LIVE INTERACTIVE DRILL ENGINE • 270 VERIFIED QUESTIONS
CSCA Interactive Question Bank & Timed Sprint Drills
Calibrated to the official 2026/2027 CSCA computer-based testing (CBT) syllabus and Chinese High School Qualification Exam (会考) benchmark. Practice topic-by-topic with bilingual EN/中文 prompts, no-calculator derivations, graduated formula hints, and a persistent personal mistake notebook.
OFFICIAL 2026/2027 CBT BLUEPRINT CALIBRATED • 270 VERIFIED QUESTIONS
Interactive CSCA Question Bank & Mistake Notebook
100% Single-Choice CBT Format • Bilingual EN/中文 Switch • No-Calculator Mental Derivation • Local Mistake Notebook
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Showing 15 of 270 matching questions (Page 1 of 18)
#1 • MATH-REC-001MathematicsFoundationModule 1: Sets and Inequalities (集合与不等式) → Logarithmic & Domain Inequalities
Find the solution set of the logarithmic inequality log₂(3 - x) < 0:
求对数不等式 log₂(3 - x) < 0 的解集：
#2 • MATH-REC-002MathematicsFoundationModule 3: Geometry and Algebra (几何与代数) → Conic Sections — Hyperbola
What are the coordinates of the foci of the hyperbola x²/4 - y²/5 = 1?
双曲线 x²/4 - y²/5 = 1 的焦点坐标是？
#3 • MATH-REC-003MathematicsStandardModule 2: Functions & Calculus (函数与微积分初步) → Derivatives & Closed-Interval Extrema
Find the maximum value of the function f(x) = 2x³ - 3x² - 36x + 1 on the closed interval [-3, 4]:
求函数 f(x) = 2x³ - 3x² - 36x + 1 在闭区间 [-3, 4] 上的最大值：
#4 • MATH-REC-004MathematicsStandardModule 2: Functions & Calculus (函数与微积分初步) → Trigonometric Identities & Double Angle
Given that tan(α) = 2, what is the exact value of sin(2α)?
已知 tan(α) = 2，则 sin(2α) 的值为：
#5 • MATH-REC-005MathematicsFoundationModule 2: Functions & Calculus (函数与微积分初步) → Arithmetic & Geometric Sequences
In a positive geometric sequence {aₙ}, if a₂ · a₆ = 16, what is the value of a₄?
在各项均为正数的等比数列 {aₙ} 中，若 a₂ · a₆ = 16，则 a₄ 的值为：
#6 • MATH-REC-006MathematicsFoundationModule 3: Geometry and Algebra (几何与代数) → Complex Numbers
If the complex number z = (2 + 4i) / (1 + i) (where i² = -1), what is the modulus |z|?
设复数 z = (2 + 4i) / (1 + i)（其中 i² = -1），则复数 z 的模 |z| 为：
#7 • MATH-REC-007MathematicsFoundationModule 3: Geometry and Algebra (几何与代数) → Plane Vectors — Orthogonality
Given plane vectors a = (2, -1) and b = (x, 3), if vector a is perpendicular to vector (a + b), find the real number x:
已知平面向量 a = (2, -1)，b = (x, 3)，若向量 a 与向量 (a + b) 垂直，则实数 x 的值为：
#8 • MATH-REC-008MathematicsStandardModule 3: Geometry and Algebra (几何与代数) → Circle Chord Length
What is the length of the chord intercepted by the line x - y + 1 = 0 on the circle (x - 1)² + y² = 4?
直线 x - y + 1 = 0 被圆 (x - 1)² + y² = 4 所截得的弦长为：
#9 • MATH-REC-009MathematicsStandardModule 4: Probability & Statistics (概率与统计) → Normal Distribution Symmetry
Suppose a random variable X follows a normal distribution N(4, σ²). If P(X > 6) = 0.18, what is P(2 < X < 4)?
设随机变量 X 服从正态分布 N(4, σ²)，若 P(X > 6) = 0.18，则 P(2 < X < 4) 等于：
#10 • MATH-REC-010MathematicsStandardModule 3: Geometry and Algebra (几何与代数) → Solid Geometry — Inscribed Sphere
All 8 vertices of a cube of edge length 2 lie on the surface of a sphere. What is the surface area of this circumscribed sphere?
棱长为 2 的正方体的 8 个顶点都在同一个球面上，则该外接球的表面积为：
#11 • PHYS-REC-001PhysicsFoundationModule 1: Mechanics (力学) → Newton's Laws & Kinetic Friction
An object of mass m = 6 kg is moving to the right on a horizontal surface with coefficient of kinetic friction μ = 0.2 (take g = 10 m/s²). If it is simultaneously acted upon by a horizontal force F = 10 N directed to the left, what is the net force on the object?
质量 m = 6 kg 的物体在动摩擦因数 μ = 0.2 的水平面上向右运动（取 g = 10 m/s²），同时受到一个水平向左、大小为 F = 10 N 的拉力作用，则物体所受的合外力为：
#12 • PHYS-REC-002PhysicsFoundationModule 2: Electromagnetism (电磁学) → Work in Uniform Electric Field
In a uniform electric field of strength E = 400 V/m, a positive point charge q = +2.0 × 10⁻⁶ C moves along a straight segment AB of length d = 0.5 m. If segment AB makes a 60° angle with the electric field direction, what is the work W done by the electric field force?
在场强 E = 400 V/m 的匀强电场中，点电荷 q = +2.0 × 10⁻⁶ C 沿直线 AB 移动了 d = 0.5 m，已知 AB 与电场线方向的夹角为 60°，则电场力做的功 W 为：
#13 • PHYS-REC-003PhysicsFoundationModule 2: Electromagnetism (电磁学) → Lorentz Force & Cyclotron Radius
A charged particle of mass m and charge q enters a uniform magnetic field B with velocity v perpendicular to B. What is the radius R of its circular trajectory?
质量为 m、电荷量为 q 的带电粒子，以垂直于磁感应强度 B 的速度 v 射入匀强磁场中，其做匀速圆周运动的轨道半径 R 为：
#14 • PHYS-REC-004PhysicsStandardModule 1: Mechanics (力学) → Universal Gravitation & Satellite Orbits
Two artificial Earth satellites A and B move in circular orbits with orbital radii r_A : r_B = 1 : 4. What is the ratio of their linear orbital speeds v_A : v_B?
两颗人造地球卫星 A、B 绕地球做匀速圆周运动，轨道半径之比 r_A : r_B = 1 : 4，则它们的线速度大小之比 v_A : v_B 为：
#15 • PHYS-REC-005PhysicsStandardModule 1: Mechanics (力学) → Automobile Constant Power Motion
A car of mass 2.0 × 10³ kg travels on a level road with constant engine power P = 60 kW and experiences a constant resistance force f = 3.0 × 10³ N. What is the maximum speed v_m the car can attain?
质量为 2.0 × 10³ kg 的汽车在水平路面上以恒定功率 P = 60 kW 行驶，所受阻力恒为 f = 3.0 × 10³ N，则汽车所能达到的最大速度 v_m 为：