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POST UTME LAUTECH 2024 Mathematics | Objective

Are you preparing for POST UTME LAUTECH 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

A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find the volume of the prism in cubic centimeters.

Correct A. 400

B. 500

C. 600

D. 800

Correct Answer: A

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Question 2

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

Correct A. 1/3

B. 1/2

C. 2/3

D. 1/6

Correct Answer: A

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Question 3

Solve the equation: $ x^2 + 5x + 6 = 0 $

Correct A. -2

B. -1

C. 2

D. 3

Correct Answer: A

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Question 4

Find the determinant of the matrix: \[ \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \]

Correct A. -120

B. 120

C. 0

D. 180

Correct Answer: A

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Question 5

A company produces two products, A and B. The profit from product A is $10 per unit, and the profit from product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. 2500

Correct B. 3000

C. 3500

D. 4000

Correct Answer: B

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Question 6

Find the volume of the frustum of a cone with height 10cm, lower base radius 4cm, and upper base radius 6cm.

A. 100π cm³

Correct B. 150π cm³

C. 200π cm³

D. 250π cm³

Correct Answer: B

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Question 7

Solve for x in the matrix equation $ egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} $.

A. x = 1, y = 2

Correct B. x = 2, y = 1

C. x = 3, y = 4

D. x = 4, y = 3

Correct Answer: B

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Question 8

Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 9

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 10

Find the value of x in the polynomial equation $ x^3 - 6x^2 + 11x - 6 = 0 $.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 11

Determine the probability of the event that a randomly selected integer from the set {1, 2, 3, 4, 5, 6} is greater than 4, given that the integer is even.

A. \frac{1}{2}

Correct B. \frac{2}{3}

C. \frac{3}{4}

D. \frac{4}{5}

Correct Answer: B

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Question 12

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio \frac{1}{2}.

Correct A. \frac{1023}{512}

B. \frac{1024}{512}

C. \frac{1025}{512}

D. \frac{1026}{512}

Correct Answer: A

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Question 13

Solve the equation \tan x + \cot x = 2, where x is an acute angle.

A. \frac{\pi}{4}

B. \frac{\pi}{6}

Correct C. \frac{\pi}{3}

D. \frac{\pi}{2}

Correct Answer: C

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Question 14

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

Correct A. 0.8413

B. 0.8419

C. 0.8423

D. 0.8427

Correct Answer: A

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Question 15

Find the vector \overrightarrow{a} + \overrightarrow{b} if \overrightarrow{a} = 2\hat{i} + 3\hat{j} and \overrightarrow{b} = -4\hat{i} + 5\hat{j}.

Correct A. -2\hat{i} + 8\hat{j}

B. 2\hat{i} - 8\hat{j}

C. -2\hat{i} - 8\hat{j}

D. 2\hat{i} + 8\hat{j}

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. f'(x) = \frac{-x}{$ x^2 + 1 $^{3/2}}

B. f'(x) = \frac{x}{$ x^2 + 1 $^{3/2}}

C. f'(x) = \frac{1}{$ x^2 + 1 $^{3/2}}

D. f'(x) = \frac{-1}{$ x^2 + 1 $^{3/2}}

Correct Answer: A

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Question 17

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

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

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

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

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

Correct Answer: A

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Question 18

Find the value of ( x ) in the equation $ 2^x + 5^x = 7^x $ u\sing \logarithms.

A. x = 2

Correct B. x = 3

C. x = 4

D. x = 5

Correct Answer: B

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Question 19

A histogram represents the distribution of exam scores in a class. If the mean score is 60 and the s\tandard deviation is 10, what is the probability that a randomly selected student scored above 70?

A. 0.25

B. 0.5

Correct C. 0.75

D. 0.9

Correct Answer: C

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Question 20

Solve the equation $ x^2 - 4x + 4 = 0 $ u\sing the quadratic formula.

Correct A. x = 2

B. x = -2

C. x = 1

D. x = -1

Correct Answer: A

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Question 21

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

Correct A. f'(x) = 2 \sin x \cos x

B. f'(x) = 2 \sin^2 x

C. f'(x) = 2 \cos^2 x

D. f'(x) = 2 \sin x

Correct Answer: A

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Question 22

Solve the inequality $ x^2 - 6x + 8 > 0 $ u\sing the quadratic formula.

Correct A. x < 2 or x > 4

B. x > 2 or x < 4

C. x < 2 or x < 4

D. x > 2 or x > 4

Correct Answer: A

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Question 23

Find the value of ( x ) in the equation $ 2^x + 3^x = 5^x $ u\sing \logarithms.

A. x = 2

Correct B. x = 3

C. x = 4

D. x = 5

Correct Answer: B

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Question 24

A histogram represents the distribution of exam scores in a class. If the mean score is 60 and the s\tandard deviation is 10, what is the probability that a randomly selected student scored above 70?

A. 0.25

B. 0.5

C. 0.75

D. 0.9

Correct Answer: VIEW ANSWER

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Question 25

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. 5 cm

Correct B. 7.07 cm

C. 10 cm

D. 15 cm

Correct Answer: B

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