Sets and inequalities
- set definitions, operations and representations
- basic properties and solution methods for inequalities, including one-variable quadratic and rational inequalities
CSCA Mathematics Preparation
Assess foundational mathematical knowledge, logical reasoning and practical problem solving needed for undergraduate study in China.
- Duration
- 60 minutes
- Score
- 100
- Format
- single-answer multiple choice
- Language
- ZH / EN
Topics in the documented syllabus
Functions
- domain, range, monotonicity and parity
- power, exponential, logarithmic and trigonometric functions
- arithmetic and geometric sequences, nth-term formulas and sums
- introductory derivatives: definition, geometric meaning and simple applications
Geometry and algebra
- equations and properties of lines, circles, ellipses, hyperbolas and parabolas
- vector operations
- basic arithmetic with complex numbers
- three-dimensional Cartesian coordinates and properties of simple solids
Probability and statistics
- classical probability models and calculations
- mean, variance and related numerical characteristics of data
- basic concepts of the normal distribution
Reviewed sample questions
Standard · FunctionsIf f(x) = 2x − 5, what is f⁻¹(x)?Standard · TrigonometryFor an acute angle θ, sin θ = 3/5. What is cos θ?Standard · SequencesThe arithmetic sequence is 3, 7, 11, … What is its 20th term?Standard · GeometryWhat is the radius of x² + y² − 6x + 4y − 12 = 0?Standard · ProbabilityTwo fair dice are rolled. What is the probability that their sum is 7?Standard · FunctionsIf f(x) = 2x − 5, what is f⁻¹(x)?