Exam Body

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POST UTME IMS U 2021 Mathematics | Objective

Are you preparing for POST UTME IMS U exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

In the diagram below, if the volume of the rec\tangular prism is 240 cm³, and the area of the base is 12 cm², what is the height of the prism?

A. 6 cm

Correct B. 8 cm

C. 10 cm

D. 12 cm

Correct Answer: B

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Question 2

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 3

In the circuit below, if the voltage across the 2 Ω resistor is 12 V, what is the current through the 4 Ω resistor?

A. 1 A

Correct B. 2 A

C. 3 A

D. 4 A

Correct Answer: B

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Question 4

Find the sum of the first 10 terms of the geometric series \( 2x^2 + 4x^4 + 8x^6 + ldots \).

A. 1023

B. 1024

Correct C. 1025

D. 1026

Correct Answer: C

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Question 5

In the diagram below, if the area of the triangle is 24 cm², and the base is 8 cm, what is the height of the triangle?

A. 3 cm

B. 4 cm

Correct C. 6 cm

D. 8 cm

Correct Answer: C

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Question 6

Find the value of 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 7

Solve for y in the equation \( 2y^2 + 5y - 3 = 0 \).

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 8

Find the volume of the cylinder with radius 4 cm and height 10 cm.

A. 400\pi

Correct B. 800\pi

C. 1600\pi

D. 3200\pi

Correct Answer: B

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Question 9

Solve the system of equations \( x + y = 2 \) and \( 2x - 3y = - 5 \).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 10

Find the area of the triangle with base 5 cm and height 6 cm.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 11

Solve for x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \).

A. \( x = -10 \)

B. \( x = 3 \)

Correct C. \( x = -3 \)

D. \( x = 10 \)

Correct Answer: C

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Question 12

Find the sum of the first 10 terms of the geometric sequence ( 2, 6, 18, 54, ... ).

Correct A. ( 10494 )

B. ( 10496 )

C. ( 10498 )

D. ( 10500 )

Correct Answer: A

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Question 13

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

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

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

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

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

Correct Answer: A

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Question 14

Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).

Correct A. ( 1 )

B. \( -1 \)

C. ( 0 )

D. ( 2 )

Correct Answer: A

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Question 15

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

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

B. \( y = 2x + 1 \)

C. \( y = x + 2 \)

D. \( y = x - 2 \)

Correct Answer: A

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

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

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

C. \( x < -\frac{3}{2} \) or \( x < \frac{1}{2} \)

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

Correct Answer: A

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Question 18

Find the area of the triangle with vertices ( A(0, 0) ), ( B(2, 0) ), and ( C(1, 3) ).

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 19

Find the sum of the first 5 terms of the geometric series with first term \( a = 2 \) and common ratio \( r = \frac{1}{2} \).

Correct A. \frac{31}{16}

B. \frac{63}{32}

C. \frac{127}{64}

D. \frac{255}{128}

Correct Answer: A

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Question 20

Solve the system of equations \( x + y = 2 \) and \( xy = 1 \).

Correct A. \( x = 1, y = 1 \)

B. \( x = 1, y = -1 \)

C. \( x = -1, y = 1 \)

D. \( x = -1, y = -1 \)

Correct Answer: A

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Question 21

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.

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

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

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

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

Correct Answer: A

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Question 22

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

A. \left\( -\frac{5}{4}, \frac{3}{2} \right \)

B. \left\( -\frac{3}{2}, \frac{5}{4} \right \)

Correct C. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{5}{4}, \infty \right \)

D. \left\( -\infty, \frac{5}{4} \right \) \cup \left\( -\frac{3}{2}, \infty \right \)

Correct Answer: C

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Question 23

Find the value of ( x ) in the equation \( \sin^2 x + \cos^2 x = 1 \).

Correct A. \frac{\pi}{4}

B. \frac{3\pi}{4}

C. \frac{5\pi}{4}

D. \frac{7\pi}{4}

Correct Answer: A

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Question 24

Solve the system of equations \( x + y = 2 \) and \( x - y = 1 \).

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 25

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

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

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

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

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

Correct Answer: A

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