H2 Maths Syllabus (9758)

This is a plain-language map of the A-Level H2 Mathematics syllabus (code 9758) as it is examined now — including the trims made in the 2025 revision, which many older notes and websites still miss.

Quick facts

• Two written papers, 3 hours each, 100 marks each, worth 50% each. All questions are compulsory.
• Paper 1 is entirely Pure Mathematics (10-12 questions). Paper 2 is Pure Mathematics (Section A, 40 marks) plus Probability and Statistics (Section B, 60 marks) — so the overall weighting is roughly 70% pure, 30% statistics.
• Each paper contains one real-world applications question worth at least 12 marks.
• A graphing calculator without CAS is expected throughout; there is no calculator-free paper.
• The exam provides the MF27 formula booklet (successor to MF26) — knowing what is and is not inside it is worth real marks.

Section A: Pure Mathematics

1. Functions and graphs — functions (domains, ranges, inverses, composites), graphs and transformations (including $y = |f(x)|$, $y = f(|x|)$ and $y = \frac{1}{f(x)}$), and equations and inequalities solved exactly and with the GC.

2. Sequences and series — arithmetic and geometric progressions, sigma notation, and sequences generated by recurrences $u_{n+1} = f(u_n)$ explored with the GC, including convergence.

3. Vectors — dot and cross products, lines and planes in 3D, angles, projections and distances. (Shortest distance between skew lines is explicitly excluded.)

4. Introduction to complex numbers — complex arithmetic in cartesian form, Argand diagrams and conjugate roots. Since 2025 the topic stops there: polar and exponential forms are no longer examined.

5. Calculus — the biggest strand: differentiation (implicit, parametric, applications), Maclaurin series and small-angle approximations, integration techniques, definite integrals with areas and volumes of revolution, and differential equations of the variable-separable kind.

Section B: Probability and Statistics

• Permutations and combinations — arrangements in a line or circle, with restrictions.
• Probability — the probability laws, conditional probability and independence.
• Discrete random variables — general DRVs and the binomial model.
• The normal distribution — including sums like $aX + bY$ of independent normals.
• Sampling — the distribution of the sample mean, the Central Limit Theorem and unbiased estimates.
• Hypothesis testing — $z$-tests on a population mean, p-values, 1-tail and 2-tail tests.
• Correlation and regression — the PMCC, least-squares lines and linearising transformations.

What is NOT in 9758

Knowing the exclusions saves wasted study time, especially if you use older materials:

• Removed in the 2025 revision: polar (modulus-argument) and exponential forms of complex numbers; the method of differences for series.
• Never in 9758 (dropped from the older 9740 syllabus in 2017): mathematical induction, complex loci on the Argand diagram, the Poisson distribution, and the normal approximation to the binomial.
• Statistics limits: hypothesis testing uses $z$-methods only (no $t$-tests), and Type I/II error concepts and two-sample mean tests are excluded.

If a school hand-me-down or website teaches any of the above as current H2 content, it is out of date.

Typical JC1 vs JC2 split

There is no official teaching order — every JC sequences the syllabus its own way — but the common pattern is:

• JC1: almost entirely Pure Mathematics — functions and graphs, inequalities, sequences and series, vectors, differentiation, Maclaurin series, and integration begun.
• JC2: the rest of calculus (differential equations, applications of integration), complex numbers, then the whole of Probability and Statistics, with Terms 3-4 given to revision and prelims.

The practical consequence: statistics is compressed into JC2 alongside prelim preparation, so students who pre-read the stats topics in the JC1 year-end break start JC2 with a real advantage.

The applications emphasis

9758 was designed around applying mathematics, not just executing techniques: 60% of marks target formulating and solving problems, including unfamiliar real-world contexts (kinematics, optimisation, population models, finance, standardised testing and more — all context information is given in the question). The guaranteed 12-mark applications question in each paper is where this bites. Practising only drill-style questions leaves you unprepared for exactly the highest-value question in the paper.

Study the syllabus with a tutor that knows it

MathChat’s AI tutor is built specifically around H2 Maths 9758 — it walks you through problems step by step Socratically instead of just handing over answers, and it knows what is (and is not) in the current syllabus.