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POST UTME PAN-ATLANTIC UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

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

Correct A. \(\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4\)

B. \(\frac{1}{2} \times 4^2 + 3 \times 4 - 2\)

C. \(\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2\)

D. \(\frac{1}{2} \times 4^3 + 3 \times 4 - 2 \times 4\)

Correct Answer: A

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Question 2 View Details

Solve for ( x ) in the equation \(2x^2 + 5x - 3 = 0\).

Correct A. \(x = \frac{-5 \pm \sqrt{25 + 24}}{4}\)

B. \(x = \frac{-5 \pm \sqrt{25 - 24}}{4}\)

C. \(x = \frac{-5 \pm \sqrt{25 + 24}}{2}\)

D. \(x = \frac{-5 \pm \sqrt{25 - 24}}{2}\)

Correct Answer: A

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Question 3 View Details

Find the value of \(\log_{10} x^2 \\) ) given that \(\log_{10} x \\)\(= 2 ).\)

Correct A. ( 4 )

B. ( 2 )

C. ( 8 )

D. ( 16 )

Correct Answer: A

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Question 4 View Details

A circle with center ( (0, 0) ) and radius ( 4 ) has a chord of length ( 6 ). Find the distance from the center to the chord.

Correct A. \(2 \sqrt{3}\)

B. \(4 \sqrt{3}\)

C. \(6 \sqrt{3}\)

D. \(8 \sqrt{3}\)

Correct Answer: A

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Question 5 View Details

A sequence is defined by \(a_n = 2n + 1\). Find the sum of the first ( 5 ) terms.

A. ( 15 )

B. ( 25 )

C. ( 35 )

Correct D. ( 45 )

Correct Answer: D

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Question 6 View Details

Let X and Y be independent random variables with probability density functions f_\(X(x) = 2x\), \(0 < x\)\(< 1\), and f_\(Y(y) =\)\(3y^2\),\((0 < y\)\) < 1. Find the probability that \(X + Y < 1\\((0 < y) < 1. Find the probability that\).

A. \(1/4\)

Correct B. \(1/2\)

C. \(3/4\)

D. 1

Correct Answer: B

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Question 7 View Details

Find the derivative of the function f(x) = \(2x^3 + 5x^2 - 3x + 1\) / \(x^2 + 2x - 1\) using the quotient rule.

Correct A. \(\frac{6x^2 + 10x - 3}{\) \(x^2 + 2x - 1\) ^2}\)\)

B. \(\frac{6x^2 + 10x - 3}{\) \(x^2 + 2x - 1\) ^2}\)\) + 1

C. \(\frac{6x^2 + 10x - 3}{\) \(x^2 + 2x - 1\) ^2}\)\) - 1

D. \(\frac{6x^2 + 10x - 3}{\) \(x^2 + 2x - 1\) ^2}\)\) + 2

Correct Answer: A

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Question 8 View Details

A circle with center (2, 3) and radius 4 passes through the point (1, 1). Find the equation of the circle.

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

B. \(x - 1\)^2 + \(y - 1\)^\(2 = 16\)

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

D. \(x - 1\)^2 + \(y - 1\)^\(2 = 25\)

Correct Answer: A

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Question 9 View Details

Find the determinant of the matrix \(\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 10 View Details

A line passes through the points (1, 2) and (3, 4). Find the equation of the line.

Correct A. \(y = 2x\)

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

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

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

Correct Answer: A

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Question 11 View Details

Find the sum of the first 10 terms of the geometric series 4, 12, 36, ...

A. 1,048,576

Correct B. 4,194,304

C. 8,388,608

D. 16,777,216

Correct Answer: B

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Question 12 View Details

A histogram of exam scores has a mean of 70 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 80?

A. 0.135

B. 0.341

C. 0.674

Correct D. 0.954

Correct Answer: D

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Question 13 View Details

Find the volume of the solid formed by rotating the region bounded by the curves \(y = x\^2\) and \(y = 4 - x\^2\) about the x-axis.

A. 32\pi

B. 64\pi

C. 128\pi

Correct D. 256\pi

Correct Answer: D

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Question 14 View Details

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

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

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

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

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

Correct Answer: A

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Question 15 View Details

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

Correct A. \(1/2\)

B. \(1/3\)

C. \(2/5\)

D. \(3/8\)

Correct Answer: A

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Question 16 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pi \(cm^3\)

Correct B. 48\pi \(cm^3\)

C. 96\pi \(cm^3\)

D. 192\pi \(cm^3\)

Correct Answer: B

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Question 17 View Details

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

Correct A. \begin{pmatrix} 1 \ 2 \ -1 \end{pmatrix}

B. \begin{pmatrix} 2 \ -1 \ 3 \end{pmatrix}

C. \begin{pmatrix} 3 \ 4 \ -2 \end{pmatrix}

D. \begin{pmatrix} 5 \ 6 \ -3 \end{pmatrix}

Correct Answer: A

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Question 18 View Details

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

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 19 View Details

A binary operation (*\) on the set \{0, 1\\((*) on the set \} is defined as a * b = begin{cases} 1 & \text{if} \(a = 0\\(begin{cases} 1 & text{if}\) \text{ and } \(b = 1\) \ 0 & text{otherwise} \end{cases} Find the value of \(1 * 0\\(text{otherwise} end{cases} Find the value of\) * \(0 * 1\)\)

A. 0

Correct B. 1

C. 10

D. 11

Correct Answer: B

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Question 20 View Details

Find the volume of the sphere with radius 4 cm.

Correct A. 268.08 \(cm^3\)

B. 268.08 \(cm^3\)

C. 268.08 \(cm^3\)

D. 268.08 \(cm^3\)

Correct Answer: A

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Question 21 View Details

Find the sum of the infinite geometric series \(sum_{n = 1}^{\infty} \frac{1}{2^n}\) using the formula \(S = \frac{a}{1 - r}\), where (a) is the first term and (r) is the common ratio.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 22 View Details

Solve the inequality \(|x - 2| > 3\).

Correct A. -\(5 < x\) < -1 or \(x > 5\)

B. -\(5 < x\) < 1 or \(x > 5\)

C. -\(5 < x\)\(< 5\)

D. -\(5 < x\)\(< 1\)

Correct Answer: A

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Question 23 View Details

Find the area under the curve \(y = x^2 + 2x + 1\) from \(x = 0\) to \(x = 2\).

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 24 View Details

Solve the equation \(x^3 - 2x^2 - 5x + 6 = 0\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 25 View Details

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

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

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

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

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

Correct Answer: A

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