Q — Must I take H2 Further Mathematics to be eligible?

No. The MOE syllabus lists H2 Mathematics as the prerequisite; Further Mathematics is optional.

Q — Does H3 hurt my other subjects?

Paper prep sits on top of H2; plan for lectures/tutorials plus proof practice. Drop H3 early if your H2s slip.

Q — Do universities care?

H3 grades (Distinction/Merit/Pass) appear on the A-Level certificate but do not enter the 70-point UAS; they are considered qualitatively for admissions and scholarships. ---

H3 Math in A-Level: 2026 Guide

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06 Nov 2025, 00:00 Z

Reviewed by

Marcus Pang·Managing Director (Maths)

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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 (syllabus 9820, first examined 2025) is a proof-heavy extension to H2.
Candidates sit one compulsory 3-hour paper marked out of 80 with six questions (Q6 includes reading/responding to a mathematical text).
Selection is school-based; H3 is graded Distinction/Merit/Pass on the A-Level certificate but is not counted in the 70-point University Admission Score (UAS).
This guide maps the syllabus, flags hidden cliffs, and shows how IP-style tuition bridges the leap from H2 to H3.

For the full H2 foundation sequence that H3 builds on, keep our H2 Maths Notes hub nearby.

Status: MOE H3 Mathematics (9820, first exam 2025) syllabus last checked 2025-11-30 (PDF last modified 2024-01-15). Scheme remains one 3 h, 80-mark paper with six compulsory questions (Q6 includes a reading-and-response task).

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	What is fixed	What varies by college
Pre-requisite	MOE syllabus lists H2 Mathematics as required	Schools may ask for stronger H2 performance or teacher recommendation
Subject briefing

Theme	Key outcomes	Example flavour
Mathematical statements & proof	Write and negate quantified statements; prove by direct arguments, induction, contradiction, construction, cases, combinatorial proofs, pigeonhole	Disprove a claim via counterexample; prove uniqueness with induction
Problem-solving heuristics	Work backwards, uncover pattern/structure, restate as contrapositive	Reframe a divisibility task using modular equivalence
Extended H2 tools	Method of differences; reduction formulae; improper integrals; bijection and inclusion-exclusion; AM-GM/Cauchy-Schwarz/triangle inequalities	Evaluate an improper integral with a reduction relation
Limits & growth	Compare polynomial, exponential, logarithmic growth; apply limit laws	Rank functions by order of growth as (x \to \infty)
Congruences	Apply modular arithmetic to integer problems	Show (n^5 - n) is divisible by 30 using congruences

H2 anchor	H3 extension	Common error
Binomial theorem $^n C_k$	Combinatorial proofs, inclusion-exclusion	Ignores boundary $k=0, n$ cases
Sigma notation	Method of differences; reduction formulae	Skips base-case when $n=1$
Inequalities	AM-GM, Cauchy-Schwarz, triangle equality cases	Forgets equality conditions, so proofs are incomplete
Calculus & limits	Improper integrals, growth order (poly vs exp vs log)	Assumes convergence without checking end behaviour

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	Inclusion-exclusion & bijections	Write 5 short PIE proofs with (\Sigma (-1)^k)
7-8	Limits & inequalities	Rank growth rates (poly/exp/log); prove AM-GM/Cauchy equality cases
9-10	Mock Paper A	Full 80-mark set in 180 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 (H3 Mathematics 9820)

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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