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POST UTME AL-HIKMAH UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 View Details

A histogram of exam scores has a mean of 60 and a standard 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 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using 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 View Details

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 View Details

Find the equation of the line passing 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, 1\) ∪ (3, ∞)

C. \(-∞, -3\) ∪ (1, ∞)

D. \(-∞, 1\) \cup \(-3, ∞\)\)

Correct Answer: A

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Question 14 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of the function f(x) = \(3x^2 + 2x - 5\) using 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 View Details

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 View Details

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 View Details

A rectangular 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 View Details

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 View Details

In a circle of radius 8cm, a chord of length 12cm subtends 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 View Details

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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