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POST UTME IMS U 2022 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 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Let X be a random variable with probability density function ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.

A. \( \frac{1}{2} \)

Correct B. \( \frac{3}{4} \)

C. \( \frac{5}{8} \)

D. \( \frac{7}{16} \)

Correct Answer: B

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Question 2

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

A. \( 72 \text{ cm}^3 \)

Correct B. \( 96 \text{ cm}^3 \)

C. \( 108 \text{ cm}^3 \)

D. \( 120 \text{ cm}^3 \)

Correct Answer: B

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Question 3

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

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

B. \( x < -2 \text{ or } x > 0 \)

C. \( x > -2 \text{ or } x < 0 \)

D. \( x > -2 \text{ and } x < 0 \)

Correct Answer: A

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Question 4

A circle has a radius of 4 cm. Find the area of the circle.

A. \( 16 pi \text{ cm}^2 \)

B. \( 32 pi \text{ cm}^2 \)

Correct C. \( 64 pi \text{ cm}^2 \)

D. \( 128 pi \text{ cm}^2 \)

Correct Answer: C

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Question 5

A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

A. \( 8 \text{ cm} \)

Correct B. \( 12 \text{ cm} \)

C. \( 14 \text{ cm} \)

D. \( 16 \text{ cm} \)

Correct Answer: B

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Question 6

A random variable X has a probability distribution given by P\( X = 1 \) = 0.4, P\( X = 2 \) = 0.3, P\( X = 3 \) = 0.2, and P\( X = 4 \) = 0.1. If two indep\endent random variables X and Y have the same probability distribution, what is the probability that X + Y = 5?

A. 0.1

B. 0.2

Correct C. 0.3

D. 0.4

Correct Answer: C

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Question 7

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. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 8

Solve the equation \frac{x^2 - 4}{x^2 - 2x - 3} = \frac{x + 2}{x - 3}.

A. x = -1

Correct B. x = 1

C. x = 2

D. x = 3

Correct Answer: B

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Question 9

A set A has 5 elements. If a set B is formed by selecting 3 elements from set A, how many different subsets of B can be formed?

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 10

Find the sum of the infinite geometric series \sum_{n=1}^\infty \frac{2}{3^n}.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 11

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

A. 0.5

B. 1

Correct C. 1.5

D. 2

Correct Answer: C

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Question 12

A circle with center ( C(2, 3) ) and radius \( r = 4 \) has a chord ( AB ) of length ( 6 ). Find the dis\tance from the center to the chord.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 13

A histogram with 5 classes has the following frequencies: 2, 3, 5, 7, 8. Find the mean of the data.

A. 4

B. 5

Correct C. 6

D. 7

Correct Answer: C

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Question 14

Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).

A. 0

Correct B. π/2

C. π

D. 3π/2

Correct Answer: B

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Question 15

A line passes through the points ( (1, 2) ) and ( (3, 4) ). Find the equation of the line in slope-intercept form.

Correct A. y = x + 1

B. y = x - 1

C. y = -x + 3

D. y = x - 2

Correct Answer: A

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Question 16

Determine the value of x in the equation \( \tan\( x \ \) = \frac{1}{\sqrt{3}} ) if \( \sin\( x \ \) = \frac{1}{2} ).

Correct A. \( \frac{pi}{6} \)

B. \( \frac{pi}{3} \)

C. \( \frac{pi}{4} \)

D. \( \frac{pi}{2} \)

Correct Answer: A

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Question 17

Find the area under the curve \( y = x^2 - 4x + 3 \) from \( x = 1 \) to \( x = 3 \).

Correct A. ( 4 )

B. ( 6 )

C. ( 8 )

D. ( 10 )

Correct Answer: A

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Question 18

A die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. \( \frac{1}{6} \)

Correct B. \( \frac{1}{3} \)

C. \( \frac{1}{2} \)

D. \( \frac{2}{3} \)

Correct Answer: B

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Question 19

Solve the differential equation \( \frac{dy}{dx} = \frac{y}{x} \) with the initial condition ( y(1) = 2 ).

A. \( y = 2x \)

B. \( y = x^2 \)

Correct C. \( y = \frac{2}{x} \)

D. \( y = x^2 + 2 \)

Correct Answer: C

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Question 20

A circle has a radius of 4 cm. What is the area of the circle?

Correct A. ( 16pi )

B. ( 32pi )

C. ( 64pi )

D. ( 128pi )

Correct Answer: A

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Question 21

Find the value of x in the quadratic equation \( x^2 + 5x + 6 = 0 \).

A. 1

Correct B. -2

C. -3

D. 4

Correct Answer: B

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Question 22

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 23

Find the derivative of the function ( f(x) = x^3 - 2x^2 + 3x - 1 ).

Correct A. 3x^2 - 4x + 3

B. 3x^2 - 4x + 1

C. 3x^2 - 4x - 1

D. 3x^2 - 4x - 3

Correct Answer: A

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Question 24

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).

A. x = 0

B. x = 90

C. x = 180

Correct D. x = 270

Correct Answer: D

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Question 25

Find the sum of the first 5 terms of the arithmetic progression 2, 5, 8, ...

A. 25

Correct B. 30

C. 35

D. 40

Correct Answer: B

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