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POST UTME BOWEN UNIVERSITY 2018 Mathematics | Objective

Are you preparing for POST UTME BOWEN UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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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. 48\pi cm^3

B. 64\pi cm^3

Correct C. 80\pi cm^3

D. 96\pi cm^3

Correct Answer: C

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Question 2

Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.

Correct A. \( -3, -2 \) \cup \( -1, 1 \) \cup (2, 3)

B. \( -3, -2 \) \cup (1, 2)

C. \( -3, -2 \) \cup (1, 3)

D. \( -3, 3 \)

Correct Answer: A

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Question 3

Find the area of the region bounded by the parabola y = x^2, the line y = 4, and the x-axis.

A. 8\pi

B. 16\pi

Correct C. 24\pi

D. 32\pi

Correct Answer: C

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Question 4

Solve the system of equations \begin{align*} x + y &= 4 \ x - 2y &= 3 \end{align*}

Correct A. \begin{pmatrix} 1 \ 3 \end{pmatrix}

B. \begin{pmatrix} -1 \ 5 \end{pmatrix}

C. \begin{pmatrix} 2 \ 2 \end{pmatrix}

D. \begin{pmatrix} -2 \ -2 \end{pmatrix}

Correct Answer: A

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Question 5

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is red?

A. \frac{1}{2}

B. \frac{3}{8}

Correct C. \frac{5}{8}

D. \frac{7}{8}

Correct Answer: C

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Question 6

Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 7

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

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 8

Solve the equation \( x^2 + 4x + 4 = 0 \).

A. x = 0

Correct B. x = -2

C. x = -1

D. x = 1

Correct Answer: B

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Question 9

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 10

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

A. 10\pi

B. 20\pi

Correct C. 50\pi

D. 100\pi

Correct Answer: C

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Question 11

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix} ].

A. 1

Correct B. -1

C. 2

D. 3

Correct Answer: B

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Question 12

A rec\tangular solid has dimensions 3 cm, 4 cm, and 5 cm. Find its surface area.

A. 94

Correct B. 96

C. 98

D. 100

Correct Answer: B

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Question 13

Solve the equation [ 2x^2 + 3x - 1 = 0 ].

A. x = -1/2

Correct B. x = 1/2

C. x = -1

D. x = 1

Correct Answer: B

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Question 14

A curve has equation [ y = x^2 + 2x + 1 ]. Find the area under the curve between x = 0 and x = 2.

A. 7

Correct B. 8

C. 9

D. 10

Correct Answer: B

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Question 15

Two events are indep\endent. If the probability of one event is 1/2 and the probability of the other event is 3/4, find the probability that both events occur.

Correct A. 3/8

B. 1/2

C. 3/4

D. 5/8

Correct Answer: A

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Question 16

A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. Calculate the coefficient of variation (CV) of the sample.

A. 10%

Correct B. 15%

C. 20%

D. 25%

Correct Answer: B

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Question 17

Find the derivative of the function f(x) = \frac{\ln x}{x^2} u\sing the quotient rule.

A. \frac{1}{x^3}

Correct B. \frac{2x}{x^4}

C. \frac{x^2}{x^4}

D. \frac{x^3}{x^4}

Correct Answer: B

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Question 18

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

Correct A. \frac{\pi}{4}

B. \frac{\pi}{2}

C. \frac{3\pi}{4}

D. \frac{5\pi}{4}

Correct Answer: A

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Question 19

A force of 10 N acts on an object, cau\sing it to accelerate at 2 m/s^2. What is the mass of the object?

A. 5 kg

Correct B. 10 kg

C. 15 kg

D. 20 kg

Correct Answer: B

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Question 20

Find the equation of the circle with center (2, 3) and radius 4.

Correct 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

Correct Answer: A

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Question 21

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the determinant method.

Correct A. \( egin{pmatrix} 10 \ -14 \end{pmatrix} \)

B. \( egin{pmatrix} -10 \ 14 \end{pmatrix} \)

C. \( egin{pmatrix} 14 \ 10 \end{pmatrix} \)

D. \( egin{pmatrix} 0 \ 0 \end{pmatrix} \)

Correct Answer: A

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Question 22

Solve the equation \( 2^x + 2^{x+1} = 3 cdot 2^x \) for ( x ).

Correct A. \( x = 1 \)

B. \( x = 2 \)

C. \( x = 3 \)

D. \( x = 4 \)

Correct Answer: A

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Question 23

Find the value of \( \log_{10} \( 1000 \ \) ).

A. ( 3 )

Correct B. ( 4 )

C. ( 5 )

D. ( 6 )

Correct Answer: B

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Question 24

Solve the inequality \( \frac{x}{2} - 1 > 3 \).

Correct A. \( x > 8 \)

B. \( x < 8 \)

C. \( x > 6 \)

D. \( x < 6 \)

Correct Answer: A

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Question 25

Find the value of \( \sin \( 2x \ \) ) given that \( \sin \( x \ \) = \frac{1}{2} ) and \( \cos \( x \ \) = \frac{\sqrt{3}}{2} ).

Correct A. \( \frac{\sqrt{3}}{2} \)

B. \( \frac{1}{2} \)

C. \( -\frac{1}{2} \)

D. \( -\frac{\sqrt{3}}{2} \)

Correct Answer: A

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