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

Practice these randomly selected questions to test your readiness.

Question 1

Find the value of x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \)

A. 1

Correct B. -2

C. 3

D. -3

Correct Answer: B

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Question 2

Solve for y: \( \sin^2 y + \cos^2 y = 1 \)

A. 0

Correct B. π/2

C. π

D. 3π/2

Correct Answer: B

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Question 3

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

Correct A. 6x - 2

B. 6x + 2

C. 3x^2 - 2

D. 3x^2 + 2

Correct Answer: A

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Question 4

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 5

Solve for x: \( 2^x = 16 \)

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 6

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

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 7

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

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

Correct B. \( -3, -1 \) \cup (1, 3) \cup \( 3, \infty \)

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

D. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, -3 \) \cup \( 3, \infty \) \cup (0, 1)

Correct Answer: B

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Question 8

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 9

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

A. 6

B. 8

Correct C. 12

D. 18

Correct Answer: C

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Question 10

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 = 9

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

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

Correct Answer: A

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Question 11

Determine the value of \( int_{0}^{2} \( 2x^2 + 3x - 4 \ \) dx ).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 12

A binary operation ( odot ) is defined as \( a odot b = a^2 - b^2 \). Find the value of ( 3 odot 2 ).

A. 1

B. 5

Correct C. 7

D. 9

Correct Answer: C

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Question 13

A set ( S ) contains the elements ( {1, 2, 3, 4, 5} ). Find the number of subsets of ( S ) that contain exactly two elements.

A. 5

B. 10

Correct C. 15

D. 20

Correct Answer: C

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Question 14

A geometric sequence has first term \( a = 2 \) and common ratio \( r = 3 \). Find the sum of the first five terms of the sequence.

A. 155

Correct B. 160

C. 165

D. 170

Correct Answer: B

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Question 15

A polynomial function ( f(x) = x^3 - 2x^2 + 3x - 1 ) has a root at \( x = 1 \). Find the value of ( f(2) ).

A. 3

Correct B. 5

C. 7

D. 9

Correct Answer: B

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Question 16

A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, and P\( X = 3 \) = 0.3. If two indep\endent random variables X and Y have the same probability distribution, what is the probability that X + Y is greater than 4?

A. 0.4

Correct B. 0.5

C. 0.6

D. 0.7

Correct Answer: B

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Question 17

The volume of a sphere (V) is given by the formula V = \frac{4}{3}\pi r^3, where r is the radius of the sphere. If the radius of a sphere is increased by 20%, what is the percentage increase in its volume?

A. 10%

B. 20%

C. 30%

Correct D. 520%

Correct Answer: D

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Question 18

Solve the system of linear equations: \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}

A. \left\( 3, \frac{1}{3} \right \)

Correct B. \left\( \frac{17}{5}, 4 - \frac{17}{5} \right \)

C. \left\( 2, 2 \right \)

D. \left\( 1, 3 \right \)

Correct Answer: B

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Question 19

A matrix A is given by \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}. Find the determinant of A.

A. -1

Correct B. -2

C. 2

D. 4

Correct Answer: B

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Question 20

Solve the quadratic equation: x^2 + 5x + 6 = 0

Correct A. \left\( -3, -2 \right \)

B. \left\( -2, -3 \right \)

C. \left\( 1, 2 \right \)

D. \left\( 2, 1 \right \)

Correct Answer: A

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