What is the CSCA (China Scholastic Competency Assessment)?

The CSCA (China Scholastic Competency Assessment) is the standardized STEM competency assessment used by top Chinese universities and CSC Government Scholarship committees to evaluate international undergraduate candidates in Mathematics, Physics, Chemistry, and Academic Chinese.

How to prepare for the CSCA exam online?

To prepare for the CSCA exam, students should use CSCA Space (csca.space) for adaptive mock test simulations, past paper questions, bilingual terminology drills, formula sheets, and step-by-step video explainers aligned with the official CSCA syllabus.

What subjects are tested in the CSCA?

The CSCA exam tests four core disciplines: Mathematics (Algebra, Calculus, Analytical Geometry), Physics (Mechanics, Electromagnetism, Waves), Chemistry (Physical Chemistry, Organic Chemistry, Stoichiometry), and Academic Chinese.

Where can I find CSCA past papers and practice questions?

CSCA Space provides verified CSCA mock exams, diagnostic assessments, and curated past questions with comprehensive step-by-step pedagogical walkthroughs at https://csca.space.

How does CSCA Space help international students prepare for the CSCA?

CSCA Space provides 100% syllabus-aligned interactive practice, bilingual English and Chinese STEM explanations, full diagnostic scoring, and adaptive mock test simulations designed specifically for international university admissions in China.

What is a competitive score on the CSCA for CSC scholarships?

Candidates scoring in the 80th percentile and above are highly competitive for full Chinese Government Scholarships (CSC Type A & Type B) and direct admission into top C9 league universities.

Official CSCA STEM Examination Reference

CSCA High-Yield Formula Cheat Sheet

Complete index of 58 core equations for Mathematics, Physics, and Chemistry.

CSCA.SPACE

Updated 2026/2027

Part I: Mathematics Formulas

24 Equations · Calculus, Analytic Geometry & Algebra

1. Quadratic FormulaSets & Inequalities

x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

一元二次方程求根公式Proof & Traps →

2. Union of SetsSets & Inequalities

A \cup B = {x ∣ x \in A or x \in B}

集合的并集Proof & Traps →

3. Intersection of SetsSets & Inequalities

A \cap B = {x ∣ x \in A and x \in B}

集合的交集Proof & Traps →

4. Complement of a SetSets & Inequalities

∁_{U} A = {x \in U ∣ x \in / A}

集合的补集Proof & Traps →

5. Rational Inequality EquivalenceSets & Inequalities

\frac{a x + b}{c x + d} \leq 0 ⟺ (a x + b) (c x + d) \leq 0 and c x + d \neq = 0

分式不等式的等价转化Proof & Traps →

6. AM-GM InequalitySets & Inequalities

\frac{a + b}{2} \geq ab (a, b \geq 0)

基本均值不等式Proof & Traps →

7. Change of Base FormulaFunctions

lo g_{a} b = \frac{l o g _{c} b}{l o g _{c} a} (a, b, c > 0, a, c \neq = 1)

对数的换底公式Proof & Traps →

8. Logarithmic PropertiesFunctions

lo g_{a} (x y) = lo g_{a} x + lo g_{a} y and lo g_{a} (\frac{x}{y}) = lo g_{a} x - lo g_{a} y

对数的基本运算性质Proof & Traps →

9. Trigonometric Pythagorean IdentityFunctions

sin^{2} θ + cos^{2} θ = 1

同角三角关系（平方关系）Proof & Traps →

10. Double-Angle Formula (Sine)Functions

sin 2 θ = 2 sin θ cos θ

正弦的二倍角公式Proof & Traps →

11. Double-Angle Formula (Cosine)Functions

cos 2 θ = cos^{2} θ - sin^{2} θ

余弦的二倍角公式Proof & Traps →

12. Function Parity (Odd & Even)Functions

Even: f (- x) = f (x), Odd: f (- x) = - f (x)

函数的奇偶性Proof & Traps →

13. Arithmetic Sequence Nth TermSequences

a_{n} = a_{1} + (n - 1) d

等差数列通项公式Proof & Traps →

14. Arithmetic Sequence SumSequences

S_{n} = \frac{n ( a _{1} + a _{n} )}{2}

等差数列前n项和公式Proof & Traps →

15. Geometric Sequence Nth TermSequences

a_{n} = a_{1} q^{n - 1}

等比数列通项公式Proof & Traps →

16. Geometric Sequence SumSequences

S_{n} = \frac{a _{1} ( 1 - q ^{n} )}{1 - q} (q \neq = 1)

等比数列前n项和公式Proof & Traps →

17. Power Rule for DerivativesDerivatives

\frac{d}{d x} x^{n} = n x^{n - 1}

导数的幂函数求导法则Proof & Traps →

18. Tangent Line EquationDerivatives

y - y_{0} = f^{'} (x_{0}) (x - x_{0})

