Exam Body

Year

Subject

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POST UTME UNN 2023 Mathematics | Objective

Are you preparing for POST UTME UNN 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.

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Question 1

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 2

A circle passes through the points (2, 3) and (4, 5). Find the equation of the circle in the form \( x - h \)^2 + \( y - k \)^2 = r^2.

Correct A. \( x - 3 \)^2 + \( y - 4 \)^2 = 10

B. \( x - 2 \)^2 + \( y - 3 \)^2 = 5

C. \( x - 4 \)^2 + \( y - 5 \)^2 = 10

D. \( x - 3 \)^2 + \( y - 4 \)^2 = 5

Correct Answer: A

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Question 3

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

Correct A. x < -1 or x > \frac{3}{2}

B. x < -1 or x < \frac{3}{2}

C. x > -1 or x > \frac{3}{2}

D. x > -1 or x < \frac{3}{2}

Correct Answer: A

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Question 4

Find the area under the curve y = x^2 from x = 0 to x = 4.

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 5

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

Correct A. 0.24

B. 0.48

C. 0.64

D. 0.72

Correct Answer: A

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Question 6

Determine the value of \( \tan left\( \frac{pi}{4} - \frac{arc\tan(2 \ \)}{2} \right) ) u\sing trigonometric identities.

Correct A. \frac{1}{3}

B. \frac{2}{3}

C. \frac{1}{2}

D. \frac{2}{5}

Correct Answer: A

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Question 7

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

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

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

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

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

Correct Answer: B

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Question 8

A histogram represents the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a range of scores. The heights of the bars are 8, 12, 15, 10, and 5 units. Calculate the mean score of the class.

A. 70

B. 75

Correct C. 80

D. 85

Correct Answer: C

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Question 9

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

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 10

Find the volume of a rec\tangular prism with dimensions 5 cm, 6 cm, and 7 cm.

A. 210 cm^3

B. 240 cm^3

Correct C. 270 cm^3

D. 300 cm^3

Correct Answer: C

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Question 11

In the diagram below, a circle with center O and radius 6 cm is \tangent to the x-axis at point A. If the point P(8, 3) lies on the circle, find the area of the shaded region.

Correct A. 36π cm^2

B. 24π cm^2

C. 48π cm^2

D. 60π cm^2

Correct Answer: A

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Question 12

A random variable X has a probability distribution given by P\( X = 1 \) = 1/4, P\( X = 2 \) = 1/2, and P\( X = 3 \) = 1/4. Find the expected value of X.

A. 1.5

Correct B. 2.5

C. 3.5

D. 4.5

Correct Answer: B

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Question 13

Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 3.

A. 27

B. 30

Correct C. 33

D. 36

Correct Answer: C

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Question 14

A line passes through the points (2, 3) and (4, 5). Find the equation of the line in slope-intercept form.

Correct A. y = x + 1

B. y = x - 1

C. y = -x + 2

D. y = x + 2

Correct Answer: A

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Question 15

A histogram of the heights of 10 students is shown below. Find the mean height of the students.

A. 170 cm

Correct B. 175 cm

C. 180 cm

D. 185 cm

Correct Answer: B

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Question 16

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

Solve the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.

Correct A. \frac{-5 + \sqrt{109}}{4}

B. \frac{-5 - \sqrt{109}}{4}

C. \frac{5 + \sqrt{109}}{4}

D. \frac{5 - \sqrt{109}}{4}

Correct Answer: A

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Question 18

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

Correct A. y = 1x + 1

B. y = 1x - 1

C. y = -1x + 1

D. y = -1x - 1

Correct Answer: A

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Question 19

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

Correct A. x < 1 or x > 3

B. x > 1 or x < 3

C. x < 3 or x > 1

D. x > 3 or x < 1

Correct Answer: A

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Question 20

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 21

Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).

Correct A. \left\( x, \, y \right \) = \left\( 3, \, 1 \right \)

B. \left\( x, \, y \right \) = \left\( 1, \, 3 \right \)

C. \left\( x, \, y \right \) = \left\( 2, \, 2 \right \)

D. \left\( x, \, y \right \) = \left\( 4, \, 0 \right \)

Correct Answer: A

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Question 22

Find the derivative of the function ( f(x) = x^2 \sin x ) u\sing the product rule.

Correct A. 2x \sin x + x^2 \cos x

B. 2x \cos x - x^2 \sin x

C. 2x \sin x - x^2 \cos x

D. 2x \cos x + x^2 \sin x

Correct Answer: A

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Question 23

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the sum of the first 5 terms of the sequence.

Correct A. 2 + 7 + 17 + 37 + 77

B. 2 + 5 + 11 + 21 + 41

C. 1 + 3 + 7 + 15 + 31

D. 3 + 5 + 9 + 17 + 33

Correct Answer: A

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Question 24

A polynomial function ( f(x) ) has roots \( x = -2, x = 3, x = -1 \). If \( f\( -x \ \) = -6x^3 + 12x^2 - 9x + 2 ), find the value of ( f(2) ).

A. -12

Correct B. 12

C. -24

D. 24

Correct Answer: B

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Question 25

A solid rec\tangular prism has dimensions \( l = 6 \) cm, \( w = 4 \) cm, and \( h = 3 \) cm. Find the volume of the prism in cubic centimeters.

Correct A. 72

B. 96

C. 108

D. 120

Correct Answer: A

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