CSCA Mathematics Syllabus 2026 — Every Topic That Can Appear

Why Mathematics Matters More Than Any Other Subject

Mathematics is the one CSCA subject almost every applicant has to sit, whatever their intended major and whatever the language of instruction. Engineering applicants need it. Business applicants need it. Liberal arts applicants need it. If you only have time to prepare thoroughly for one paper, this is the one.

This guide sets out every topic that can appear, how the paper is structured, and roughly how the marks are distributed — so you can plan your revision around what is actually tested rather than guessing.

Paper Format

• 48 questions in 60 minutes — about 75 seconds per question.
• Marked out of 100, reported separately from your other subjects.
• Available in both Chinese and English, so you can sit it in whichever language you read faster.
• No calculator. Every calculation is done by hand, which is why arithmetic fluency is worth practising in its own right.

The difficulty sits at the level of a strong senior high school curriculum. Nothing is exotic; the challenge is breadth and pace.

Module 1 — Sets and Inequalities

Typically 3 to 5 questions. This is the vocabulary of the whole paper, so weakness here quietly costs marks elsewhere.

• Set notation: roster form, set-builder form, interval notation, cardinality
• Union, intersection and complement, including De Morgan's laws
• Venn diagrams with two and three circles, and the counting formula
• Subsets and power sets
• Linear inequalities and systems of inequalities
• Quadratic inequalities, including the perfect-square edge cases
• Absolute value inequalities of the form |f(x)| < a and |f(x)| > a

The recurring exam trap is the boundary: whether an endpoint is included, and whether a strict inequality changes the answer. Work through the Sets and Inequalities module for the full treatment.

Module 2 — Functions

Typically 5 to 7 questions, and one of the highest-yield areas on the paper. Note that sequences and series live inside this module on the official syllabus, not under algebra.

• Domain and range, including domains restricted by square roots and logarithms
• Piecewise functions
• Even, odd and injective (one-to-one) functions
• Inverse functions and their domains
• Composite functions, evaluated and decomposed
• Exponential functions, growth and decay models
• Logarithmic functions, log rules and logarithmic equations
• Transformations: shifts, stretches and reflections
• Arithmetic sequences and series: nth term, sum of the first n terms
• Geometric sequences and series: nth term, sum, and sum to infinity when |r| < 1

Composition order is the single most common error — always work from the inside out. The Functions module covers each of these with worked examples.

Module 3 — Geometry and Trigonometry

Typically 6 to 8 questions. Heavily formula-driven, which means it rewards memorisation more than any other module.

• Coordinate geometry: slopes, distances, midpoints, parallel and perpendicular lines
• Circle equations, tangent lines and tangent length
• Trigonometric ratios and the unit circle
• Trigonometric identities and the standard formula set
• Law of Sines and Law of Cosines for solving triangles
• Ellipses and hyperbolas: equations, foci, eccentricity
• Vectors: components, magnitude, dot product, applications

Always sketch. A rough diagram takes fifteen seconds and eliminates most sign and configuration errors. See the Geometry and Trigonometry module.

Module 4 — Calculus and Statistics

Typically 8 to 10 questions — the largest single block on the paper.

• Limits and continuity
• Derivative rules: power, product, quotient
• The chain rule
• Applications of derivatives: turning points, concavity, optimisation, related rates
• Integration basics and antiderivatives
• Definite integrals and areas under curves
• Probability basics, including complementary and conditional probability
• Permutations and combinations
• Probability distributions: binomial and normal
• Statistics: mean, median, mode, variance, standard deviation, quartiles, correlation and regression

Because this module carries the most marks, it deserves the most revision time — and because it builds on Modules 1 and 2, it is the worst place to start. Work forwards. The Calculus and Statistics module covers the lot.

How the Marks Are Spread

Module	Approximate questions
Sets and Inequalities	3–5
Functions	5–7
Geometry and Trigonometry	6–8
Calculus and Statistics	8–10

These ranges are estimates based on the shape of past papers, and they do not add up to all 48 questions — the remainder is spread across general numerical reasoning that sits between modules. Treat the table as a guide to where to spend revision time, not as a guarantee.

Exam Strategy

1. Bank the easy marks first. At 75 seconds a question there is no prize for answering in order. Take a first pass for everything you can do quickly, then return.
2. Never leave a blank. There is no penalty for a wrong answer, so a guess is strictly better than an omission.
3. Practise arithmetic without a calculator now, not in the exam hall. Fraction and surd manipulation is where hand-calculation time disappears.
4. Check the question you were asked. Finding x when the question wanted x squared is the most expensive kind of error, because the working was right.
5. Sketch anything geometric. It is faster than reasoning in the abstract and far more reliable.

Where to Start

Work the modules in order — Sets, then Functions, then Geometry, then Calculus — because each leans on the one before. Every module on CSCA.HELP is free, with worked examples, common-mistake warnings and practice questions, and you can test yourself under real time pressure with the practice exams.