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POST UTME MOUNTAIN TOP UNIVERSITY 2019 Mathematics | Objective

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Question 1

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

A. -120

B. 120

Correct C. 0

D. 180

Correct Answer: C

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Question 2

Solve the equation [ \sin^2 x + \cos^2 x = 1 ].

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

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

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

D. x = \frac{\pi}{6}

Correct Answer: A

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Question 3

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

A. 1040

Correct B. 1080

C. 1100

D. 1120

Correct Answer: B

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Question 4

Find the derivative of the function [ f(x) = \frac{1}{x^2 + 1} \].

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

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

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

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

Correct Answer: A

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Question 5

Solve the inequality [ 2x^2 - 5x - 3 > 0 \].

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 6

Determine the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 50\pi cm^3

B. 75\pi cm^3

Correct C. 100\pi cm^3

D. 125\pi cm^3

Correct Answer: C

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Question 7

A particle moves in a straight line with initial velocity 5 m/s and acceleration 2 m/s^2. Find its velocity after 4 seconds.

A. 10 m/s

B. 12 m/s

Correct C. 14 m/s

D. 16 m/s

Correct Answer: C

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Question 8

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

Correct A. x \in $ -\infty, -1 $ \cup [3, \infty)

B. x \in $ -\infty, -3 $ \cup [1, \infty)

C. x \in $ -\infty, -3 $ \cup [1, \infty)

D. x \in $ -\infty, -1 $ \cup [3, \infty)

Correct Answer: A

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Question 9

Find the area under the curve $ y = 2x^2 + 3x - 1 $ from x = 0 to x = 2.

A. 13

B. 15

Correct C. 17

D. 19

Correct Answer: C

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Question 10

A right-angled triangle has sides 3 cm, 4 cm, and 5 cm. Find the area of the triangle.

Correct A. 6 cm^2

B. 8 cm^2

C. 10 cm^2

D. 12 cm^2

Correct Answer: A

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Question 11

Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.

A. 64\pi cm^3

Correct B. 128\pi cm^3

C. 256\pi cm^3

D. 512\pi cm^3

Correct Answer: B

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Question 12

Solve for x in the equation $ \log_{10} \( x^2 \ $ = 4).

Correct A. \pm 2

B. \pm 4

C. \pm 8

D. \pm 16

Correct Answer: A

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Question 13

A particle moves along the curve $ y = x^2 + 2x + 1 $ with a velocity of 2m/s. Find the acceleration at the point where x = 1.

Correct A. -4 m/s^2

B. -2 m/s^2

C. 2 m/s^2

D. 4 m/s^2

Correct Answer: A

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Question 14

Find the equation of the \tangent to the curve $ y = x^3 - 6x^2 + 9x + 2 $ at the point where x = 2.

Correct A. y = 3x - 5

B. y = 3x + 5

C. y = -3x + 5

D. y = -3x - 5

Correct Answer: A

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Question 15

A company produces two products, A and B. The profit from the sale of product A is $10 per unit, and the profit from the sale of 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. $1500

Correct B. $2000

C. $2500

D. $3000

Correct Answer: B

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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 < \frac{3}{2} \text{ or } x > 1

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

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

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

Correct Answer: A

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Question 18

Find the sum of the first 10 terms of the geometric series $ 2 + 6 + 18 + \cdots $.

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 19

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 20

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 = 25

C. $ x - 2 $^2 + $ y - 3 $^2 = 36

D. $ x - 2 $^2 + $ y - 3 $^2 = 49

Correct Answer: A

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Question 21

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

A. \frac{1}{3}

B. \frac{1}{2}

C. \frac{2}{3}

Correct D. \frac{5}{6}

Correct Answer: D

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Question 22

A set of 5 cards is drawn from a s\tandard deck of 52 cards. What is the probability that the set contains at least one ace?

A. \frac{1}{52}

B. \frac{1}{26}

C. \frac{1}{13}

Correct D. \frac{51}{52}

Correct Answer: D

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Question 23

A box contains 3 red balls and 2 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. \frac{1}{5}

Correct B. \frac{2}{5}

C. \frac{3}{5}

D. \frac{4}{5}

Correct Answer: B

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Question 24

A set of 4 cards is drawn from a s\tandard deck of 52 cards. What is the probability that the set contains at least one pair?

A. \frac{1}{52}

B. \frac{1}{26}

C. \frac{1}{13}

D. \frac{48}{52}

Correct Answer: VIEW ANSWER

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Question 25

Determine the mean of the data set {2, 4, 6, 8, 10} u\sing the formula for the mean.

Correct A. $ \frac{2+4+6+8+10}{5} $

B. $ \frac{2+4+6+8+10}{4} $

C. $ \frac{2+4+6+8+10}{3} $

D. $ \frac{2+4+6+8+10}{2} $

Correct Answer: A

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