CSCA Mathmatics Placement Test

 

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⚠️Privacy Notice⚠️

The information provided in the form below will be collected, used, and securely maintained for the purposes of exam registration, identity verification, exam administration, and communication regarding examination details and results. The information will be accessed or disclosed only when necessary and handled in accordance with applicable data protection requirements.
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Examination Instructions
 
  1. Please read the following rules carefully before starting the examination
  2. This is placement test for CSCA Mathematics.
  3. The examination consists of 20 questions. The full score is 20 points.
  4. You have 60 minutes to complete the exam.
  5. To move to the next question, press the Next button only.
  6. To return to the previous question, press the Back button only.
  7. Do NOT refresh the website during the examination.
Examination Instructions
 
  1. Please read the following rules carefully before starting the examination
  2. This is placement test for CSCA Mathematics.
  3. The examination consists of 20 questions. The full score is 20 points.
  4. You have 60 minutes to complete the exam.
  5. To move to the next question, press the Next button only.
  6. To return to the previous question, press the Back button only.
  7. Do NOT refresh the website during the examination.
1. Let U = {1, 2, …, 10}, A = {2, 4, 6, 8, 10}, and B = {2, 3, 5, 7}. What is A ∩ B?

A. {2}
B. {2, 4}
C. {2, 3, 5, 7}
D. ∅
2. Solve x − 1 x + 2  ≥ 0.
A. −2 < x ≤ 1
B. x ≤ −2 or x ≥ 1
C. x < −2 or x ≥ 1
D. x < −2 or x > 1
3. What is the domain of f(x) = √5 − 2x ?
A. x ≥ 5 2
B. x ≤ 5 2
C. x > − 5 2
D. all real numbers
4. Which statement about f(x) = x3- 4x is true?
A. f is even
B. f is odd
C. f is neither even nor odd
D. f is constant
5. Solve 3x + 1 = 27.
A. x = 1
B. x = 2
C. x = 3
D. x = 4
6. Solve log2(x - 1) = 3.
A. x = 7
B. x = 8
C. x = 9
D. x = 10
7. Which expression is equivalent to 2(sinx)(cosx)?

A. sin(2x)
B. cos(2x)
C. 2sinx
D. 2cosx
8. For x ≥ 0, simplify x 3 2 · x 1 2 . x3
A. x
B. x2
C. x3
D. x4
9. Let f(x) = 2x − 1 and g(x) = x2 + 3. Find (g ∘ f)(2).
A. 7
B. 9
C. 12
D. 19
10. If f(x) = 3x − 2 5 , what is f−1(x)?
A. 5x − 2 3
B. 5x + 2 3
C. 3x + 2 5
D. 5 3x − 2
11. For the ellipse x2 25 + y2 9 = 1, what is the distance between its two foci?
A. 4
B. 6
C. 8
D. 10
12. In an arithmetic sequence, a₄ = 11 and a₁₀ = 29. Find the common difference.
 
A. 2
B. 3
C. 4
D. 6
13. An arithmetic sequence has first term 5 and common difference 3. Find the sum of its first 12 terms.

A. 198
B. 216
C. 246
D. 258
14. An infinite geometric series has first term 12 and common ratio − 1 3 . Find its sum.
A. 8
B. 9
C. 12
D. 18
15. Find the center and radius of (x + 3)2 + (y − 2)2 = 25.
A. Center (−3, 2), radius 5
B. Center (3, −2), radius 5
C. Center (3, −2), radius 25
D. Center (−3, 2), radius 25
16. What is the focus of the parabola y² = 8x?
A. (0, 2)
B. (0, 4)
C. (2, 0)
D. (4, 0)
17. Which equation represents the line through (2, 1) perpendicular to 2x − 3y = 6?

A. y = 2 3 x − 1 3
B. y = − 2 3 x + 7 3
C. y = 3 2 x − 2
D. y = − 3 2 x + 4
18. Find the distance from (3, −1) to the line 4x − 3y + 5 = 0.
A. 2
B. 3
C. 4
D. 5
19. What is the product (2 + 3i)(1 − i)?

 
A. −1 + i
B. 5 + i
C. 5 − i
D. −1 + 5i
20. An integer is selected at random from {1, 2, …, 12}. What is the probability that it is divisible by 2 or 3?


 
A. 1/3
B. 1/2
C. 2/3
D. 3/4

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