Exam Body

Year

Subject

Paper Type

POST UTME RHEMA UNIVERSITY 2023 Mathematics | Objective

Are you preparing for POST UTME RHEMA UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

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

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

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

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

In the diagram below, the graph of \( y = \sin\( x \ \) ) is shown. If the graph is reflected about the line \( y = x \), 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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