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POST UTME AL-HIKMAH UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

Solve the inequality \(\frac{x^2 - 4}{x + 2} \geq 0\) for ( x in mathbb{R} ).

Correct A. \(x \leq -2\) or ( x geq 2 )

B. \(x < -2\) or \(x > 2\)

C. ( x leq 2 ) or \(x \geq -2\)

D. \(x = -2\) or \(x = 2\)

Correct Answer: A

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Question 2 View Details

Find the area under the curve \(y = \sin^2 x\) from \(x = 0\) to \(x = \frac{\pi}{2}\).

Correct A. \(\frac{\pi}{4}\)

B. \(\frac{\pi}{2}\)

C. \(\frac{\pi}{3}\)

D. \(\frac{\pi}{6}\)

Correct Answer: A

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Question 3 View Details

The equation of a circle is given by \(x^2 + y^2 - 6x + 8y + 12 = 0\). Find the center and radius of the circle.

Correct A. Center: \(3, -4 \\) ), Radius: ( 2 )

B. Center: ( (4, 3) ), Radius: ( 2 )

C. Center: ( (3, 4) ), Radius: ( 2 )

D. Center: \(4, -3 \\) ), Radius: ( 2 )

Correct Answer: A

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Question 4 View Details

A polynomial function is defined as ( f(x) = \((x^3 - 6x^2 + 11x - 6\)\) ). Find the value of \(f -1 \\((x^3 - 6x^2 + 11x - 6) ). Find the value of \\) ).

Correct A. ( 4 )

B. ( 5 )

C. ( 6 )

D. ( 7 )

Correct Answer: A

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Question 5 View Details

Two events A and B are independent. If ( P(A) = \(\frac{1}{3}\)\) ) and ( P(B) = \(\frac{2}{5}\)\) ), find the probability that both events occur.

A. \(\frac{1}{5}\)

Correct B. \(\frac{2}{15}\)

C. \(\frac{4}{15}\)

D. \(\frac{1}{15}\)

Correct Answer: B

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Question 6 View Details

Find the value of 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 7 View Details

A survey of 100 students found that 60% preferred Mathematics, 20% preferred Science, and 20% preferred both. What is the number of students who prefer Mathematics but not Science?

A. 24

B. 30

Correct C. 36

D. 42

Correct Answer: C

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Question 8 View Details

In the diagram below, what is the value of x?

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 9 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is the volume of the prism?

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 10 View Details

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 \(km/h\\((km/h) and returns at an average speed of 40\). What is the average speed for the round trip?

A. 45

B. 50

Correct C. 55

D. 60

Correct Answer: C

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Question 11 View Details

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

A. 24

B. 30

Correct C. 36

D. 42

Correct Answer: C

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Question 12 View Details

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

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 13 View Details

A sequence is defined by \(a_n = 2n + 1\). Find the sum of the first five terms of the sequence.

A. 30

Correct B. 35

C. 40

D. 45

Correct Answer: B

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Question 14 View Details

A histogram is shown below. Find the mean of the data.

A. 10

B. 15

Correct C. 20

D. 25

Correct Answer: C

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Question 15 View Details

A vector ( mathbf{a} ) is defined by \(\mathbf{a} = 2\mathbf{i} + 3\mathbf{j}\). Find the magnitude of ( mathbf{a} ).

A. 2.5

B. 3.5

Correct C. 4.5

D. 5.5

Correct Answer: C

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Question 16 View Details

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

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 17 View Details

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

A. 10

B. 12

Correct C. 15

D. 20

Correct Answer: C

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Question 18 View Details

The first term of an arithmetic progression is ( a ) and the common difference is ( d ). Find the sum of the first five terms of the progression.

Correct A. \(\frac{5}{2}\)\)\(2a + 3d\)

B. \(\frac{5}{2}\)\)\(a + 3d\)

C. \(\frac{5}{2}\)\)\(2a + d\)

D. \(\frac{5}{2}\)\)\(a + d\)

Correct Answer: A

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Question 19 View Details

A solid cylinder has a radius of 4 cm and a height of 10 cm. Find the volume of the cylinder.

A. 800\pi

Correct B. 1600\pi

C. 3200\pi

D. 6400\pi

Correct Answer: B

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Question 20 View Details

The mean of a set of numbers is 25. If the sum of the numbers is 100, find the mode of the set.

A. 20

Correct B. 25

C. 30

D. 35

Correct Answer: B

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Question 21 View Details

Simplify the expression \(\sqrt{\frac{16}{25}} \\).

Correct A. \(\frac{4}{5}\)\)

B. \(\frac{2}{5}\)\)

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

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

Correct Answer: A

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Question 22 View Details

Find the value of ( x ) in the equation \(2^x = 64\).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 23 View Details

A histogram has a mean of 25 and a standard deviation of 5. Find the range of the histogram.

A. 20

B. 25

C. 30

Correct D. 35

Correct Answer: D

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Question 24 View Details

Simplify the expression \(\log_{10} 1000 \\).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 25 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). Find the sum of the first five terms of the sequence.

A. 15

B. 20

C. 25

Correct D. 30

Correct Answer: D

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