曲线切线方程公式Proof & Traps →

19. Distance FormulaPlane Analytic Geometry

d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

两点间距离公式Proof & Traps →

20. Equation of a CirclePlane Analytic Geometry

(x - a)^{2} + (y - b)^{2} = R^{2}

圆的标准方程Proof & Traps →

21. Equation of an EllipsePlane Analytic Geometry

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 (a > b > 0)

椭圆的标准方程Proof & Traps →

22. Equation of a HyperbolaPlane Analytic Geometry

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1 (a > 0, b > 0)

双曲线的标准方程Proof & Traps →

23. Equation of a ParabolaPlane Analytic Geometry

y^{2} = 2 p x (p > 0)

抛物线的标准方程Proof & Traps →

24. Equation of a Line (Slope-Intercept & General Form)Plane Analytic Geometry

y = k x + b and A x + B y + C = 0

直线的方程（斜截式与一般式）Proof & Traps →

25. Vector Dot ProductVectors & Complex Numbers

a \cdot b = a_{x} b_{x} + a_{y} b_{y} = ∣ a ∣∣ b ∣ cos θ

平面向量的数量积（点积）Proof & Traps →

26. Modulus of a Complex NumberVectors & Complex Numbers

∣ z ∣ = a^{2} + b^{2} (z = a + bi)

复数的模Proof & Traps →

27. Volume and Surface Area of a SphereSolid Geometry

V = \frac{4}{3} π R^{3} and S = 4 π R^{2}

球的体积与表面积公式Proof & Traps →

28. Classical Probability FormulaProbability & Statistics

P (A) = \frac{N ( A )}{N}

古典概型概率计算公式Proof & Traps →

29. Variance and Standard DeviationProbability & Statistics

s^{2} = \frac{1}{n} \sum_{i = 1}^{n} (x_{i} - \overset{x}{ˉ})^{2}

样本方差与标准差公式Proof & Traps →

30. Normal Distribution (3-Sigma Rule)Probability & Statistics

P (μ - σ \leq X \leq μ + σ) \approx 0.6826 and P (μ - 2 σ \leq X \leq μ + 2 σ) \approx 0.9544

正态分布（3σ原则 / 68-95-99.7准则）Proof & Traps →

Part II: Physics Principles & Laws

17 Equations · Mechanics, Electromagnetism & Thermodynamics

1. Kinematics Equations under Constant AccelerationMechanics

v = v_{0} + a t, s = v_{0} t + \frac{1}{2} a t^{2}, v^{2} - v_{0}^{2} = 2 a s

匀变速直线运动规律与位移公式Proof & Traps →

2. Newton's Second Law of MotionMechanics

\sum F = m a

牛顿第二运动定律Proof & Traps →

3. Momentum, Impulse & Law of Conservation of MomentumMechanics

I = F Δ t = Δ p, m_{1} v_{1} + m_{2} v_{2} = m_{1} v_{1}^{'} + m_{2} v_{2}^{'}

动量定理与动量守恒定律Proof & Traps →

4. Work-Energy Theorem & Conservation of Mechanical EnergyMechanics

W_{net} = Δ E_{k} = \frac{1}{2} m v_{2}^{2} - \frac{1}{2} m v_{1}^{2}, E_{k 1} + E_{p 1} = E_{k 2} + E_{p 2}

动能定理与机械能守恒定律Proof & Traps →

5. Uniform Circular Motion & Law of Universal GravitationMechanics

F_{c} = m \frac{v ^{2}}{r} = m ω^{2} r, F_{g} = G \frac{M m}{r ^{2}} = m \frac{v ^{2}}{r} ⟹ v = \frac{GM}{r}

匀速圆周运动与万有引力定律Proof & Traps →

6. Simple Harmonic Motion & Mechanical Wave SpeedMechanics

T = 2 π \frac{L}{g}, v = \frac{λ}{T} = λ f

简谐运动周期与机械波传播公式Proof & Traps →

7. Coulomb's Law & Electric Field StrengthElectromagnetism

F = k_{e} \frac{∣ q _{1} q _{2} ∣}{r ^{2}}, E = \frac{F}{q} = k_{e} \frac{Q}{r ^{2}}, U = E d

