POST UTME BOWEN UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the first 5 terms of the arithmetic sequence 2, 5, 8, ...
A. S_5 = 30
B. S_5 = 25
C. S_5 = 20
D. S_5 = 15
Question 2
Find the value of \( \sin 2x \) given that \( \sin x = \frac{3}{5} \) and \( \cos x = \frac{4}{5} \).
A. \( \frac{24}{25} \)
B. \( \frac{12}{25} \)
C. \( \frac{16}{25} \)
D. \( \frac{20}{25} \)
Question 3
Find the equation of the circle with center ( (2, 3) ) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
Question 5
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.
A. 30
B. 40
C. 50
D. 60
Question 6
A function f(x) = 2x^2 + 5x - 3 has a local maximum at x = -1. Find the value of the function at this point.
A. -5
B. -3
C. 1
D. 5
Question 7
A curve is defined by the equation y = 2x^3 - 5x^2 + x + 1. Find the area under the curve between x = 0 and x = 1.
A. 0.5
B. 1.0
C. 1.5
D. 2.0
Question 8
A cylindrical \tank with a radius of 7m and height of 10m is filled with water. If the water level is raised by 2m, calculate the increase in volume of water in the \tank.
A. 980\pi \text{ m}^3
B. 980\pi \text{ m}^3
C. 980\pi \text{ m}^3
D. 980\pi \text{ m}^3
Question 9
A company produces light bulbs with a mean lifespan of 1200 hours and a s\tandard deviation of 120 hours. If a sample of 36 light bulbs is selected, what is the probability that the sample mean lifespan is less than 1150 hours?
A. 0.025
B. 0.05
C. 0.10
D. 0.20
Question 10
Find the magnitude of the vector \( vec{a} = egin{pmatrix} 3 \ 4 \end{pmatrix} \).
A. \( \sqrt{3^2 + 4^2} \)
B. \( 3 + 4 \)
C. \( 3 \times 4 \)
D. \( \frac{3}{4} \)
Question 11
A set of 5 numbers has a mean of 10. If 2 more numbers are added to the set, the new mean is 12. Find the sum of the original 5 numbers.
A. 40
B. 50
C. 60
D. 70
Question 12
Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?
A. 0.12
B. 0.20
C. 0.24
D. 0.30
Question 13
Solve for x in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. 1
B. 2
C. 3
D. 4
Question 14
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^3 + 3 \times 4 - 2 \times 4 \)
Question 15
Solve for x in the equation \log_{10} \( x^2 \) = 4.
A. x = 10^4
B. x = 10^2
C. x = 10^8
D. x = 10^6

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