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POST UTME MADONNA UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME MADONNA UNIVERSITY 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

Evaluate the definite integral \( int_{0}^{2} \( 2x^2 + 3x - 4 \ \) dx )

Correct A. \( \frac{8}{3} + \frac{6}{2} - \frac{8}{2} \ \)

B. \( \frac{8}{3} + \frac{6}{2} + \frac{8}{2} \ \)

C. \( \frac{8}{3} - \frac{6}{2} - \frac{8}{2} \ \)

D. \( \frac{8}{3} - \frac{6}{2} + \frac{8}{2} \ \)

Correct Answer: A

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Question 2

Solve for ( x ) in the equation \( 2^x = 64 \)

A. \( x = 3 \ \)

Correct B. \( x = 4 \ \)

C. \( x = 5 \ \)

D. \( x = 6 \ \)

Correct Answer: B

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Question 3

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

Correct A. \( \frac{8}{3} \ \)

B. \( \frac{10}{3} \ \)

C. \( \frac{12}{3} \ \)

D. \( \frac{14}{3} \ \)

Correct Answer: A

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Question 4

Solve the system of equations \( 2x + 3y = 7 \) and \( x - 2y = -3 \)

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

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

C. \( x = 3, y = 4 \ \)

D. \( x = 4, y = 3 \ \)

Correct Answer: A

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Question 5

Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) )

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

B. \( y = 2x + 1 \ \)

C. \( y = 3x - 2 \ \)

D. \( y = 3x + 2 \ \)

Correct Answer: A

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Question 6

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

A. \( -2, -∞ \) ∪ (2, ∞)

B. \( -∞, -2 \) ∪ (2, ∞)

Correct C. \( -∞, -2 \) ∪ \( -2, 2 \) ∪ (2, ∞)

D. \( -∞, 2 \) ∪ (2, ∞)

Correct Answer: C

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Question 7

Find the equation of the circle with center \( C\( -2, 3 \ \) ) and radius \( r = 4 \).

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 system of linear equations \( egin{cases} x + 2y - 3z = 7 \ 2x - 3y + z = -3 \ 3x + y + 2z = 5 \end{cases} \).

Correct A. x = 1, y = 2, z = 3

B. x = 2, y = 1, z = 3

C. x = 3, y = 2, z = 1

D. x = 1, y = 3, z = 2

Correct Answer: A

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Question 9

Find the value of ( x ) in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 10

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

Correct A. \( y = \frac{1}{2}x + \frac{1}{2} \)

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

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

D. \( y = 2x + 1 \)

Correct Answer: A

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Question 11

Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).

Correct A. x^2 + y^2 - 6x - 4y + 12 = 0

B. x^2 + y^2 - 4x - 2y + 4 = 0

C. x^2 + y^2 - 2x - 6y + 9 = 0

D. x^2 + y^2 + 2x + 4y - 8 = 0

Correct Answer: A

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Question 12

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

Correct A. -\frac{1}{2} \cos 1 + \frac{1}{2} \cos 0

B. \frac{1}{2} \cos 1 - \frac{1}{2} \cos 0

C. \frac{1}{2} \sin 1 - \frac{1}{2} \sin 0

D. -\frac{1}{2} \sin 1 + \frac{1}{2} \sin 0

Correct Answer: A

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Question 13

Solve the inequality \frac{2x - 1}{x + 1} > 0.

Correct A. x < -1 \text{ or } x > \frac{1}{2}

B. x < -1 \text{ or } x < \frac{1}{2}

C. x > -1 \text{ or } x > \frac{1}{2}

D. x < -1 \text{ or } x < \frac{1}{2}

Correct Answer: A

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Question 14

Find the sum of the infinite geometric series \sum_{n=1}^\infty \frac{2}{3^n}.

Correct A. \frac{2}{3}

B. \frac{4}{3}

C. \frac{6}{3}

D. \frac{8}{3}

Correct Answer: A

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Question 15

A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?

A. \frac{1}{2}

Correct B. \frac{1}{3}

C. \frac{2}{3}

D. \frac{4}{5}

Correct Answer: B

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Question 16

Let A = \{1, 2, 3, 4, 5\} and B = \{2, 3, 5, 6, 7\}. Find the symmetric difference of A and B.

Correct A. \{1, 4, 6, 7\}

B. \{1, 4, 6, 7, 8\}

C. \{1, 4, 6, 7, 8, 9\}

D. \{1, 4, 6, 7, 8, 9, 10\}

Correct Answer: A

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Question 17

Find the sum of the first 5 terms of the arithmetic sequence 2, 5, 8, ...

A. 25

B. 30

C. 35

D. 40

Correct Answer: VIEW ANSWER

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Question 18

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

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

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

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

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

Correct Answer: C

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Question 19

A set of data has a mean of 25 and a s\tandard deviation of 3. If the data follows a normal distribution, what is the probability that a randomly selected value is between 20 and 30?

Correct A. 0.8413

B. 0.8413

C. 0.6827

D. 0.6827

Correct Answer: A

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Question 20

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

A. 2x^2\( 1 + 2 + 4 + ... + 512 \)

B. 2x^2\( 1 - 2 + 4 - ... + 512 \)

Correct C. 2x^2\( 1 + 2 + 4 + ... + 512 \)

D. 2x^2\( 1 - 2 + 4 - ... + 512 \)

Correct Answer: C

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Question 21

A vector ( vec{a} ) has a magnitude of 5 and makes an angle of 30° with the positive x-axis. Find the magnitude of the vector \( vec{a} + vec{b} \), where ( vec{b} ) is a vector with a magnitude of 3 and is perp\endicular to ( vec{a} ).

Correct A. 8

B. 6

C. 8

D. 6

Correct Answer: A

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Question 22

A random experiment has two indep\endent events, A and B. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. What is the probability that both events A and B occur?

Correct A. 0.24

B. 0.24

C. 0.24

D. 0.24

Correct Answer: A

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Question 23

Find the value of k such that the quadratic equation \( x^2 + kx + 16 = 0 \) has equal roots.

A. 4

B. 8

Correct C. -4

D. -8

Correct Answer: C

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Question 24

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

Correct A. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)

B. \left\( -\infty, -1 \right \) \cup \left\( 1, \infty \right \)

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

D. \left\( -\infty, -3 \right \) \cup \left\( 1, \infty \right \)

Correct Answer: A

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Question 25

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

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

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

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

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

Correct Answer: A

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