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POST UTME AL-HIKMAH UNIVERSITY 2020 Mathematics | Objective

Are you preparing for POST UTME AL-HIKMAH UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^2 + 3 \times 4^2 - 2 \times 4 \)

D. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \)

Correct Answer: A

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Question 2

Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).

Correct A. \( x = \frac{-5 pm \sqrt{25 + 24}}{4} \)

B. \( x = \frac{-5 pm \sqrt{25 - 24}}{4} \)

C. \( x = \frac{-5 pm \sqrt{25 + 24}}{2} \)

D. \( x = \frac{-5 pm \sqrt{25 - 24}}{2} \)

Correct Answer: A

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Question 3

Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. \( 1 \times \( 5 \times 9 - 6 \times 8 \ \) - 2 \times \( 4 \times 9 - 6 \times 7 \) + 3 \times \( 4 \times 8 - 5 \times 7 \) )

B. \( 1 \times \( 5 \times 9 - 6 \times 8 \ \) - 2 \times \( 4 \times 9 - 6 \times 7 \) - 3 \times \( 4 \times 8 - 5 \times 7 \) )

C. \( 1 \times \( 5 \times 9 - 6 \times 8 \ \) + 2 \times \( 4 \times 9 - 6 \times 7 \) + 3 \times \( 4 \times 8 - 5 \times 7 \) )

D. \( 1 \times \( 5 \times 9 - 6 \times 8 \ \) + 2 \times \( 4 \times 9 - 6 \times 7 \) - 3 \times \( 4 \times 8 - 5 \times 7 \) )

Correct Answer: A

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Question 4

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 50 and 70?

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

B. \( \frac{1}{4} \)

Correct C. \( \frac{3}{4} \)

D. \( \frac{1}{4} \)

Correct Answer: C

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Question 5

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

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

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

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

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

Correct Answer: A

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Question 6

Determine the sum of the first 10 terms of the geometric series with first term 3 and common ratio 2.

Correct A. 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536

B. 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1537

C. 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1538

D. 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1539

Correct Answer: A

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Question 7

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

A. y - 3 = \frac{1}{2} \( x - 2 \)

Correct B. y - 3 = \frac{2}{2} \( x - 2 \)

C. y - 3 = \frac{3}{2} \( x - 2 \)

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

Correct Answer: B

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Question 8

Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}.

Correct A. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 3 \end{bmatrix}

C. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 4 \ 5 \end{bmatrix}

Correct Answer: A

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Question 9

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

Correct A. f'(x) = 6x + 2

B. f'(x) = 6x - 2

C. f'(x) = 3x + 2

D. f'(x) = 3x - 2

Correct Answer: A

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Question 10

A set of 5 numbers has a mean of 12. Find the sum of the numbers.

Correct A. 60

B. 61

C. 62

D. 63

Correct Answer: A

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Question 11

Solve for 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 12

A histogram of exam scores is shown below. What is the mean of the scores?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 13

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, 1 \) ∪ (3, ∞)

C. \( -∞, -3 \) ∪ (1, ∞)

D. \( -∞, 1 \) ∪ \( -3, ∞ \)

Correct Answer: A

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Question 14

Find the value of \( \sin^2 \( 60^\circ \ \) + \cos^2 \( 60^\circ \) ).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 15

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

A. 50\pi

B. 75\pi

Correct C. 100\pi

D. 125\pi

Correct Answer: C

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Question 16

In a certain number base, the representation of the number 27 is 101. What is the value of the number base?

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 17

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

A. 1/4

B. 1/3

Correct C. 3/8

D. 5/8

Correct Answer: C

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Question 18

The surface area of a cube with side length 4 cm is 96 cm^2. What is the volume of the cube?

Correct A. 64

B. 96

C. 128

D. 256

Correct Answer: A

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Question 19

Find the derivative of the function f(x) = 3x^2 + 2x - 5 u\sing the chain rule.

Correct A. 6x + 2

B. 3x + 1

C. 2x - 5

D. x^2 + 2x - 5

Correct Answer: A

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Question 20

Evaluate the definite integral \int_0^1 x^2 dx.

Correct A. 1/3

B. 1/2

C. 2/3

D. 3/4

Correct Answer: A

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Question 21

A circle has a radius of 4 cm. What is the area of the circle?

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 22

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is the volume of the prism?

Correct A. 72

B. 96

C. 120

D. 144

Correct Answer: A

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Question 23

A sphere has a radius of 5 cm. What is the volume of the sphere?

Correct A. \frac{500\pi}{3}

B. \frac{1000\pi}{3}

C. \frac{2000\pi}{3}

D. \frac{5000\pi}{3}

Correct Answer: A

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Question 24

In a circle of radius 8cm, a chord of length 12cm subt\ends an angle of 60° at the centre. Find the area of the sector formed by the chord and the radii drawn to the \ends of the chord.

A. 48π cm^2

Correct B. 64π cm^2

C. 72π cm^2

D. 80π cm^2

Correct Answer: B

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Question 25

A bag contains 5 red marbles, 8 white marbles, and 4 blue marbles. If a marble is drawn at random, what is the probability that it is either red or blue?

Correct A. \frac{9}{17}

B. \frac{5}{17}

C. \frac{3}{17}

D. \frac{1}{17}

Correct Answer: A

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