H3 Mathematics in A-Level — 2026 Evergreen Guide
Download printable cheat-sheet (CC-BY 4.0)06 Nov 2025, 00:00 Z
TL;DR
H3 Mathematics is a research-style extension to the core H2 course.
Candidates sit one 3-hour paper that probes proof techniques, combinatorial reasoning and applications such as graph theory or number theory.
Only the top ~10 % of each cohort receive an invitation; distinctions earn bonus rank points that can tip competitive courses.
This guide maps the syllabus, flags hidden cliffs, and shows how IP-style tuition bridges the leap from H2 to H3.
1 | What exactly is H3 Mathematics?
- Purpose — stretch and expose mathematically inclined JC2 students to university-level ideas.
- Award — graded Distinction / Merit / Pass / Ungraded and shown separately on the A-Level certificate.
- Weight — does not count towards the usual 90 rank points, but Distinction fetches +1 RP under MOE's revised score-cap rules.
2 | Eligibility & enrolment timeline
| Stage | Window | Typical cut-off | Action |
| Sec 4 / JC 1 EOY | Oct - Nov | H2 Math promo ≥ B or ≥ 70 % | Indicate interest during subject combi briefing |
| JC2 Term 1 | Mid-Jan | School calculates Math MSG + teacher rec | Shortlisted list published |
| JC2 Term 1 Wk 3 | Late Jan | Internal qualifying quiz (proof, Olympiad) | Top scorers offered H3 slot |
| JC2 Term 2 | Apr | SEAB registration closes | Pay exam fee via school finance office |
Tip — a B at JC1 Promo often beats the formal A-grade rule if tutors vouch for proof potential.
3 | Syllabus at a glance
| Theme | Key outcomes | Typical question flavour |
| Combinatorics | Use Pigeonhole and Inclusion-Exclusion | Prove minimum edges in a friendship graph |
| Number Theory | Modular arithmetic, Fermat's Little Theorem | Show (n^5 - n \text{ is divisible by } 30) |
| Graph Theory | Eulerian/Hamiltonian paths, planar graphs | Decide if a road network admits an Euler trail |
| Proof & Reasoning | Direct, contrapositive, induction, extremal | Induct on (k) for a binomial sum |
| Advanced Calculus / Series | Taylor, L'Hôpital, improper integrals | Show [\sum_{n=1}^{\infty}\frac{1}{n^2} = \frac{\pi^2}{6}] via comparison |
4 | Assessment structure
- One 3-hour written paper — 100 marks
- Section A (60 marks): 6 structured questions — proof steps required
- Section B (40 marks): choose 2 of 3 long problems — multi-topic synthesis
Tip to pace yourself and finish the paper:
\[ \text{Marks per minute} = \frac{100}{180} \approx 0.56 \]
5 | How H3 builds on H2 (and where students slip)
| H2 anchor | H3 extension | Common error |
| Binomial theorem \(^n C_k\) | Combinatorial proofs & Stirling | Ignores boundary \(k=0, n\) cases |
| Sigma notation | Induction on sums & products | Skips base-case when \(n=1\) |
| Vectors & matrices | Adjacency matrices for graphs | Treats order as commutative |
| Power series | Taylor remainder bounds | Uses \(\le\) instead of \(<\) — loses rigor |
6 | 12-week preparation sprint
| Weeks | Focus | Concrete drill |
| 1-2 | Proof warm-up | Daily 2-line contrapositive exercises |
| 3-4 | Number theory | 20 modular congruence MCQs / night |
| 5-6 | Combinatorics | Write 5 short PIE proofs with (\Sigma (-1)^k) |
| 7-8 | Graph theory | Draw 3 planar vs non-planar proofs |
| 9-10 | Mock Paper A | 60-mark timed in 110 min |
| 11-12 | Mock Paper B | 2x20 mark problems under exam rules |
Follow the same error-journal loop described in Developing IP-Level Problem-Solving Habits.
7 | Tuition & enrichment strategies
- IP-only micro-classes (≤8) — maintain rigor yet allow white-board proof walk-throughs.
- Olympiad cross-training — SMO Senior & Open papers mirror H3 style.
- Research modules — RI & HCI Raffles Academy / CTP projects can double-count as H3 prep.
- WhatsApp screencast support — clarifies proof gaps within 24 h during promo crunch.
See how this dovetails with our Bridging the Gap from IP Y4 to JC1 plan.
8 | FAQs
Q — Must I take H2 Further Mathematics to be eligible?
No. H3 is stand-alone; many schools pair it with H2 Math only.
Q — Does H3 hurt my other subjects?
Time cost ≈ 2 h lecture + 2 h tutorial / week; schedule around CCA off-seasons.
Q — Do universities care?
Yes — NUS, NTU and overseas STEM faculties regard a Distinction as evidence of proof maturity.
9 | Further reading
Last updated 6 Nov 2025 — next auto-refresh when SEAB publishes the 2027 H3 specimen paper.
