1219_Mock_Math_Basic.pdf

2. 3. 4. PrepPals 19th December 2025 CSCA [Mathl Mock Questions Collection [Basic Versionl Important Disclaimer Nature of this material: All the questions in this material are compiled and inferred based on the examination syllabus and are not official original exam questions. While we strive to reconstruct the questions as close to the originals as possible, we cannot guarantee that the wording or the order of the options is the same those in the actual exam. For reference only: This material is intended to help candidates understand exam trends and review priorities and does not constitute any promise or guarantee regarding the exam. Candidates should use the officially designated textbooks and syllabus as their final study reference. Copyright notice: Copyright of this material belongs to PrepPals and is intended only for the purchaser's personal study use. Any form of commercial reposting, copying, or use in training courses is strictly prohibited. Offenders will be held legally responsible. Accuracy: Although we have proofread multiple times, there may still be oversights. If you find any issues, please report them through official channels; we will investigate and update promptly. @ 2026 PrepPals. copyright.

Part I: Single Choice Questions There are 48 questions in this section, each worth I point, for a total of 48 points. 1. Let the universal set U =. Find the number of proper subsets of the complement set CUA. KC. 15 D. 31 2. 3. 4. 5. The domain of the function f (x) B. (—00, 4] c. (0, +00) D. [0,4] Given the function f(2x — 1) = x + 1, find the inverse function f-l(x). A. f-l(x) = 2x — 1, x e R B. f-l(x) = 2x + e R C. f-l(x) = 2x - e R 2 Determine the quadrant in which the point (5, -8) lies. A. First Quadrant B. Second Quadrant C. Third Quadrant D. Fourth Quadrant Which quadrant does the graph of the power function f (x) = xa never pass through? A. First Quadrant B. Second Quadrant C. Third Quadrant D. Fourth Quadrant @ 2026 PrepPals. copyright.

6. 7. 8. 9. Which of the following functions is symmetric about the origin? D.y=x+l Among the following functions, which one is decreasing on the interval = Inlxl For the power functions y x3 and y , which of the following statements is correct? A. Both graphs are symmetric with respect to the origin. B. Both functions are not monotonic on R. C. Both functions have the domain x > O. D. The two functions are inverses of each other, but their graphs are not symmetric about the line y = x. The range of the function y = is: A. [0, 21 B. [O, 41 c. (-00, 2] 10. Given that the power function f (x) of R, find the value of m. C. -lor3 = (m2 — 2m — 2)xm+l has a domain @ 2026 PrepPals. copyright.

11. If point P (-6, 8) lies on the terminal side of angle a, then sina — 12. Find the maximum value of the function y = 3sinx 4cosx. 13. Ifa > b, which of the following inequalities is true? B. a2 > b2 C.a+b>2€7B D. a2 -F b2 > 2ab 14. log28- B.O 2 20 15. Which of the following inequalities is true? B. 0.3-2 < 0.3-3 C. log2 3 < log2 2 D. sin 100 > sin 200 @ 2026 PrepPals. copyright.

16. If is arithmetic withal —2, d = A. 29 B. 28 c. 22 D. 25 3, find (110. 17. Determine the minimum positive period of the function y = 3 sin(2x — Z). 18. Given cosa = — and a is an acute angle, find cos D. 4Tt 25 24 25 25 19. Which of the following is true? A. sin(—x) = sin x B. tan(Tt + x) = tan x C. cos(—x) = —cosx D. sin — + x = sin x — —and sinß -2, witha e (E, 20. Given sina — 13 sin(a + ß) and sin(a — ß). sin(cr — {3) = —2 A. sin(a + P) = , B. sin(a 4- = —2 , sin(a — {3) = 65 65 C. sin(a +ß) = 2, sin(a — P) = 65 65 sin(a — [3) = 65 65 n) andß e (0, E). Calculate @ 2026 PrepPals. copyright.

21. A recurrence sequence satisfies an = an-I + n (n 2) and al = 1. Find (14. A. 12 c. 11 D. 10 22. Given tana = 2, then 23. sin 150 cos 150 = 24. Given that sina — — sin a+cosa sin a—cosa — — and a 2m), find tan a. 25. Ina geometric sequence, ifa2 = 3 and as = 24, find the common ratio q. @ 2026 PrepPals. copyright.

26. Solve the inequality x2 -l- x A. x < —3 or x > 2 c.x -3 D.x22 27. Given that sin a — — - and 25 25 — < a < m, find cos2a. 28. In an arithmetic sequence (an) with a common difference of 2, the terms ctl, (12, form a geometric sequence. Find the sum of the first nine terms Sq. A. 63 B. 72 c. 81 D. 90 29. = 30. The terms of sequence {an) are all positive, and the sum of the first n terms Sn -L — 2Sn. Find the general term formula for an. satisfies an + — an c. an = fi-v•-r @ 2026 PrepPals. copyright.

31. The distance between points P(-l, 2) and Q(il -2) is: D. 25 32. Solve the inequality > 1. 33. Which of the following sequences is geometric? A. 1, 3, 5,7 C. Inl, ln2, ln3,1n4 D. 1, -2, 4,-8 2 + Y2 — 6x + 4y — 3 = 0 , the center is: 34. For the circle x 35. Let I be perpendicular to 11 intersection of 12: x + y — : x— 2Y+5 2 = O and 13: 2x = O and passing through the equation of I is: B.2x —y—I = 0 -I — O, then the @ 2026 PrepPa1s. copyright.

40. The directrix of the parabola xz = 36. Find the equation of the line passing through (O, 1) that is parallel to the line B. 2x + = 0 D. 2x-y-1=O 37. Calculate the slope Of the line passing through points 2) and B(3, 4). B.y=l c.x—l 38 Ifthe line ax + 2Y ¯ 1 = O is parallel to x + y 39. Find the distance from point P (3, 4) to the line 3x —4y is: 41. Find the eccentricity of the ellipse x 2 + 4y — = O, find the value of a. @ 2026 PrepPa1s. copyright.

42. A circle has its center at (28) and passes through the origin (O, O). Determine its equation. A. (x 2) 2 — = 13 C. 3) 2 13 D. (x +2)2 + (y- -5 43. An ellipse + _ _ — I has an eccentricity e = - and its foci lie on the x-axis. Find the value of m. 16 44. Find the equations of the asymptotes for the hyperbola — 16 45. If vector a— 2 parallel to b = 16 , find the value of m. 46. Determine the interval on which the function f (x) monotonically decreasing. B. (0,2) c. (2, +00) D. (—00, O) U (2, +00) @ 2026 PrepPa1s. copyright.

47. In the complex plane, the distance between the two points representing the roots of the equation x2.- 2x + p 0 (p e R) is vfi. Find the value of p. 48. Players A and B compete in a points-based Go match. I point is awarded for a win; 0 points are awarded for a loss or a draw. The match ends immediately when a player reaches 2 points. If neither player has reached 2 points after 4 rounds, the player with the higher score wins; if scores are tied, the match is a draw. In each round, the probability of A winning is — , A losing is —, and drawing is-. Round results are independent. Calculate the probability that A wins the match. 265 432 13 24 @ 2026 PrepPa1s. copyright.

Reference answers 11 18 19 21 45 23 33 42 43 44 48 @ 2026 PrepPa1s. copyright.