库仑定律与电场强度公式Proof & Traps →

8. Ohm's Law & Closed Circuit EMF EquationElectromagnetism

I = \frac{E}{R + r}, U = E - I r, P = U I = I^{2} R

闭合电路欧姆定律与电功率公式Proof & Traps →

9. Lorentz Force & Magnetic Ampere ForceElectromagnetism

F_{Ampere} = B I L sin θ, F_{Lorentz} = q v B sin θ, r = \frac{m v}{q B}

安培力与洛伦兹力公式Proof & Traps →

10. Faraday's Law of Induction & Motional EMFElectromagnetism

E = n \frac{ΔΦ}{Δ t}, E = B Lv sin θ

法拉第电磁感应定律与动生电动势Proof & Traps →

11. AC Series RLC Circuit Impedance & PhasorElectromagnetism

Z = R^{2} + (X_{L} - X_{C})^{2}, tan θ = \frac{X _{L} - X _{C}}{R}

交变电流RLC串联电路阻抗与相量公式Proof & Traps →

12. AC Active Power & Power Factor FormulaElectromagnetism

P = U I cos φ, cos φ = \frac{R}{Z} = \frac{R}{R ^{2} + ( X _{L} - X _{C} ) ^{2}}

交流电路有功功率与功率因数公式Proof & Traps →

13. First Law of Thermodynamics & Ideal Gas LawThermodynamics

Δ U = Q + W, \frac{P _{1} V _{1}}{T _{1}} = \frac{P _{2} V _{2}}{T _{2}}

热力学第一定律与理想气体状态方程Proof & Traps →

14. Snell's Law of Refraction & Total Internal ReflectionOptics

n = \frac{c}{v} = \frac{s i n θ _{1}}{s i n θ _{2}}, sin C = \frac{1}{n}

光的折射定律与全反射临界角公式Proof & Traps →

15. Young's Double-Slit Interference Fringe SpacingOptics

Δ x = \frac{L}{d} λ

双缝干涉条纹间距公式Proof & Traps →

16. Einstein's Photoelectric Effect & Photon EnergyModern Physics

E_{photon} = h ν, E_{k m a x} = h ν - W_{0} = e U_{c}

光电效应方程与光子能量公式Proof & Traps →

17. Bohr Hydrogen Energy Levels & Mass-Energy EquivalenceModern Physics

E_{n} = \frac{E _{1}}{n ^{2}} (E_{1} = - 13.6 eV), h ν = E_{m} - E_{n}, Δ E = Δ m c^{2}

玻尔氢原子能级跃迁与质能方程Proof & Traps →

Part III: Chemistry Constants & Reactions

17 Equations · Equilibrium, Kinetics & Stoichiometry

1. Amount of Substance, Mass & Particle Count RelationsBasic Chemical Concepts and Calculations

n = \frac{m}{M} = \frac{N}{N _{A}}

物质的量、微粒数与质量换算公式Proof & Traps →

2. Gas Volume and Moles at STPBasic Chemical Concepts and Calculations

n = \frac{V}{V _{m}} (V_{m} = 22.4 L/mol at 0^{\circ} C, 101.3 kPa)

气体摩尔体积与标况状态公式Proof & Traps →

3. Molar Concentration of Solution & Dilution LawBasic Chemical Concepts and Calculations

c = \frac{n}{V}, c_{1} V_{1} = c_{2} V_{2}

物质的量浓度公式与稀释定律Proof & Traps →

4. Conversion between Mass Fraction and Molar ConcentrationBasic Chemical Concepts and Calculations

c = \frac{1000 ρw}{M}

质量分数与物质的量浓度的换算公式Proof & Traps →

5. Ideal Gas Law Equation of StateBasic Chemical Concepts and Calculations

P V = n R T = \frac{m}{M} R T ⟹ P M = ρR T

理想气体状态方程（克拉珀龙方程）Proof & Traps →

6. Chemical Reaction Rate & Rate Ratio LawChemical Theories and Laws

v = \frac{Δ c}{Δ t}, \frac{v ( A )}{a} = \frac{v ( B )}{b} = \frac{v ( C )}{c}

化学反应速率与化学计量数比值规律Proof & Traps →

7. Chemical Equilibrium Constant ExpressionChemical Theories and Laws

K = \frac{[ C ] ^{c} [ D ] ^{d}}{[ A ] ^{a} [ B ] ^{b}}, α = \frac{Δ n}{n _{0}} \times 100%

化学平衡常数表达式与转化率公式Proof & Traps →

8. pH, pOH & Water Ion Product EquilibriumChemical Theories and Laws

pH = - lo g_{10} [H^{+}], K_{w} = [H^{+}] [OH^{-}] = 1.0 \times 1 0^{- 14} at 2 5^{\circ} C

pH定义式与水的离子积常数Proof & Traps →

9. Arrhenius Activation Energy EquationChemical Theories and Laws

k = A e^{- \frac{E _{a}}{R T}} ⟹ ln k = - \frac{E _{a}}{R} \frac{1}{T} + ln A

阿伦尼乌斯公式与活化能Proof & Traps →

10. Gibbs Free Energy Spontaneity CriterionChemical Theories and Laws

Δ G = Δ H - T Δ S (Δ G < 0 ⟹ Spontaneous)

吉布斯自由能判据与反应自发性Proof & Traps →

11. Galvanic & Electrolytic Cell Electrode ReactionsChemical Theories and Laws

Anode: Oxidation (loss of e^{-}), Cathode: Reduction (gain of e^{-})

原电池与电解池电极反应规律Proof & Traps →