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POST UTME MADONNA UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the equation of the line passing 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 View Details

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. \(-∞, -2\) \cup \(-2, 2\)\)∪ (2, ∞)

D. \(-∞, 2\) ∪ (2, ∞)

Correct Answer: C

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Question 7 View Details

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 View Details

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 View Details

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 View Details

Find the equation of the line passing 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 View Details

Find the equation of the circle passing 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Let ( f(x) = \(\frac{x^2 - 4}{x - 2}\)\)\) ). Find the derivative of ( f(x) ) using 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 View Details

A set of data has a mean of 25 and a standard 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 View Details

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 View Details

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 perpendicular to ( vec{a} ).

Correct A. 8

B. 6

C. 8

D. 6

Correct Answer: A

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Question 22 View Details

A random experiment has two independent 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 View Details

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 View Details

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 View Details

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