🎓 CSCA Math · 留学生考中国大学数学
12 units · 60 topics · ~50% MCQ exam · drawn from real Jan/Dec CSCA papers
- Ch 1
Sets & Inequalities
集合与不等式 · roster/builder/interval · sign-chart method · monotonicity comparisons
Set notation, union/intersection/subset, linear/quadratic/rational/absolute-value inequalities, and the powers-vs-logs comparison trick. The single highest-frequency CSCA topic.
1 1 - Ch 2
Functions and Their Properties
函数及其性质 · domain · odd/even · monotonicity · inverse · composition
Function definitions and the four core properties tested heavily on CSCA: domain/range, parity, monotonic intervals, and inverses.
1 1 - Ch 3
Elementary Functions
基本初等函数 · power · exponential · logarithmic · quadratic · translations
The standard function families and how their graphs transform under shifts and scales.
1 1 - Ch 4
Trigonometric Functions
三角函数 · radians · identities · reduction formulae · sum/diff · double/half angle
The single biggest CSCA topic by question count. Memorise the reduction-formula mnemonic and the sum/difference identities.
1 1 - Ch 5
Sequences
数列 · arithmetic · geometric · recursive · sum techniques
Arithmetic and geometric sequences plus the four classic sum techniques (错位相减, 裂项相消, etc.).
1 1 - Ch 6
Plane Vectors
平面向量 · operations · dot product · collinearity · coordinate form
Vectors as algebraic objects and as geometric arrows. Dot product reveals angles and perpendicularity.
1 1 - Ch 7
Lines in the Plane
平面直线 · slope · inclination · 4 forms · distance · intersection
Four equivalent line equations, parallel/perpendicular conditions, and the distance formula.
1 1 - Ch 8
Circles
圆 · standard form · general form · tangent · chord
Standard and general equations of a circle; how to find tangent lines and analyse a circle-line relationship.
1 1 - Ch 9
Conic Sections
圆锥曲线 · ellipse · hyperbola · parabola · eccentricity · focal properties
The three conics and their focal-radius identities. Eccentricity unifies them.
1 1 - Ch 10
Complex Numbers
复数 · algebraic form · conjugate · modulus · arithmetic
Complex arithmetic, conjugate-multiply division trick, geometric interpretation in the complex plane.
1 1 - Ch 11
Counting & Probability
计数与概率 · counting principles · permutations · combinations · classical probability
Permutations, combinations, classical probability, independent events.
1 1 - Ch 12
Statistics
统计 · mean · variance · frequency distributions
Descriptive statistics, variance/standard deviation, frequency histograms.
1 1