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POST UTME RHEMA UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details

Determine the value of the definite integral \(int_{0}^{2} 2x^2 + 3x - 4 \\) dx ).

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 2 View Details

A histogram is constructed from the following data: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23. Determine the class width.

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 3 View Details

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

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 4 View Details

A matrix A is given by \(A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \\). Find the determinant of A.

Correct A. -2

B. 0

C. 2

D. 4

Correct Answer: A

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Question 5 View Details

A circle has an equation of the form \(x - h \\)^2 + \(y - k\)^\(2 = r\^2\) \). If the center of the circle is at (3, 4) and the radius is 5, determine the equation of the circle.

Correct A. \(x - 3\)^2 + \(y - 4\)^\(2 = 25\)

B. \(x - 4\)^2 + \(y - 3\)^\(2 = 25\)

C. \(x - 3\)^2 + \(y - 4\)^\(2 = 9\)

D. \(x - 4\)^2 + \(y - 3\)^\(2 = 9\)

Correct Answer: A

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Question 6 View Details

In the diagram below, the graph of (y = \(1x \\) ) is shown. If the graph is reflected about the line \\((y =\)1x \(y = x\), what is the equation of the new graph?

Correct A. \(y =\)\sin^\(-1\)(x)

B. \(y =\)\cos^\(-1\)(x)

C. \(y =\)\tan^\(-1\)(x)

D. \(y = \cot\)^\(-1\)(x)

Correct Answer: A

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Question 7 View Details

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

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 8 View Details

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

A. 2

Correct B. 4

C. 8

D. 16

Correct Answer: B

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Question 9 View Details

In the diagram below, the circle has a radius of 5 units. If the line segment AB is a chord of the circle, what is the length of AB?

A. 5\sqrt{3}

Correct B. 10\sqrt{3}

C. 15\sqrt{3}

D. 20\sqrt{3}

Correct Answer: B

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Question 10 View Details

Find the area of the triangle with vertices A(2, 3), B(4, 5), and C(6, 7).

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 11 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

B. 32\pi

Correct C. 48\pi

D. 64\pi

Correct Answer: C

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Question 12 View Details

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 13 View Details

A survey of 100 students found that 60 students preferred pizza, 30 students preferred burgers, and 10 students preferred both. What is the probability that a randomly selected student prefers pizza or burgers?

A. 0.7

Correct B. 0.75

C. 0.8

D. 0.85

Correct Answer: B

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Question 14 View Details

Find the surface area of the sphere with radius 5 cm.

A. 100\pi

B. 200\pi

Correct C. 300\pi

D. 400\pi

Correct Answer: C

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Question 15 View Details

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 16 View Details

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 17 View Details

Solve for x in the equation: \(\log_{2} x^2 \\)\(= 4 ).\)

A. 4

B. 8

Correct C. 16

D. 32

Correct Answer: C

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Question 18 View Details

A set of 5 consecutive integers has a median of 10. What is the sum of the integers?

A. 50

B. 100

Correct C. 150

D. 200

Correct Answer: C

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Question 19 View Details

In a geometric sequence, the first term is 2 and the common ratio is 3. Find the 5th term.

A. 486

B. 729

C. 2187

Correct D. 6561

Correct Answer: D

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Question 20 View Details

Solve the inequality: \(x^2 + 4x + 4 > 0\).

Correct A. \(-\infty, -2\) \cup \(2, \infty\)

B. \(-\infty, -4\) \cup \(4, \infty\)

C. \(-\infty, 2\) \cup \(4, \infty\)

D. \(-\infty, -2\) \cup \(2, \infty\)

Correct Answer: A

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Question 21 View Details

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

Correct A. 24

B. 32

C. 48

D. 64

Correct Answer: A

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Question 22 View Details

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

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 23 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 + \(y - 3\)^\(2 = 9\)

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

Correct Answer: A

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Question 24 View Details

Solve the inequality [ \(2x - 5 > 3x + 2\) ].

Correct A. \(x < -1\)

B. \(x > -1\)

C. \(x < 1\)

D. \(x > 1\)

Correct Answer: A

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Question 25 View Details

Find the value of [ x ] in the equation [ \log_{10} \(x^2\)\(= 4\)].

A. 2

B. 4

C. 8

Correct D. 16

Correct Answer: D

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