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 the official syllabus (2025 edition) lists and how the paper is structured — so you can plan your revision around the syllabus 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

The syllabus lists the definition, operations and representation of sets, and the properties and solution of inequalities (e.g. quadratic and rational inequalities). 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
• Rational (fractional) inequalities such as (x − 1)/(x + 2) > 0, solved by sign analysis without multiplying by an unknown-sign denominator
• Absolute value inequalities of the form |f(x)| < a and |f(x)| > a

The classic 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

The largest module of the syllabus. Note that sequences, trigonometric functions and derivatives all live inside this module on the official syllabus, not under algebra, geometry or a separate calculus module.

• 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
• Power functions, and trigonometric functions: radians, the unit circle, graphs and periods of sin, cos and tan, and the standard identities
• Derivatives: definition, geometric meaning (slope of the tangent), the basic rules, and simple applications (monotonicity, extrema)
• 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 except derivatives, which are taught in the Calculus and Statistics module; the full set of trigonometric identities is collected in the Geometry and Trigonometry module.

Module 3 — Geometry and Algebra

The syllabus lists plane analytic geometry (lines, circles, ellipses, hyperbolas and parabolas), vectors and complex numbers, and solid geometry (the rectangular coordinate system in space and simple solids). Heavily formula-driven, so memorise the standard forms.

• Coordinate geometry: slopes, distances, midpoints, parallel and perpendicular lines
• Circle equations, tangent lines and tangent length
• Ellipses, hyperbolas and parabolas: standard equations, foci, eccentricity, asymptotes, focus and directrix
• Vectors: components, magnitude, dot product, applications (including the Law of Sines and Law of Cosines for solving triangles)
• Complex numbers: the form a + bi, modulus, conjugate, and the four operations
• Solid geometry: the rectangular coordinate system in space, distance between two points in space, and surface area and volume of prisms, pyramids, cylinders, cones and spheres

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

Module 4 — Probability and Statistics

The syllabus lists the classical probability model, numerical characteristics of data (mean, variance, etc.) and the basic concepts of the normal distribution. Our course teaches it together with calculus, so the list below marks what goes beyond the syllabus.

• Classical probability: equally likely outcomes, complementary and mutually exclusive events
• Counting with permutations and combinations (not named in the syllabus, but useful for counting outcomes in classical probability)
• Statistics: mean, median, mode, variance, standard deviation and quartiles
• The normal distribution: the bell curve, symmetry about μ, and the meaning of σ
• Beyond the syllabus, taught in our course for depth: limits and continuity, product/quotient/chain rules in depth, concavity and related rates, integrals and areas, conditional probability, the binomial distribution, correlation and regression

Because probability leans on counting, sets and functions, it builds on Modules 1 and 2, so it is the worst place to start. Work forwards. The Calculus and Statistics module covers the lot.

How the Marks Are Spread

The CSCA does not publish how many of the 48 questions come from each module, and no past papers have been released, so any per-module count you see online is a guess. Revise all four modules; give more time to Functions, the longest module of the syllabus, and to whichever module your practice results show is weakest.

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. The CSCA has announced no penalty for wrong answers, so an educated guess is 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 and Algebra, then Probability and Statistics — because each leans on the one before. Every module on CSCA.HELPCSCA by Foorsa is free, with worked examples, common-mistake warnings and practice questions, and you can test yourself under real time pressure with the practice exams.