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POST UTME UNILAG 2022 Mathematics | Objective

Are you preparing for POST UTME UNILAG exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Determine the volume of the frustum of a cone with height 12 cm, lower base radius 6 cm, and upper base radius 4 cm.

A. 120π cm³

Correct B. 240π cm³

C. 360π cm³

D. 480π cm³

Correct Answer: B

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Question 2

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

A. 1792

B. 2046

Correct C. 2187

D. 2430

Correct Answer: C

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Question 3

A vector α has magnitude 5 and direction 60°. Find the magnitude of the vector 2α.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 4

Find the determinant of the matrix Θ = egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 5

A histogram represents the distribution of exam scores. If the mean score is 60 and the s\tandard deviation is 10, what is the probability that a randomly selected score is between 50 and 70?

A. 0.25

Correct B. 0.5

C. 0.75

D. 1

Correct Answer: B

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Question 6

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

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 7

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 8

A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first 5 terms.

A. 15

B. 30

C. 45

Correct D. 60

Correct Answer: D

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Question 9

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).

Correct A. 6x + 2

B. 6x - 2

C. 3x^2 + 2

D. 3x^2 - 2

Correct Answer: A

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Question 10

A set of numbers is defined as \( S = \{ 1, 2, 3, 4, 5 \} \ \). Find the number of subsets of S.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 11

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

A. \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

B. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

Correct C. \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

D. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

Correct Answer: C

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Question 12

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

Correct A. \frac{-5 + \sqrt{25 + 24}}{4}

B. \frac{-5 - \sqrt{25 + 24}}{4}

C. \frac{-5 + \sqrt{25 + 24}}{4}

D. \frac{-5 - \sqrt{25 + 24}}{4}

Correct Answer: A

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Question 13

Find the area of the triangle with vertices ( A(0, 0), B(2, 3), ) and ( C(4, 0) ).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 14

Solve the system of equations \( x + y = 2 \) and \( xy = 3 \).

Correct A. \left\( 1, 1 \right \)

B. \left\( -1, -1 \right \)

C. \left\( 1, -1 \right \)

D. \left\( -1, 1 \right \)

Correct Answer: A

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Question 15

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

Correct A. \left\( 2x \sin x + x^2 \cos x \right \)

B. \left\( 2x \sin x - x^2 \cos x \right \)

C. \left\( 2x \sin x + x^2 \cos x \right \)

D. \left\( 2x \sin x - x^2 \cos x \right \)

Correct Answer: A

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Question 16

Solve the inequality \( x^2 - 4x + 3 > 0 \) u\sing the quadratic formula.

Correct A. \left\( 1, 3 \right \)

B. \left\( -1, -3 \right \)

C. \left\( 1, -3 \right \)

D. \left\( -1, 3 \right \)

Correct Answer: A

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Question 17

Find the area of the circle with radius \( r = 4 \) cm.

Correct A. 50.24

B. 50.26

C. 50.28

D. 50.30

Correct Answer: A

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Question 18

Find the volume of the solid formed by revolving the region bounded by the parabola y = x^2, the x-axis, and the line x = 2 about the x-axis.

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 19

Solve the inequality \frac{x-2}{x+1} > 0.

Correct A. \( -\infty, -1 \) \cup \( 2, \infty \)

B. \( -\infty, -1 \) \cup \( 1, \infty \)

C. \( -\infty, 1 \) \cup \( 2, \infty \)

D. \( -\infty, 1 \) \cup \( 2, \infty \)

Correct Answer: A

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Question 20

Find the area of the region bounded by the curve y = x^3 - 6x^2 + 9x + 2, the x-axis, and the lines x = 0 and x = 3.

A. 18

B. 36

Correct C. 54

D. 72

Correct Answer: C

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Question 21

A circle with center (0, 0) and radius 4 is revolved about the x-axis. Find the volume of the solid formed.

Correct A. 256\pi

B. 128\pi

C. 64\pi

D. 32\pi

Correct Answer: A

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Question 22

Find the equation of the plane pas\sing through the points (1, 2, 3), (4, 5, 6), and (7, 8, 9).

Correct A. x - y + z = 0

B. x + y - z = 0

C. x - y + z = 0

D. x + y + z = 0

Correct Answer: A

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Question 23

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

Correct A. y = \frac{1}{2}x + 1

B. y = 2x - 1

C. y = -\frac{1}{2}x + 2

D. y = x + 2

Correct Answer: A

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Question 24

Solve the inequality \frac{x^2 - 4}{x + 2} > 0.

A. x < -2 \text{ or } x > 2

Correct B. x > -2 \text{ and } x < 2

C. x < -2 \text{ and } x > 2

D. x > -2 \text{ or } x < 2

Correct Answer: B

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Question 25

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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