Singapore A-Level H2 Mathematics (9758): complete 2026 guide to the five content areas and Papers 1-2

Singapore GCE A-Level H2 Mathematics (SEAB syllabus 9758) is a rigorous two-year course that develops mathematical reasoning across Pure Mathematics and Statistics, from functions and graphs through calculus and complex numbers to probability distributions and hypothesis testing.

This page is the index. Below: the five content-area breakdown, the two-paper assessment structure, the graphing-calculator expectations, study strategy, and links to every dot-point answer we have shipped for H2 Mathematics in 2026.

The five content areas of H2 Mathematics

Functions and Graphs

Functions, domains and ranges, composite and inverse functions, the modulus function, graphing techniques for rational and other curves, asymptotes, transformations of graphs, and solving inequalities including those involving the modulus.

Sequences and Series

Arithmetic and geometric progressions, sigma notation, the method of differences, convergence of geometric series, binomial expansion for rational indices, and recurrence relations.

Vectors and Complex Numbers

Vectors in two and three dimensions, scalar and vector products, lines and planes and their intersections, complex numbers in Cartesian and polar and exponential form, the Argand diagram, and loci.

Calculus

Differentiation including implicit and parametric forms, techniques of integration (substitution, by parts, partial fractions), definite integrals and areas and volumes of revolution, differential equations, and the Maclaurin series.

Probability and Statistics

Permutations and combinations, probability and conditional probability, discrete random variables, the binomial, Poisson and normal distributions, sampling and the Central Limit Theorem, hypothesis testing, and correlation and regression.

Assessment structure

H2 Mathematics 9758 is assessed across two papers, each 3 hours and worth 100 marks, weighted equally.

• Paper 1: Pure Mathematics (100 marks, 3 hours). Covers functions and graphs, sequences and series, vectors, complex numbers and calculus.
• Paper 2: Pure Mathematics and Statistics (100 marks, 3 hours). Section A is Pure Mathematics; Section B is Probability and Statistics covering the full statistics content.

Both papers reward clear working, exact answers where required, correct notation, and well-justified statistical modelling decisions. A graphing calculator is required for both.

Using the graphing calculator

The calculator is a tool, not a substitute for method:

1. Solving and checking. Use it to solve equations numerically, find intersection points, and verify turning points found by calculus.
2. Calculus support. Evaluate definite integrals and derivatives at a point, and sketch curves to confirm the shape of a hand analysis.
3. Statistics. Compute binomial, Poisson and normal probabilities, run regression, and find correlation coefficients without manual tables.
4. Show the method. When a question asks to show a result or give an exact answer, the working must be algebraic; the calculator only confirms it.

Our 2026 H2 Mathematics syllabus answers

For content-area coverage, every H2 Mathematics learning outcome we have shipped has its own focused answer page with worked exam-style questions and cross-links to related points.

Browse the full set at /sg-a-level/mathematics/syllabus.

Study strategy

H2 Mathematics rewards systematic technique combined with conceptual understanding. The recipe:

1. Build technique fluency. Each topic has a small set of core methods (partial fractions, integration by parts, the scalar product). Drill them until they are automatic so the exam time goes to thinking, not recall.
2. Sketch before you solve. A quick graph of a curve, an Argand diagram, or a tree diagram in probability turns an abstract question into a concrete one.
3. Respect exact form. Know when a question wants an exact surd or logarithm answer rather than a decimal, and keep working exact until the final line.
4. Practise full timed papers. From the second year, sit several complete 3-hour papers. The Statistics section rewards a confident routine for choosing the right distribution and stating hypotheses cleanly.

For the official syllabus

SEAB publishes the full 9758 syllabus document and examination requirements at seab.gov.sg. Always confirm content and assessment weightings against the current syllabus year, as SEAB reviews syllabuses periodically.