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POST UTME DELSU 2025 Mathematics | Objective

Are you preparing for POST UTME DELSU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2025 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Solve the inequality \( \frac{x}{x+1} > \frac{1}{x+1} \) for \( x in mathbb{R} setminus {-1} \).

Correct A. \( x > 0 \)

B. \( x < 0 \)

C. \( x > -1 \)

D. \( x < -1 \)

Correct Answer: A

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Question 2

Find the volume of the frustum of a cone with height \( h = 6 \) cm, lower base radius \( r_1 = 4 \) cm, and upper base radius \( r_2 = 2 \) cm.

Correct A. \( \frac{1}{3} pi \( 4^2 + 2^2 + 4 cdot 4 cdot 2 \ \) ) cm³

B. \( \frac{1}{3} pi \( 4^2 + 2^2 + 4 cdot 4 cdot 2 \ \) ) cm³

C. \( \frac{1}{3} pi \( 4^2 + 2^2 + 4 cdot 4 cdot 2 \ \) ) cm³

D. \( \frac{1}{3} pi \( 4^2 + 2^2 + 4 cdot 4 cdot 2 \ \) ) cm³

Correct Answer: A

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Question 3

Determine the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).

Correct A. \( 2 left\( \frac{1 - 3^{10}}{1 - 3} \right \ \) )

B. \( 2 left\( \frac{1 - 3^{10}}{1 - 3} \right \ \) )

C. \( 2 left\( \frac{1 - 3^{10}}{1 - 3} \right \ \) )

D. \( 2 left\( \frac{1 - 3^{10}}{1 - 3} \right \ \) )

Correct Answer: A

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Question 4

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{-2x}{\( x^2 + 1 \)^2} )

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

Correct Answer: A

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Question 5

Solve the system of linear equations \( egin{cases} x + 2y = 6 \ 3x - 2y = -3 \end{cases} \).

Correct A. \( x = 3, y = 1.5 \)

B. \( x = 3, y = -1.5 \)

C. \( x = 3, y = 1.5 \)

D. \( x = 3, y = -1.5 \)

Correct Answer: A

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Question 6

In a random experiment, two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.5, what is the probability that both events occur?

Correct A. 0.2

B. 0.6

C. 0.8

D. 0.9

Correct Answer: A

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Question 7

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 8

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

A. x = π/4, 3π/4

B. x = π/4, 5π/4

Correct C. x = π/4, 3π/4, 5π/4

D. x = π/4, 3π/4, 5π/4, 7π/4

Correct Answer: C

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Question 9

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.68

Correct B. 0.84

C. 0.95

D. 0.99

Correct Answer: B

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Question 10

Solve the inequality [ x^3 - 6x^2 + 11x - 6 geq 0 ] for x.

A. x ≤ 1, x ≥ 2

B. x ≤ 1, 2 ≤ x ≤ 3

Correct C. x ≤ 1, 2 ≤ x ≤ 3, x ≥ 6

D. x ≤ 1, 2 ≤ x ≤ 3, x ≥ 6, x ≤ 7

Correct Answer: C

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Question 11

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

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

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

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

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

Correct Answer: A

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Question 12

Solve the system of linear equations u\sing the method of substitution: \( egin{cases} 2x + 3y = 7 \ x - 2y = -3 \end{cases} \).

Correct A. \( x = 2, y = 1 \)

B. \( x = -1, y = 2 \)

C. \( x = 1, y = 2 \)

D. \( x = 2, y = -1 \)

Correct Answer: A

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Question 13

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

Correct A. \( \frac{5}{3} \)

B. \( \frac{7}{3} \)

C. \( \frac{9}{3} \)

D. \( \frac{11}{3} \)

Correct Answer: A

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Question 14

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

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

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

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

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

Correct Answer: A

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Question 15

Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.

Correct A. \( 2 \sin x \cos x \)

B. \( 2 \sin x \cos^2 x \)

C. \( 2 \cos x \sin^2 x \)

D. \( 2 \sin^2 x \cos x \)

Correct Answer: A

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Question 16

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

Correct A. \( \frac{-x}{\( 1-x^2 \ \)^{3/2}} )

B. \( \frac{x}{\( 1-x^2 \ \)^{3/2}} )

C. \( \frac{1}{\( 1-x^2 \ \)^{3/2}} )

D. \( \frac{-1}{\( 1-x^2 \ \)^{3/2}} )

Correct Answer: A

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Question 17

In the diagram below, find the equation of the circle with center ( C(2,3) ) and radius ( 4 ).

Correct A. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )

B. \( x-2 \ \)^2 + \( y-3 \)^2 = 4 )

C. \( x-3 \ \)^2 + \( y-2 \)^2 = 16 )

D. \( x-3 \ \)^2 + \( y-2 \)^2 = 4 )

Correct Answer: A

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Question 18

Find the sum of the first 10 terms of the geometric series \( 2x^2 + 4x^3 + 8x^4 + ldots \).

Correct A. \( 2x^2 left\( \frac{1 - 2^{10} x^{10}}{1 - 2x} \right \ \) )

B. \( 2x^2 left\( \frac{1 - 2^{10} x^{10}}{1 + 2x} \right \ \) )

C. \( 2x^2 left\( \frac{1 - 2^{10} x^{10}}{1 - 2x} \right \ \) + 4x^3 left\( \frac{1 - 2^{10} x^{10}}{1 - 2x} \right \) )

D. \( 2x^2 left\( \frac{1 - 2^{10} x^{10}}{1 + 2x} \right \ \) + 4x^3 left\( \frac{1 - 2^{10} x^{10}}{1 + 2x} \right \) )

Correct Answer: A

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Question 19

Solve the inequality \( \log_2 \( x^2 + 1 \ \) > 3 ).

Correct A. \( x > \sqrt{7} \)

B. \( x < \sqrt{7} \)

C. \( x > -\sqrt{7} \)

D. \( x < -\sqrt{7} \)

Correct Answer: A

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Question 20

Find the mean deviation of the data set ( 2, 4, 6, 8, 10 ).

Correct A. \( \frac{20}{5} \)

B. \( \frac{40}{5} \)

C. \( \frac{60}{5} \)

D. \( \frac{80}{5} \)

Correct Answer: A

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Question 21

A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is 6.1 cm, calculate the 95% confidence interval for the mean height of all students in the university.

A. 169.4 cm, 181.6 cm

Correct B. 171.1 cm, 179.9 cm

C. 173.5 cm, 177.5 cm

D. 175.1 cm, 175.9 cm

Correct Answer: B

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Question 22

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. \( x + 3 \)^2 + \( y - 2 \)^2 = 16

D. \( x - 3 \)^2 + \( y + 2 \)^2 = 16

Correct Answer: A

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Question 23

A vector \mathbf{a} has a magnitude of 5 and makes an angle of 30° with the positive x-axis. Find the magnitude of the vector \mathbf{a} + \mathbf{b}, where \mathbf{b} is a unit vector in the direction of the negative y-axis.

A. 5.83

B. 6.07

Correct C. 6.35

D. 6.67

Correct Answer: C

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Question 24

Solve the equation \frac{1}{x + 1} + \frac{1}{x + 2} = \frac{3}{x + 3} for x.

A. x = -1

Correct B. x = -2

C. x = -3

D. x = -4

Correct Answer: B

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Question 25

A histogram is constructed with 5 classes of equal width. The first class has a frequency of 10, the second class has a frequency of 15, the third class has a frequency of 20, the fourth class has a frequency of 12, and the fifth class has a frequency of 8. Find the class width.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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