H3 Math in A-Level: 2026 Guide

Name: Eclat Institute Clementi Campus
Address: 442 Clementi Ave 3, #01-105, Singapore, 120442, SG

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06 Nov 2025, 00:00 Z

Q: What does H3 Math in A-Level: 2026 Guide cover?
A: What parents and Integrated-Programme students need to know about H3 Math: how it builds on H2, who should take it, syllabus structure, assessment formats.

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.
Selection is school-based; H3 grades appear on the A-Level certificate and may be considered by universities, but do not contribute to the UAS.
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 - H3 does not contribute to the UAS; it is listed on the certificate and may be considered qualitatively by universities.

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

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

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

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

H3 Math in A-Level: 2026 Guide

1 | What exactly is H3 Mathematics?

2 | Eligibility & enrolment timeline

3 | Syllabus at a glance

4 | Assessment structure

5 | How H3 builds on H2 (and where students slip)

6 | 12-week preparation sprint

Practice Quiz

7 | Tuition & enrichment strategies

8 | FAQs

9 | Further reading

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