Exam Body

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Subject

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POST UTME MADONNA UNIVERSITY 2023 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 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

In the diagram below, what is the equation of the circle with center at point A?

Correct A. \( x^2 + y^2 = 4 \)

B. \( x^2 + y^2 = 9 \)

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

D. \( x^2 + y^2 = 25 \)

Correct Answer: A

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Question 2

If the polynomial ( p(x) = x^3 - 6x^2 + 11x - 6 ) has a factor of \( x - 1 \), what is the other factor?

Correct A. \( x^2 - 5x + 6 \)

B. \( x^2 - 5x + 5 \)

C. \( x^2 - 5x + 4 \)

D. \( x^2 - 5x + 3 \)

Correct Answer: A

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Question 3

A right circular cone has a height of 8 cm and a base radius of 4 cm. What is the volume of the cone?

A. ( 32pi ) cm^3

B. ( 64pi ) cm^3

Correct C. ( 128pi ) cm^3

D. ( 256pi ) cm^3

Correct Answer: C

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Question 4

In a set of 10 integers, the average of the first 5 integers is 10, and the average of the next 3 integers is 15. What is the average of all 10 integers?

A. 12

Correct B. 13

C. 14

D. 15

Correct Answer: B

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Question 5

If the matrix \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) is multiplied by the matrix \( B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \), what is the value of the element in the first row and second column of the product matrix?

A. 19

B. 20

Correct C. 21

D. 22

Correct Answer: C

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Question 6

Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 7

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

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

B. \( -3, -1 \) \cup (1, 3) \cup (4, 5)

C. \( -3, -1 \) \cup (1, 3) \cup (4, 5) \cup (6, 7)

D. \( -3, -1 \) \cup (1, 3) \cup (4, 5) \cup (6, 7) \cup (8, 9)

Correct Answer: A

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Question 8

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

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

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

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

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

Correct Answer: A

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Question 9

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

A. \frac{\pi}{4}

Correct B. \frac{\pi}{2}

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

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

Correct Answer: B

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Question 10

Find the area of the region bounded by the curves y = x^2, y = 0, and x = 2.

Correct A. \frac{8}{3}

B. \frac{16}{3}

C. \frac{32}{3}

D. \frac{64}{3}

Correct Answer: A

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Question 11

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

Correct A. 27

B. 30

C. 33

D. 36

Correct Answer: A

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Question 12

Solve the inequality x^2 - 4x - 5 > 0.

Correct A. \( -∞, -1 \) ∪ (5, ∞)

B. \( -∞, -5 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (5, ∞)

D. \( -∞, -5 \) ∪ (1, ∞)

Correct Answer: A

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Question 13

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 14

A die is rolled. What is the probability that the number obtained is greater than 4?

A. 1/3

B. 1/2

Correct C. 2/3

D. 1/6

Correct Answer: C

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Question 15

Find the sum of the first 10 terms of the geometric series 3x^2 + 6x + 12.

Correct A. 300x^2 + 600x + 1200

B. 300x^2 + 600x + 12000

C. 300x^2 + 6000x + 1200

D. 300x^2 + 6000x + 12000

Correct Answer: A

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Question 16

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

A. f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

Correct B. f'(x) = \frac{\( x^2 + 2x - 3 \)\( 2x - 8 \) - \( x^2 - 4 \)\( 2x + 2 \)}{\( x^2 - 4 \)^2}

C. f'(x) = \frac{\( x^2 + 2x - 3 \)\( 2x + 8 \) - \( x^2 - 4 \)\( 2x - 2 \)}{\( x^2 - 4 \)^2}

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

Correct Answer: B

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Question 17

A rec\tangular box has dimensions 5 cm, 8 cm, and 3 cm. Find the surface area of the box.

Correct A. A = 2(5)(8) + 2(5)(3) + 2(8)(3)

B. A = 2(5)(8) + 2(5)(3) + 2(8)(5)

C. A = 2(5)(8) + 2(3)(8) + 2(5)(3)

D. A = 2(5)(8) + 2(3)(5) + 2(8)(3)

Correct Answer: A

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Question 18

The mean of a set of numbers is 25. If the sum of the numbers is 100, what is the median?

Correct A. The median is 25.

B. The median is 20.

C. The median is 30.

D. The median is 35.

Correct Answer: A

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Question 19

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

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

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

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

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

Correct Answer: A

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Question 20

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

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = -2x + 1

D. y = -2x - 1

Correct Answer: A

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Question 21

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

Correct A. x^2 + y^2 - 6x + 4y + 7 = 0

B. x^2 + y^2 - 4x - 2y + 3 = 0

C. x^2 + y^2 + 2x - 4y + 2 = 0

D. x^2 + y^2 + 6x - 2y + 1 = 0

Correct Answer: A

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Question 22

If f(x) = x^3 - 6x^2 + 11x - 6, find f'(x) u\sing the chain rule.

Correct A. 3x^2 - 12x + 11

B. 3x^2 - 12x + 6

C. 3x^2 - 12x - 11

D. 3x^2 - 12x + 5

Correct Answer: A

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Question 23

Solve the system of equations u\sing matrices: x + 2y - z = 4, 2x - 3y + z = -3, x + y + 2z = 2.

Correct A. [x = 1, y = 1, z = 1]

B. [x = 2, y = 1, z = 0]

C. [x = 1, y = 2, z = 0]

D. [x = 0, y = 1, z = 2]

Correct Answer: A

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Question 24

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

A. 10

Correct B. 12

C. 15

D. 20

Correct Answer: B

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Question 25

A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed for the round trip?

A. 48 km/h

B. 50 km/h

Correct C. 52 km/h

D. 55 km/h

Correct Answer: C

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