.
(a) Show that dS/dt + 2S/(50 + t) = 0.6. [2 marks]
(b) Find S in terms of t. [6 marks]
(c) Find the amount of salt in the tank at the moment it becomes full. [2 marks]
This plan adds about three to four hours of Further Maths self-study a week on top of homework, and keeps H2 Maths in step, since Further Maths builds on it.
A sample week in JC2 Term 2 looks like this.
| Day | H2 Maths | H2 Further Maths |
|---|---|---|
| Monday | Homework | 45 minutes on the new topic |
| Wednesday | 45 minutes of mixed practice | Homework |
| Friday | Error log review | One timed application question |
| Weekend | One timed past paper section | 90 minutes of mixed questions |
If the plan keeps slipping by more than a week, cut back elsewhere or get help early. For the H2 Maths side, see how to score a distinction in H2 Maths.
No. SEAB's syllabus says it is offered with H2 Mathematics as a double mathematics course, and it assumes the whole H2 Maths content.
No. The 2027 and 2026 syllabus documents for 9649 have the same topics, papers and marks, with only small wording changes.
No. ACJC, NYJC, TMJC, Temasek JC and VJC, for example, list it on their own websites. Others may also offer it, so check the JC's subject combination page or ask at the open house.
Some do. ACJC allows the subject only for students who clear a proficiency test at orientation. Rules differ by college.
No. It counts like any other H2 subject in the University Admission Score. A strong grade helps and a weak one hurts, in the same way as Physics or Chemistry.
No. NUS accepts it as an alternative to H2 Maths for some prerequisites, and NTU's A-Level requirements ask for H2 Mathematics. Neither list requires Further Maths.
Our plan above assumes about three to four hours of self-study a week beyond lessons and homework.
Written by Theon Teo, Founder and Mathematics Tutor, The Singapore Syllabus. DigiPen Institute of Technology Singapore, Game Development & Computer Science · 3 years' Mathematics teaching (Primary & Secondary). More about Theon
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