POST UTME ACHIEVERS UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi cm^3
B. 48\pi cm^3
C. 72\pi cm^3
D. 96\pi cm^3
Question 2
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
A. 2 < x < 4
B. x > 4
C. x > 2
D. x < 2
Question 3
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
A. \[ P\( \text{multiple of 3} \) = \frac{1}{2} \]
B. \[ P\( \text{multiple of 3} \) = \frac{1}{3} \]
C. \[ P\( \text{multiple of 3} \) = \frac{2}{3} \]
D. \[ P\( \text{multiple of 3} \) = \frac{1}{6} \]
Question 4
Solve the trigonometric equation \( 2 \sin^2 x + 3 \cos x - 1 = 0 \) for ( 0 leq x leq 2 pi ).
A. \frac{\pi}{6}, \frac{5\pi}{6}
B. \frac{\pi}{4}, \frac{3\pi}{4}
C. \frac{\pi}{3}, \frac{2\pi}{3}
D. \frac{\pi}{2}, \pi
Question 5
Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 4 \ 3 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. ( 2 )
D. ( 3 )
Question 6
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 4 \)^2 = 16
Question 7
Find the volume of the frustum of a cone with height 10 cm, base radius 6 cm, and top radius 4 cm.
A. 120\pi cm^3
B. 150\pi cm^3
C. 180\pi cm^3
D. 200\pi cm^3
Question 8
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{pmatrix} ].
A. 25
B. 30
C. 35
D. 40
Question 9
A survey of 100 students found that 70% preferred pizza, 20% preferred burgers, and 10% preferred sandwiches. What is the probability that a randomly selected student prefers pizza or burgers?
A. 0.9
B. 0.8
C. 0.7
D. 0.6
Question 10
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{8}
D. \frac{5}{8}
Question 11
Find the volume of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 16π
B. 32π
C. 64π
D. 128π
Question 12
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 4 \) about the x-axis.
A. \( \frac{64}{5} pi \)
B. \( \frac{32}{3} pi \)
C. \( \frac{16}{3} pi \)
D. \( \frac{8}{3} pi \)
Question 13
A company produces two products, A and B. The profit from the sale of one unit of product A is ₦50, and the profit from the sale of one unit of product B is ₦75. If the company produces 100 units of product A and 50 units of product B, what is the total profit?
A. ₦12500
B. ₦15000
C. ₦17500
D. ₦20000
Question 14
Solve the inequality \( 2x^2 + 5x - 3 > 0 \)
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 15
A polynomial has roots at x = -2, x = 3, and x = 4. What is the polynomial in factored form?
A. \( x + 2 \)\( x - 3 \)\( x - 4 \)
B. \( x + 2 \)\( x - 3 \)\( x - 4 \)
C. \( x + 2 \)\( x - 3 \)\( x - 4 \)
D. \( x + 2 \)\( x - 3 \)\( x - 4 \)

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