CSCA Sample Questions - Mathematics
Multiple-Choice Questions (Each question has four options among which only one is correct.)
1. The inverse function of y = 3x - 2 is ( ).
A. y = (x + 3)/2
B. y = (x - 3)/2
C. y = (x + 2)/3
D. y = (x - 2)/3 ✓
2. The solution set of the inequality (x - 3)/(x + 1) ≥ 0 is ( ).
A. (-∞, -1] ∪ [3, +∞)
B. (-∞, -1) ∪ [3, +∞) ✓
C. (-∞, -3] ∪ [1, +∞)
D. (-∞, -3] ∪ (1, +∞)
3. The distance from point P(-1, 2) to point Q(2, 3) is ( ).
A. 3
B. 4
C. √26
D. √10 ✓
4. If a < b and c < d, which of the following is correct? ( )
A. a² < b²
B. a - c < b - d
C. ac < bd
D. c³ < d³ ✓
5. If cos α = -1/4, then cos 2α = ( ).
A. -7/8 ✓
B. -3/16
C. 1/2
D. 3/4
6. The foci of the hyperbola x²/4 - y²/5 = 1 have coordinates ( ).
A. (0, ±3)
B. (±3, 0) ✓
C. (0, ±1)
D. (±1, 0)
7. If the sum of the first n terms of the sequence {aₙ} is given by Sₙ = n² - 1, then a₁₀ = ( ).
A. 18
B. 19 ✓
C. 20
D. 21
8. Which of the following lines is parallel to 3x + y - 1 = 0? ( )
A. 3x - y + 2 = 0
B. 3x + y - 2 = 0
C. 6x + 2y - 3 = 0 ✓
D. 6x - 2y + 1 = 0
9. If cos α = -1/2 and π < α < 3π/2, then sin(α/2) = ( ).
A. √3/2 ✓
B. -√3/2
C. -√3/2
D. 1/2
10. The domain of the function y = 5tan(x - π/4) is ( ).
A. {x | x ≠ kπ + 3π/4, k ∈ Z} ✓
B. {x | x ≠ kπ + π/4, k ∈ Z}
C. {x | x ≠ 2kπ + 3π/4, k ∈ Z}
D. {x | x ≠ 2kπ + π/4, k ∈ Z}
11. A sequence {aₙ} satisfies a₁ = 2, aₙ = 1 + 1/aₙ₋₁ (n ≥ 2). Then a₄ = ( ).
A. 3/2
B. 5/3
C. 8/5 ✓
D. 13/8
12. The solution set of the inequality log₂(3 - x) > 0 is ( ).
A. (1, 3)
B. (-∞, 3)
C. (2, +∞)
D. (2, 3) ✓
13. If a function satisfies f(2x - 1) = 3x + 3, then f(-3) = ( ).
A. -3
B. 0
C. 6
D. -5 ✓
14. Which of the following is correct? ( )
A. (0.3)^2.1 > (0.2)^2.1
B. (2.1)^0.12 < (2.2)^0.12 ✓
C. (3.2)^1.1 > (3.2)^0.9
D. (0.25)^1.5 > (0.25)^1.4
15. Let be two vectors. Then ( ). Note: Vector information is missing in the original document
A. (1, 1)
B. (0, 3) ✓
C. 4
D. (-2, -2)
16. A bag contains five equal-sized balls. Three of them are black and two of them are red. Two balls are
drawn randomly from the bag. The probability that the balls have the same color is ( ).
A. 1/5
B. 2/5 ✓
C. 3/5
D. 4/5
17. Suppose that the center of an ellipse C is at the origin, and the foci are on the x-axis. Suppose also that it
has a vertex at (0, 1), and an eccentricity of (2√5)/5. The equation of C is ( ).
A. x²/20 + y²/4 = 1
B. x²/4 + y²/20 = 1
C. x² + y²/5 = 1
D. x²/5 + y² = 1 ✓
18. Suppose that a complex number z satisfies (1 + i)² = 3z + 2i, where i is the unit imaginary number. Then
z = ( ).
A. 3/2 - i
B. 3/2 + i
C. 1/3 - 2i
D. 1/3 + 2i ✓
19. The maximum value of the function f(x) = 2x³ - 3x² - 36x + 1 over the interval [-3, 4] is ( ).
A. 63
B. 1
C. 28
D. 45 ✓
20. The angle between the planes x + 2y - z + 1 = 0 and x - 2y + z - 3 = 0 is ( ).
A. π/3
B. 2π/3
C. arccos(1/6) ✓
D. π - arccos(1/6)
Answer Key
Q 1 2 3 4 5 6 7 8 9 10
Answer D B D D A B B C A A
Q 11 12 13 14 15 16 17 18 19 20
Answer C D D B B B D D D C
These sample questions may not be published, commercially used, or disseminated without prior
authorization from the China Scholarship Council (CSC).
