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POST UTME IMS U 2020 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 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the derivative of the function ( 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 2

Solve the inequality $ 2^x > 3^x $ for ( x ).

Correct A. $ x < -1 $

B. $ x > -1 $

C. $ x < 1 $

D. $ x > 1 $

Correct Answer: A

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Question 3

A matrix ( A ) is given by $ A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} $. Find the determinant of ( A ).

A. ( 2 )

B. $ -2 $

Correct C. ( 0 )

D. ( 1 )

Correct Answer: C

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Question 4

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

A. ( 15 )

B. ( 20 )

Correct C. ( 25 )

D. ( 30 )

Correct Answer: C

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Question 5

A set ( S ) is defined as $ S = { x | x in mathbb{R}, x > 0 } $. Find the complement of ( S ).

Correct A. $ { x | x in mathbb{R}, x leq 0 } $

B. $ { x | x in mathbb{R}, x geq 0 } $

C. $ { x | x in mathbb{R}, x < 0 } $

D. $ { x | x in mathbb{R}, x > 1 } $

Correct Answer: A

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Question 6

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. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 7

Solve the inequality $ x^2 + 4x - 5 > 0 $.

Correct A. $ x < -5 $ or $ x > 1 $

B. $ x < -5 $ or $ x < 1 $

C. $ x > -5 $ or $ x > 1 $

D. $ x < -5 $ or $ x = 1 $

Correct Answer: A

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Question 8

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 = 16 )

C. $ x + 2 \ $^2 + $ y + 3 $^2 = 16 )

D. $ x - 2 \ $^2 + $ y - 3 $^2 = 16 )

Correct Answer: A

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Question 9

A particle moves along the curve $ y = x^2 $ with a velocity of 2 m/s. Find the acceleration at the point where $ x = 2 $.

A. 4 m/s²

Correct B. 8 m/s²

C. 12 m/s²

D. 16 m/s²

Correct Answer: B

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Question 10

Find the area under the curve $ y = x^3 - 6x^2 + 9x + 2 $ from $ x = 0 $ to $ x = 4 $.

A. 128

Correct B. 192

C. 256

D. 320

Correct Answer: B

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Question 11

Determine the value of $x$ in the equation $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ 5 \end{bmatrix} = \begin{bmatrix} 3 \ 11 \end{bmatrix}$

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 12

A particle moves in a straight line with its position given by $s(t) = 2t^3 - 5t^2 + 3t + 1$. Find the velocity of the particle at $t = 2$ seconds.

A. -14

B. -10

Correct C. 10

D. 14

Correct Answer: C

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Question 13

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. 1/2

Correct B. 2/5

C. 3/8

D. 1/3

Correct Answer: B

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Question 14

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 15

Find the surface area of the sphere with radius $r = 4$ cm.

A. 32π

Correct B. 64π

C. 128π

D. 256π

Correct Answer: B

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Question 16

In a certain number base, the value of the digit 5 is represented as $ overline{1011}_5 $. What is the decimal equivalent of this number?

A. 21

Correct B. 25

C. 31

D. 35

Correct Answer: B

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Question 17

Solve for ( x ) in the equation $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} $.

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 18

Find the equation of the circle with center ( (2, 3) ) and radius 4.

Correct A. $ x - 2 \ $^2 + $ y - 3 $^2 = 16 )

B. $ x - 3 \ $^2 + $ y - 2 $^2 = 16 )

C. $ x - 4 \ $^2 + $ y - 3 $^2 = 16 )

D. $ x - 2 \ $^2 + $ y - 4 $^2 = 16 )

Correct Answer: A

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Question 19

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.

Correct A. 72

B. 80

C. 90

D. 96

Correct Answer: A

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Question 20

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

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 21

Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].

A. 0

B. 1

C. 2

Correct D. 3

Correct Answer: D

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Question 22

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

Correct A. 1/2

B. 2/3

C. 3/5

D. 4/7

Correct Answer: A

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Question 23

Solve for x in the equation [ x^2 + 4x + 4 = 0 ].

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 24

Find the value of [ \log_{10} $ x^2 $ = 4 ].

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 25

In the diagram below, what is the value of x?

A. 30

Correct B. 60

C. 90

D. 120

Correct Answer: B

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