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POST UTME ACHIEVERS UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

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

Correct A. \(\frac{16\pi}{3}\)\)

B. \(\frac{32\pi}{3}\)\)

C. \(\frac{64\pi}{3}\)\)

D. \(\frac{128\pi}{3}\)\)

Correct Answer: A

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Question 2 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 85?

A. 0.1587

B. 0.3413

C. 0.4772

Correct D. 0.6915

Correct Answer: D

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Question 3 View Details

Find the area under the curve \(y = 2x^3 - 5x^2 + x + 1\) from \(x = 0\) to \(x = 2\).

A. \(\frac{23}{3}\)\)

Correct B. \(\frac{47}{6}\)\)

C. \(\frac{97}{12}\)\)

D. \(\frac{191}{15}\)\)

Correct Answer: B

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Question 4 View Details

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

A. 30

B. 60

Correct C. 90

D. 120

Correct Answer: C

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Question 5 View Details

A circle has a radius of 4 cm. Find the area of the circle.

A. 50.24

B. 100.48

C. 201.06

Correct D. 314.16

Correct Answer: D

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Question 6 View Details

A solid right circular cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone in cubic centimeters.

A. 256\pi

Correct B. 512\pi

C. 1024\pi

D. 2048\pi

Correct Answer: B

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Question 7 View Details

Find the area of the region bounded by the parabola (y = x\^2\), the x-axis, and the line \\((y = x^2\(x = 4\).

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 8 View Details

A vector \overrightarrow{a} has a magnitude of 6 units and makes an angle of 30° with the positive x-axis. Find the x and y components of \overrightarrow{a}.

Correct A. 3\hat{i} + 3\hat{j}

B. 6\hat{i} + 3\hat{j}

C. 3\hat{i} + 6\hat{j}

D. 6\hat{i} + 6\hat{j}

Correct Answer: A

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Question 9 View Details

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

Correct A. x < -1 or \(x > 3/2\)\)

B. \(x < 1\) or \(x > 3\)

C. x < -3 or \(x > 1\)

D. \(x < 1\) or \(x < 3\)

Correct Answer: A

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Question 10 View Details

A binary operation ast is defined as a \ast \(b = ab + 1\\(ast is defined as a ast\). Find the value of \(2 \ast 3\) \ast 4.

A. 25

Correct B. 26

C. 27

D. 28

Correct Answer: B

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Question 11 View Details

Find the equation of the line passing through the points (2, 3) and (4, 5).

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

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

C. \(y = x - 1\)

D. \(y = x + 1\)

Correct Answer: B

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Question 12 View Details

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

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

B. \(x = 2\), \(y = 0\)

C. \(x = 0\), \(y = 2\)

D. \(x = 1\), \(y = 0\)

Correct Answer: A

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Question 13 View Details

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 2).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 14 View Details

Solve the quadratic equation: \\((x^2 + 5x + 6\)\(= 0.\)\)

Correct A. \(x = -2\),\(x = -3\)

B. \(x = -1\),\(x = -6\)

C. \(x = 2\), \(x = 3\)

D. \(x = 1\), \(x = 6\)

Correct Answer: A

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Question 15 View Details

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 + \(y - 3\)^\(2 = 4\)

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

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

Correct Answer: A

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Question 16 View Details

Solve the system of linear equations: \begin{align*} x + y &= 2 \ x - y &= 1 \end{align*}

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

Correct B. \(x = 2\), \(y = 0\)

C. \(x = 0\), \(y = 2\)

D. \(x = 1\), \(y = 0\)

Correct Answer: B

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Question 17 View Details

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 2).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 18 View Details

Solve the quadratic equation: \\((x^2 + 5x + 6\)\(= 0.\)\)

A. \(x = -2\),\(x = -3\)

B. \(x = -1\),\(x = -6\)

C. \(x = 2\), \(x = 3\)

D. \(x = 1\), \(x = 6\)

Correct Answer: VIEW ANSWER

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Question 19 View Details

Let X be a random variable with probability density function (pdf) given by f(x) = (\(\frac{1}{2}\\()e^{-\)|x|}\) for -∞\(< x\)< ∞. Find the probability that X lies in the interval \\((frac{1}{2}e^{-|x|}\(-2, 3\).

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 20 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9} > 0\).

Correct A. \(-∞, -3\) ∪ (2, ∞)

B. \(-∞, -3\) ∪ (2, 3)

C. \(-∞, -3\) ∪ (3, ∞)

D. \(-∞, 3\) ∪ (4, ∞)

Correct Answer: A

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Question 21 View Details

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

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 22 View Details

Let A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}. Find the symmetric difference of A and B.

Correct A. {1, 2, 3}

B. {4, 5, 6, 7, 8}

C. {1, 2, 3, 4, 5}

D. {6, 7, 8}

Correct Answer: A

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Question 23 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. \(\frac{1}{x^2 + 1\) \ ^2}\)\))

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

Correct Answer: A

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Question 24 View Details

Solve the equation \(\log_{10} x^2 \\)\(= 4).\)

A. 2

B. 4

Correct C. 10

D. 20

Correct Answer: C

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Question 25 View Details

A. 0.6

Correct B. 0.7

C. 0.8

D. 0.9

Correct Answer: B

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