POST UTME COAL CITY UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A sphere has a radius of 3 cm. Find its volume.
A. 36π
B. 54π
C. 72π
D. 90π
Question 2
Find the sum of the first 10 terms of the geometric series \( 2x^2 + 3x + 1 \).
A. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + ... + 2x^2 + 3x + 1
B. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + ... + 2x^2 + 3x + 1 + 2x^2 + 3x + 1
C. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + ... + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1
D. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + ... + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1
Question 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x < \frac{3}{2} \)
D. \( x > -1 \) or \( x > \frac{3}{2} \)
Question 4
Find the equation of the line pas\sing through the points ( (2,3) ) and ( (4,5) ).
A. \( y - 3 = \frac{2}{2}\( x - 2 \ \) )
B. \( y - 5 = \frac{2}{2}\( x - 4 \ \) )
C. \( y - 3 = \frac{2}{2}\( x - 4 \ \) )
D. \( y - 5 = \frac{2}{2}\( x - 2 \ \) )
Question 5
Solve the system of equations \( x + y = 3 \) and \( xy = 2 \).
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 1, y = 1
D. x = 2, y = 2
Question 6
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( -2, 0 \)
B. \( -1, 0 \)
C. \( 0, -2 \)
D. \( 0, -1 \)
Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > 3/2
B. x < 1 or x > -3/2
C. x < -3/2 or x > 1
D. x < 3/2 or x > -1
Question 8
Find the determinant of the matrix: \begin{bmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{bmatrix}.
A. -1
B. 1
C. 3
D. 5
Question 9
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.
A. 72
B. 80
C. 96
D. 108
Question 10
In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the height of a student is normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?
A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6827
Question 11
Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 12
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.
A. \( \frac{1}{2} \)
B. \( \frac{1}{4} \)
C. \( \frac{3}{4} \)
D. \( \frac{1}{4} \)
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -1 \) ∪ (1, ∞)
Question 14
Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{bmatrix} \).
A. -2
B. 2
C. -1
D. 1
Question 15
Find the value of k such that the equation \( x^2 + kx + 16 = 0 \) has equal roots.
A. -8
B. 8
C. -4
D. 4

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