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POST UTME BOWEN UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation $$12x \$ = $\frac{1}{2}$\) ) given that ( 0 leq x leq 2pi ).

Correct A. $\frac{\pi}{6}$

B. $\frac{\pi}{4}$

C. $\frac{\pi}{3}$

D. $\frac{\pi}{2}$

Correct Answer: A

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Question 2 View Details

Find the area under the curve $y = x^2$ from $x = 0$ to $x = 4$ using the method of integration.

Correct A. $\frac{64}{3}$

B. $\frac{32}{3}$

C. $\frac{16}{3}$

D. $\frac{8}{3}$

Correct Answer: A

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Question 3 View Details

Solve for x in the equation $2^x + 3^x = 5^x$.

A. $x = 2$

B. $x = 3$

Correct C. $x = 4$

D. $x = 5$

Correct Answer: C

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Question 4 View Details

A particle moves in a straight line with a velocity given by ( v(t) = 2t + 5 ). Find the displacement of the particle from $t = 0$ to $t = 3$.

A. ( 27 )

B. ( 30 )

Correct C. ( 33 )

D. ( 36 )

Correct Answer: C

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Question 5 View Details

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. ( 16pi )

B. ( 32pi )

C. ( 64pi )

D. ( 128pi )

Correct Answer: A

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Question 6 View Details

Find the area under the curve $y = x^2 + 2x + 1$ from $x = 0$ to $x = 2$.

Correct A. 10

B. 12

C. 14

D. 16

Correct Answer: A

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Question 7 View Details

A circle has a radius of 5 cm. Find the area of the circle.

Correct A. 25\pi

B. 50\pi

C. 75\pi

D. 100\pi

Correct Answer: A

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Question 8 View Details

Find the volume of a rectangular prism with length 10 cm, width 5 cm, and height 3 cm.

Correct A. 150

B. 200

C. 250

D. 300

Correct Answer: A

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Question 9 View Details

A histogram has a mean of 25 and a standard deviation of 5. Find the median.

A. 20

Correct B. 25

C. 30

D. 35

Correct Answer: B

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Question 10 View Details

A line passes through the points (2, 3) and (4, 5). Find the equation of the line.

A. $y = 1x + 1$

Correct B. $y = 2x + 1$

C. $y = 3x + 1$

D. $y = 4x + 1$

Correct Answer: B

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Question 11 View Details

Find the area under the curve $y = \frac{1}{2}x^2$ from $x = 0$ to $x = 4$.

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 12 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$.

Correct A. $-∞, -1$ ∪ (3, ∞)

B. $-∞, 1$ ∪ (3, ∞)

C. $-∞, -1$ ∪ (1, ∞)

D. $-∞, 3$ ∪ (1, ∞)

Correct Answer: A

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Question 13 View Details

Find the determinant of the matrix $egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{bmatrix}$.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 14 View Details

Solve the equation $x^3 - 2x^2 - 5x + 6 = 0$.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 15 View Details

Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).

A. 3

B. 6

Correct C. 9

D. 12

Correct Answer: C

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Question 16 View Details

Solve the inequality ($\frac{x+2}{x-1}\(> 0$\) for x in \$(frac{x+2}{x-1}\(> 0$$-infty$, infty \ ).

Correct A. $x < -2$ or $x > 1$

B. $x < -2$ or $x < 1$

C. $x > -2$ or $x > 1$

D. $x > -2$ or $x < 1$

Correct Answer: A

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Question 17 View Details

Find the derivative of the function ( f(x) = \$\sin^2(x)$ ) using the chain rule.

Correct A. ( f'$(x) = 2$\sin$x)\cos(x$ )

B. ( f'$(x) =$\sin(x) + \cos(x) )

C. ( f'$(x) = 2$\$\sin^2(x)$ )

D. ( f'$(x) =$\$\cos^2(x)$ )

Correct Answer: A

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Question 18 View Details

Solve the trigonometric equation $\sin^2 x \$ + \$\cos^2(x)$ = 1 ) for ( x in [0, 2pi] ).

Correct A. $x = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}$

B. $x = \frac{\pi}{2}, \frac{3\pi}{2}$

C. $x = 0, \pi, 2\pi$

D. $x = \frac{\pi}{6}, \frac{5\pi}{6}$

Correct Answer: A

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Question 19 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.

A. ( 30 ) cm³

B. ( 50 ) cm³

Correct C. ( 60 ) cm³

D. ( 70 ) cm³

Correct Answer: C

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Question 20 View Details

Solve the quadratic equation $x^2 + 4x + 4 = 0$ using the quadratic formula.

Correct A. $x = -2$

B. $x = -1$

C. $x = 0$

D. $x = 1$

Correct Answer: A

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Question 21 View Details

Given that $\sin^2 x + \cos^2 x = 1$, find the value of (\$tan^2$ x\) in terms of \$(tan^2 x\(\(1x$ and 1x\).

Correct A. $\frac{\sin^2 x}{\cos^2 x}$

B. $\frac{\cos^2 x}{\sin^2 x}$

C. $\frac{1}{\sin^2 x \cos^2 x}$

D. $\frac{\sin^2 x + \cos^2 x}{\sin^2 x \cos^2 x}$

Correct Answer: A

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Question 22 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

Correct A. $P 60 < X < 90$ = $\frac{1}{2}$\) \)

B. $P 60 < X < 90$ = $\frac{1}{4}$\) \)

C. $P 60 < X < 90$ = $\frac{3}{4}$\) \)

D. $P 60 < X < 90$ = $\frac{1}{3}$\) \)

Correct Answer: A

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Question 23 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = $x^2$\), the x-axis, and the line $x = 2\\((y = x^2), the x-axis, and the line$ about the x-axis.

Correct A. $V = \frac{\pi}{3}$

B. $V = \frac{\pi}{2}$

C. $V = \frac{\pi}{4}$

D. $V = \frac{\pi}{6}$

Correct Answer: A

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Question 24 View Details

A circle has a radius of 4 cm. If a chord of the circle is 6 cm long, what is the angle subtended by the chord at the center of the circle?

Correct A. $\theta = \frac{1}{2} \sin^{-1} \frac{3}{4}$

B. $\theta = \frac{1}{2} \sin^{-1} \frac{1}{2}$

C. $\theta = \frac{1}{2} \sin^{-1} \frac{3}{5}$

D. $\theta = \frac{1}{2} \sin^{-1} \frac{2}{3}$

Correct Answer: A

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Question 25 View Details

A particle moves in a straight line with a velocity of 5 $(m/s$\). If the acceleration of the particle is 2 $m/s\\((m/s). If the acceleration of the particle is 2 \^2$, what is the distance traveled by the particle in 4 seconds?

Correct A. $s = 20$

B. $s = 25$

C. $s = 30$

D. $s = 35$

Correct Answer: A

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