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POST UTME MADONNA UNIVERSITY 2019 Mathematics | Objective

Are you preparing for POST UTME MADONNA 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

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

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

B. \( x = 2 \)

C. \( x = -1 \)

Correct D. \( x = \frac{1}{2} \)

Correct Answer: D

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Question 2

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

Correct A. \( \frac{64}{3} \)

B. ( 16 )

C. ( 32 )

D. ( 64 )

Correct Answer: A

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Question 3

In the circuit below, identify the part labeled A.

Correct A. Batteries

B. Resistor

C. Capacitor

D. Inductor

Correct Answer: A

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Question 4

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)

B. \( x > -\frac{3}{2} \) or \( x < \frac{1}{2} \)

C. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)

D. \( x > -\frac{1}{2} \) or \( x < \frac{3}{2} \)

Correct Answer: A

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Question 5

Find the derivative of the function ( f(x) = x^3 - 2x^2 + x - 1 ).

Correct A. ( f'(x) = 3x^2 - 4x + 1 )

B. ( f'(x) = x^2 - 2x + 1 )

C. ( f'(x) = 3x^2 - 4x - 1 )

D. ( f'(x) = x^2 - 2x - 1 )

Correct Answer: A

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Question 6

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 256\pi cm^3

B. 512\pi cm^3

Correct C. 768\pi cm^3

D. 1024\pi cm^3

Correct Answer: C

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Question 7

Solve for x in the equation \tan x = \frac{1}{\sqrt{3}}.

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

B. \frac{\pi}{3}

C. \frac{\pi}{2}

D. \frac{2\pi}{3}

Correct Answer: A

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Question 8

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

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

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

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

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

Correct Answer: A

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Question 9

Simplify the expression \frac{2x^2 - 5x + 3}{x^2 - 2x - 3}.

Correct A. 2x - 1

B. 2x + 1

C. x - 1

D. x + 1

Correct Answer: A

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Question 10

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

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 11

In a circle of radius 5 cm, a chord of length 8 cm subt\ends an angle of 60° at the centre. Find the area of the sector.

A. ( 20pi ) cm²

Correct B. ( 30pi ) cm²

C. ( 40pi ) cm²

D. ( 50pi ) cm²

Correct Answer: B

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Question 12

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

A. \( \frac{1}{6} \)

Correct B. \( \frac{1}{3} \)

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

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

Correct Answer: B

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Question 13

Solve for x: \( 2^x + 3^x = 5^x \).

A. \( x = 2 \)

Correct B. \( x = 3 \)

C. \( x = 4 \)

D. \( x = 5 \)

Correct Answer: B

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Question 14

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

A. \( y = 2x - 1 \)

Correct B. \( y = 2x + 1 \)

C. \( y = -2x + 1 \)

D. \( y = -2x - 1 \)

Correct Answer: B

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Question 15

A circle has a radius of 4 cm. Find the area of the sector subt\ended by a central angle of 60°.

A. ( 12pi ) cm²

Correct B. ( 16pi ) cm²

C. ( 20pi ) cm²

D. ( 24pi ) cm²

Correct Answer: B

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Question 16

Find the volume of the frustum of the cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.

A. 256\pi cm^3

B. 512\pi cm^3

Correct C. 768\pi cm^3

D. 1024\pi cm^3

Correct Answer: C

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Question 17

Solve the inequality \frac{x^2 - 4x + 3}{x^2 - 2x - 3} > 0.

Correct A. \left\( -\infty, -1 \right \) \cup \left\( 1, \infty \right \)

B. \left\( -\infty, 1 \right \) \cup \left\( 3, \infty \right \)

C. \left\( -\infty, -3 \right \) \cup \left\( 1, \infty \right \)

D. \left\( -\infty, 1 \right \) \cup \left\( 3, \infty \right \)

Correct Answer: A

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Question 18

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

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

B. \( x - 2 \)^2 + \( y - 3 \)^2 = 25

Correct C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49

Correct Answer: C

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Question 19

Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 4.

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 20

Find the mean of the data set: 2, 4, 6, 8, 10.

A. 6

B. 7

Correct C. 8

D. 9

Correct Answer: C

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Question 21

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the co\sine rule.

A. 8 cm

Correct B. 12 cm

C. 6 cm

D. 4 cm

Correct Answer: B

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Question 22

A solid cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone in cubic centimeters.

A. 256π cm³

Correct B. 128π cm³

C. 512π cm³

D. 2048π cm³

Correct Answer: B

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Question 23

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

A. -1

B. 0

Correct C. 1

D. 2

Correct Answer: C

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Question 24

A set of 5 consecutive integers has a median of 8. Find the sum of the integers.

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 25

A circle has a diameter of 14 cm. Find the area of the circle in square centimeters.

A. 154 cm²

B. 196 cm²

Correct C. 308 cm²

D. 784 cm²

Correct Answer: C

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