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POST UTME IMS U 2021 Mathematics | Objective

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Question 1 View Details

In the diagram below, if the volume of the rectangular 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 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 3 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the equation of the line passing 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 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{\(x^2 + 1}}\)\) ) using 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\(\sqrt{x}\)}\) ) using 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 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\) using 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 View Details

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 View Details

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 View Details

Find the derivative of the function ( f(x) = \(x^2\) \sin x ) using 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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