Exam Body

Year

Subject

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POST UTME BOWEN UNIVERSITY 2019 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 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].

Correct A. 13

B. 15

C. 17

D. 19

Correct Answer: A

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Question 2

Solve the equation [ x^2 + 4x + 4 = 0 ].

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 3

Find the sum of the first 5 terms of the geometric progression [ 2, 6, 18, 54, ... ].

Correct A. 728

B. 7280

C. 72800

D. 728000

Correct Answer: A

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Question 4

In the circuit below, find the current through the 2-ohm resistor.

A. 1 A

Correct B. 2 A

C. 3 A

D. 4 A

Correct Answer: B

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Question 5

Find the derivative of the function [ f(x) = 3x^2 + 2x - 5 ].

Correct A. 6x + 2

B. 6x - 2

C. 3x^2 + 2

D. 3x^2 - 2

Correct Answer: A

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Question 6

Find the equation of the line pas\sing through the points (2, 3) and (4, 5) in the coordinate plane.

Correct A. \frac{y - 3}{x - 2} = \frac{5 - 3}{4 - 2}

B. \frac{y - 2}{x - 3} = \frac{5 - 3}{4 - 2}

C. \frac{y - 3}{x - 4} = \frac{5 - 3}{4 - 2}

D. \frac{y - 2}{x - 4} = \frac{5 - 3}{4 - 2}

Correct Answer: A

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Question 7

Find the derivative of the function f(x) = \frac{1}{x^2 + 1} u\sing the chain rule.

A. \frac{-2x}{\( x^2 + 1 \)^2}

Correct B. \frac{2x}{\( x^2 + 1 \)^2}

C. \frac{2}{\( x^2 + 1 \)^2}

D. \frac{-2}{\( x^2 + 1 \)^2}

Correct Answer: B

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Question 8

Simplify the expression \sqrt{\frac{16}{25}}.

Correct A. \frac{4}{5}

B. \frac{2}{5}

C. \frac{4}{3}

D. \frac{2}{3}

Correct Answer: A

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Question 9

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. \( x - 3 \)^2 + \( y - 4 \)^2 = 16

Correct Answer: A

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Question 10

Find the sum of the first 5 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 2 + 6 + 18 + 54 + 162

B. 2 + 6 + 18 + 54 + 162 + 486

C. 2 + 6 + 18 + 54 + 162 + 486 + 1458

D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374

Correct Answer: A

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Question 11

A cylindrical water \tank has a height of 10m and a radius of 4m. If the water level is 6m, find the volume of water in the \tank.

A. 1000\pi

Correct B. 1200\pi

C. 1500\pi

D. 1800\pi

Correct Answer: B

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Question 12

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, find 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 13

In a game of chance, two events A and B are indep\endent. If the probability of event A occurring is 0.4 and the probability of event B occurring is 0.6, find the probability that both events occur.

A. 0.2

Correct B. 0.24

C. 0.28

D. 0.32

Correct Answer: B

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Question 14

Solve the equation \( x^2 + 4x - 5 = 0 \) u\sing the quadratic formula.

Correct A. \( x = -5, 1 \)

B. \( x = -1, 5 \)

C. \( x = 1, -5 \)

D. \( x = -1, -5 \)

Correct Answer: A

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Question 15

A cone has a height of 8cm and a radius of 4cm. If the volume of the cone is 256\pi cubic cm, find the height of the cone.

A. 2cm

B. 4cm

Correct C. 6cm

D. 8cm

Correct Answer: C

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Question 16

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

B. 64\pi

Correct C. 72\pi

D. 80\pi

Correct Answer: C

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Question 17

A die is rolled twice. What is the probability that the sum of the two numbers shown is 7?

Correct A. 1/6

B. 1/12

C. 1/36

D. 1/24

Correct Answer: A

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Question 18

Solve the inequality \frac{x-2}{x+1} > 0.

Correct A. x < -1 or x > 2

B. x > -1 or x < 2

C. x < 2 or x > -1

D. x > 2 or x < -1

Correct Answer: A

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Question 19

Find the value of \sin 2x if \cos x = \frac{3}{5} and \sin x = \frac{4}{5}.

Correct A. \frac{24}{25}

B. \frac{16}{25}

C. \frac{20}{25}

D. \frac{12}{25}

Correct Answer: A

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Question 20

Simplify the expression \frac{\sqrt{12}}{\sqrt{3}}.

Correct A. 2\sqrt{3}

B. \sqrt{3}

C. 2

D. \sqrt{12}

Correct Answer: A

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Question 21

Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).

Correct A. \boxed{x^2 + y^2 - 12x - 8y + 36 = 0}

B. x^2 + y^2 - 10x - 6y + 20 = 0

C. x^2 + y^2 - 14x - 10y + 40 = 0

D. x^2 + y^2 - 16x - 12y + 48 = 0

Correct Answer: A

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Question 22

Solve the equation \( \sin^2 x + \cos^2 x - \sin x \cos x = 0 \) for x.

Correct A. \boxed{x = \frac{\pi}{4} + 2k\pi}

B. x = \frac{3\pi}{4} + 2k\pi

C. x = \frac{5\pi}{4} + 2k\pi

D. x = \frac{7\pi}{4} + 2k\pi

Correct Answer: A

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Question 23

Find the derivative of the function \( f(x) = \frac{x^2 + 3x + 2}{x^2 - 4x + 3} \) u\sing the quotient rule.

Correct A. \boxed{\frac{2x^2 + 5x + 4}{\( x^2 - 4x + 3 \)^2}}

B. \frac{2x^2 + 3x + 2}{\( x^2 - 4x + 3 \)^2}

C. \frac{2x^2 + 5x + 4}{\( x^2 - 4x + 3 \)^2}

D. \frac{2x^2 + 3x + 2}{\( x^2 - 4x + 3 \)^2}

Correct Answer: A

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Question 24

Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \) u\sing the quadratic formula.

Correct A. \boxed{x \leq -\frac{3}{2} \text{ or } x \geq \frac{1}{2}}

B. x \leq -\frac{3}{2} \text{ or } x \geq -\frac{1}{2}

C. x \leq -\frac{1}{2} \text{ or } x \geq \frac{3}{2}

D. x \leq -\frac{1}{2} \text{ or } x \geq -\frac{3}{2}

Correct Answer: A

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Question 25

Find the equation of the line pas\sing through the points (2, 3) and (4, 5).

Correct A. \boxed{y = \frac{2}{2}x + \frac{1}{2}}

B. y = \frac{2}{3}x + \frac{1}{3}

C. y = \frac{2}{4}x + \frac{1}{4}

D. y = \frac{2}{5}x + \frac{1}{5}

Correct Answer: A

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