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POST UTME IMS U 2024 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 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

Correct A. 0

B. 1

C. π/2

D. π

Correct Answer: A

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Question 2

Solve for y in the equation $ y = \frac{1}{2} left\( x + \frac{1}{x} \right \ $ ).

A. x

Correct B. x^2

C. x^3

D. x^4

Correct Answer: B

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Question 3

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

A. 0

B. 1

Correct C. 2

D. 3

Correct Answer: C

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Question 4

A water \tank has a height of 10 meters and a base radius of 5 meters. Find the volume of water in the \tank.

A. 100π

B. 200π

Correct C. 300π

D. 400π

Correct Answer: C

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Question 5

Solve the inequality $ 2x^2 + 5x - 3 > 0 $.

Correct A. $ -∞, -1 $ ∪ (3, ∞)

B. $ -∞, -3 $ ∪ (1, ∞)

C. $ -∞, -2 $ ∪ (2, ∞)

D. $ -∞, -4 $ ∪ (4, ∞)

Correct Answer: A

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Question 6

Find the volume of the solid formed by rotating the region bounded by $y=x^2$, $y=0$, and $x=2$ about the x-axis.

Correct A. $ \frac{32}{3} pi $

B. ( 16 pi )

C. ( 32 pi )

D. ( 64 pi )

Correct Answer: A

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Question 7

If $f(x) = \frac{1}{x^2+1}$, find $f'(x)$ u\sing the chain rule.

Correct A. $ \frac{-2x}{\( x^2+1 \ $^2} )

B. $ \frac{2x}{\( x^2+1 \ $^2} )

C. $ \frac{2}{\( x^2+1 \ $^2} )

D. $ \frac{-2}{\( x^2+1 \ $^2} )

Correct Answer: A

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Question 8

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If 80% of the scores lie within 2 s\tandard deviations of the mean, what is the range of scores?

A. [50, 100]

B. [60, 110]

Correct C. [70, 120]

D. [80, 130]

Correct Answer: C

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Question 9

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

Correct A. $x = 0, \pi/2, \pi, 3\pi/2$

B. $x = 0, \pi/4, \pi/2, 3\pi/4$

C. $x = \pi/4, \pi/2, 3\pi/4, \pi$

D. $x = 0, \pi/2, \pi, 3\pi/2, 2\pi$

Correct Answer: A

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Question 10

Find the magnitude of the vector $\vec{a} = 3\hat{i} + 4\hat{j} + 5\hat{k}$.

A. 5

B. 10

Correct C. 15

D. 20

Correct Answer: C

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Question 11

Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.

A. 2x

B. -2x

Correct C. \frac{-2x}{$ x^2 + 1 $^2}

D. \frac{2x}{$ x^2 + 1 $^2}

Correct Answer: C

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Question 12

A set of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 90?

Correct A. 0.8413

B. 0.8413

C. 0.8413

D. 0.8413

Correct Answer: A

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Question 13

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

Correct A. 121

B. 122

C. 123

D. 124

Correct Answer: A

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Question 14

Solve the inequality $ 2x^2 + 5x - 3 > 0 $.

Correct A. $ -\infty, -1 $ \cup $ 3, \infty $

B. $ -\infty, -3 $ \cup $ 1, \infty $

C. $ -\infty, -1 $ \cup $ 1, \infty $

D. $ -\infty, 1 $ \cup $ 3, \infty $

Correct Answer: A

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Question 15

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

Correct A. 50.27

B. 50.28

C. 50.29

D. 50.30

Correct Answer: A

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Question 16

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 17

A particle moves along the x-axis with a velocity given by ( v(x) = 2x + 5 ). Find the acceleration at x = 3.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 18

Find the area under the curve $ y = x^2 + 2x $ from x = 0 to x = 2.

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 19

A circle with center (0, 0) and radius 4 passes through the point (3, 4). Find the equation of the circle.

Correct A. $ x - 0 $^2 + $ y - 0 $^2 = 16

B. $ x - 0 $^2 + $ y - 0 $^2 = 4

C. $ x - 0 $^2 + $ y - 0 $^2 = 9

D. $ x - 0 $^2 + $ y - 0 $^2 = 25

Correct Answer: A

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Question 20

Find the value of x in the equation $ \frac{x^2 - 4x + 4}{x^2 - 4x + 3} = 1 $.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 21

Find the value of x in the equation $ 2x^2 + 5x - 3 = 0 $.

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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Question 22

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

Correct A. x < -1 or x > 5

B. x > -1 or x < 5

C. x < 1 or x > 5

D. x > 1 or x < 5

Correct Answer: A

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Question 23

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 24

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

A. x = \frac{\pi}{2}

Correct B. x = \frac{\pi}{4}

C. x = \frac{3\pi}{4}

D. x = \frac{5\pi}{4}

Correct Answer: B

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Question 25

Find the area under the curve $ y = x^2 $ from x = 0 to x = 4.

Correct A. \frac{64}{3}

B. \frac{32}{3}

C. \frac{16}{3}

D. \frac{8}{3}

Correct Answer: A

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