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POST UTME MOUNTAIN TOP UNIVERSITY 2025 Mathematics | Objective

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Question 1 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. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 2 View Details

A particle moves along the curve (y = x² + 2x + 1\). Find the area under the curve between \(x = 0\\((y = x² + 2x + 1). Find the area under the curve between\) and \(x = 2\).

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 3 View Details

Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, find P(\(A \cap B\)).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 4 View Details

Solve the quadratic equation x² + \(5x + 6 = 0\).

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 5 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. \(x + 2\)² + \(y + 3\)\(² = 16\)

D. \(x + 2\)² + \(y + 3\)\(² = 4\)

Correct Answer: A

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Question 6 View Details

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 7 View Details

A circle with center ( C(2, 3) ) and radius 4 passes through the point ( P(6, 5) ). Find the equation of the circle.

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

B. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 20\) )

C. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 24\) )

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 28\) )

Correct Answer: A

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Question 8 View Details

Two events ( A ) and ( B ) are independent. If ( P(A) = 0.3 ) and ( P(B) = 0.4 ), find \(P A \cap B \\) ).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 9 View Details

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

Correct A. \(x = \frac{\pi}{4} \\) or \(x = \frac{5\pi}{4} \\)

B. \(x = \frac{\pi}{2} \\) or \(x = \frac{3\pi}{2} \\)

C. \(x = \frac{\pi}{4} \\) or \(x = \frac{3\pi}{4} \\)

D. \(x = \frac{\pi}{2} \\) or \(x = \frac{5\pi}{2} \\)

Correct Answer: A

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Question 10 View Details

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

A. 0

Correct B. 10

C. 20

D. 30

Correct Answer: B

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Question 11 View Details

Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 1 \ -2 end{pmatrix}\). Find the vector \(\\(end{pmatrix}). Find the vector \mathbf{a} \times \mathbf{b}\) using the cross product formula.

Correct A. \(egin{pmatrix} 6 \ -4 \end{pmatrix}\)

B. \(egin{pmatrix} 4 \ -6 \end{pmatrix}\)

C. \(egin{pmatrix} 3 \ -2 \end{pmatrix}\)

D. \(egin{pmatrix} 2 \ -3 \end{pmatrix}\)

Correct Answer: A

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Question 12 View Details

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

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

Correct Answer: A

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Question 13 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.

Correct A. 30

B. 50

C. 60

D. 70

Correct Answer: A

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Question 14 View Details

Simplify the expression \(\frac{1}{2} \times \frac{3}{4}\) using binary operations.

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

B. \(\frac{1}{8}\)

C. \(\frac{3}{4}\)

D. \(\frac{1}{4}\)

Correct Answer: A

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Question 15 View Details

Find the surface area of a sphere with a radius of 4 cm.

Correct A. 201.06

B. 202.06

C. 203.06

D. 204.06

Correct Answer: A

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Question 16 View Details

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

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

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

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

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

Correct Answer: A

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Question 17 View Details

A set ( A ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( A ) that contain exactly two elements.

A. 6

Correct B. 10

C. 12

D. 15

Correct Answer: B

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Question 18 View Details

The first five terms of a geometric sequence are ( 2, 6, 18, 54, 162 ). Find the common ratio.

Correct A. 3

B. 4

C. 5

D. 6

Correct Answer: A

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Question 19 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the highest score is 95, find the lowest score.

A. 55

B. 60

C. 65

Correct D. 70

Correct Answer: D

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Question 20 View Details

A number is divisible by 3 if the sum of its digits is divisible by 3. Find the smallest number greater than 1000 that is divisible by 3.

Correct A. 1002

B. 1005

C. 1008

D. 1011

Correct Answer: A

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Question 21 View Details

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

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

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

C. \(y = x + 2\)

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

Correct Answer: A

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Question 22 View Details

A coin is tossed 5 times. What is the probability that exactly 3 heads appear?

A. \(1/32\)

Correct B. \(5/32\)

C. \(10/32\)

D. \(15/32\)

Correct Answer: B

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Question 23 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\).

Correct A. \(x = -2\)

B. \(x = 2\)

C. \(x = -1\)

D. \(x = 1\)

Correct Answer: A

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Question 24 View Details

Find the mean of the following data set: 2, 4, 6, 8, 10.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 25 View Details

A set of numbers has a mean of 10 and a standard deviation of 2. What is the probability that a randomly selected number from this set is greater than 12?

Correct A. 0.25

B. 0.5

C. 0.75

D. 1

Correct Answer: A

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