CSCA Math (Maths) Syllabus 2026/2027: 48-Question Exam Topics, Weights & Prep Materials

The CSCA math syllabus serves as the core quantitative benchmark required by top Chinese universities for international STEM undergraduate admissions. Whether preparing for engineering at Tsinghua, computer science at Zhejiang University, or economics at Fudan, mastering the csca exam math syllabus and specific csca math topics is essential. This comprehensive csca maths syllabus guide details the exact examination chapters, question types, scoring distributions, and essential csca resources and csca materials for your csca prep journey.

1. Sets and Inequalities (集合与不等式)

This foundational module of the csca math syllabus tests fundamental mathematical set notation, interval logic, and algebraic inequalities under real number systems.

Definition, Operations & Representation of Sets

Definition of elements and sets, membership notation (∈, ∉), set representation (listing method, set-builder notation, interval notation), subset relations (⊆, ⊂), and fundamental operations: union (A ∪ B), intersection (A ∩ B), complement (∁_UA), and Venn diagram interpretations.

Properties & Solution Methods of Inequalities

Basic properties of inequalities (transitivity, addition, multiplication by positive/negative constants); solution sets and sign-chart analysis for quadratic inequalities in one variable (ax² + bx + c > 0), rational fractional inequalities (P(x) / Q(x) ≥ 0), absolute value inequalities, and systems of linear/quadratic inequalities.

2. Functions & Elementary Analysis (函数)

Functions represent the highest-frequency domain on the csca exam math syllabus, evaluating an applicant's ability to analyze algebraic structures, model real-world relationships, and interpret functional dynamics.

Concepts & Fundamental Properties of Functions

Function definition, mapping, natural domain and range determination; core analytical properties including monotonicity (strictly increasing/decreasing intervals), parity (odd functions f(−x) = −f(x), even functions f(−x) = f(x)), periodicity, composite functions, and inverse functions.

Basic Elementary Functions

Equations, graphs, and operational properties of four cornerstone function families: power functions (y = x^α), exponential functions (y = a^x, natural base e), logarithmic functions (y = log_ax, ln x, base-change formula), and trigonometric functions (sin x, cos x, tan x, unit circle definitions, standard angle values, trigonometric identities, and transformations of y = A sin(ωx + φ)).

Sequences & Series Progressions

General concept of sequence as a special discrete function; arithmetic sequences (common difference d, general term a_n = a₁ + (n − 1)d, sum of first n terms S_n = n(a₁ + a_n) / 2); geometric sequences (common ratio q, general term a_n = a₁qⁿ⁻¹, summation formula S_n), and standard sequence recurrence relations.

Basics of Derivatives & Calculus

Definition of the derivative as an instantaneous rate of change; geometric significance of the derivative as the slope of the tangent line to a curve; basic derivative formulas for elementary functions (C′, (xⁿ)′, (sin x)′, (cos x)′, (e^x)′, (ln x)′); simple differentiation rules and application to determining local extrema and monotonic intervals.

3. Geometry and Algebra (几何与代数)

Testing spatial visualization and analytical geometric deduction, this module bridges algebraic formulations with geometric representations in 2D coordinate planes and 3D spatial systems.

Plane Analytic Geometry & Conic Sections

Straight lines in Cartesian planes: slope, inclination angle, point-slope form, slope-intercept form, general linear equation, parallel and perpendicular conditions, intersection points, and point-to-line distance formula. Equations and properties of circles (standard equation (x − a)² + (y − b)² = r², general form, tangent lines). Standard equations, focal properties, vertices, directrix lines, and eccentricity of standard conic sections: ellipse, hyperbola, and parabola.

Vectors & Complex Numbers

Plane vectors: geometric and coordinate representations, vector addition, subtraction, scalar multiplication, dot product (a · b = |a||b| cos θ = x₁x₂ + y₁y₂), vector modulus, collinearity and orthogonality conditions. Complex numbers: imaginary unit i (i² = −1), standard form z = a + bi (a, b ∈ ℝ), real and imaginary parts, complex conjugate z̄, modulus |z| = √(a² + b²), and the four basic arithmetic operations (addition, subtraction, multiplication, and division).

Solid Geometry & Spatial Rectangular Coordinates

Introduction to three-dimensional rectangular coordinate systems (x, y, z), spatial distance formula between two points; basic geometric and spatial properties of elementary solids (prisms, pyramids, cylinders, cones, and spheres), including surface area and volume formulas.

4. Probability and Statistics (概率与统计)

This module evaluates an applicant's foundational stochastic reasoning and statistical data processing capabilities required for STEM coursework.

Classical Probability Model & Probability Calculations

Random experiments, sample spaces, sample points, and random events; characteristics of classical probability models (finite equally likely outcomes); classical probability formula P(A) = m / n; addition rule for mutually exclusive events, multiplication rule for mutually independent events, and complementary event probabilities.

Numerical Characteristics of Data

Descriptive statistics for sample data: frequency distribution tables, calculations and statistical interpretations of central tendency and dispersion, including sample mean (x̄), median, mode, sample variance (s²), and standard deviation (s).

Basic Concepts of Normal Distribution

Continuous random variables, normal distribution curves and density functions, characteristics of the bell-shaped curve, positional parameter mean (μ), dispersion parameter standard deviation (σ), symmetry properties, and standard probability intervals (μ ± σ, μ ± 2σ, μ ± 3σ).

Official Question Types, Exam Structure & Score Distribution

According to the official CSCA Mathematics Examination Syllabus and verified historical past papers, the examination is administered as a 100% objective, computer-based test with no written proofs or long subjective calculation questions: