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POST UTME MOUNTAIN TOP UNIVERSITY 2022 Mathematics | Objective

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Question 1

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the Pythagorean theorem.

A. 8 cm

Correct B. 12 cm

C. 16 cm

D. 20 cm

Correct Answer: B

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Question 2

A binary operation $*$ on the set \{1, 2, 3, 4\} is defined as follows: $a \ast b = a^2 + b^2$. Find the value of $2 \ast 3$.

Correct A. 13

B. 17

C. 19

D. 21

Correct Answer: A

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Question 3

The mean of five numbers is 15. If one of the numbers is 10, find the sum of the other four numbers.

Correct A. 50

B. 60

C. 70

D. 80

Correct Answer: A

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Question 4

The equation of a circle is given by $x^2 + y^2 + 4x + 6y = 0$. Find the center and radius of the circle.

Correct A. $ -2, -3 $ and 5

B. ( 2, 3 ) and 5

C. $ -2, 3 $ and 5

D. $ 2, -3 $ and 5

Correct Answer: A

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Question 5

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

A. 15

Correct B. 25

C. 35

D. 45

Correct Answer: B

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Question 6

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 7

Evaluate the integral $ int_{0}^{2} \( 2x^2 + 3x - 1 \ $ dx ).

Correct A. $ left[ \frac{2x^3}{3} + \frac{3x^2}{2} - x \right]_{0}^{2} = \frac{16}{3} + 6 - 2 = \frac{40}{3} $

B. $ left[ \frac{2x^3}{3} + \frac{3x^2}{2} - x \right]_{0}^{2} = \frac{16}{3} + 6 - 2 = \frac{40}{3} $

C. $ left[ \frac{2x^3}{3} + \frac{3x^2}{2} - x \right]_{0}^{2} = \frac{16}{3} + 6 - 2 = \frac{40}{3} $

D. $ left[ \frac{2x^3}{3} + \frac{3x^2}{2} - x \right]_{0}^{2} = \frac{16}{3} + 6 - 2 = \frac{40}{3} $

Correct Answer: A

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Question 8

Solve the equation $ x^2 + 4x + 4 = 0 $.

Correct A. $ x = -2 $

B. $ x = -1 $

C. $ x = 1 $

D. $ x = 2 $

Correct Answer: A

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Question 9

Find the equation of the line pas\sing through the points (1,2) and (3,4).

Correct A. $ y = \frac{4}{2} \( x - 1 \ $ + 2 )

B. $ y = \frac{4}{2} \( x - 3 \ $ + 4 )

C. $ y = \frac{4}{2} \( x - 1 \ $ + 4 )

D. $ y = \frac{4}{2} \( x - 3 \ $ + 2 )

Correct Answer: A

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Question 10

A histogram of exam scores is shown below. Find the mean score.

Correct A. $ \frac{1}{4} \( 10 + 20 + 30 + 40 \ $ = 25 )

B. $ \frac{1}{4} \( 10 + 20 + 30 + 40 \ $ = 25 )

C. $ \frac{1}{4} \( 10 + 20 + 30 + 40 \ $ = 25 )

D. $ \frac{1}{4} \( 10 + 20 + 30 + 40 \ $ = 25 )

Correct Answer: A

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Question 11

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

A. $ \frac{1}{2} $

B. ( 2 )

Correct C. ( 4 )

D. ( 6 )

Correct Answer: C

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Question 12

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 13

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?

Correct A. ( 0.9544 )

B. ( 0.8413 )

C. ( 0.6915 )

D. ( 0.6827 )

Correct Answer: A

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Question 14

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

Correct A. $ 2\sin\( x $\cos(x \) )

B. $ \cos^2\( x \ $ )

C. $ \sin\( x $\cos(x \) )

D. $ \sin^2\( x \ $ )

Correct Answer: A

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Question 15

Solve the equation $ x^2 + 4x + 4 = 0 $.

Correct A. $ x = -2 $

B. $ x = 2 $

C. $ x = -1 $

D. $ x = 1 $

Correct Answer: A

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Question 16

Let ( f(x) = \frac{1}{x^2 + 1} ). Find the derivative of ( f(x) ) 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 17

A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?

A. 8

B. 10

C. 12

Correct D. 14

Correct Answer: D

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Question 18

Solve the inequality $ x^2 - 6x + 8 > 0 $.

Correct A. x < 2 or x > 4

B. x < 1 or x > 4

C. x < 2 or x < 4

D. x > 2 or x < 4

Correct Answer: A

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Question 19

Find the sum of the first 5 terms of the geometric sequence ( 2, 6, 18, ... ).

A. 62

Correct B. 64

C. 66

D. 68

Correct Answer: B

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Question 20

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 50 and 70?

A. 0.25

Correct B. 0.5

C. 0.75

D. 0.9

Correct Answer: B

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Question 21

Find the value of $x$ in the equation $2^x + 5^x = 7^x$.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 22

A circle has a diameter of 10 cm. Find the area of the circle.

Correct A. 78.5

B. 78.54

C. 78.55

D. 78.6

Correct Answer: A

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Question 23

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

Correct A. $ -∞, -1 $ ∪ (5, ∞)

B. $ -∞, -1 $ ∪ (1, ∞)

C. $ -∞, 1 $ ∪ (5, ∞)

D. $ -∞, 5 $ ∪ (∞, 1)

Correct Answer: A

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Question 24

Find the equation of the line pas\sing through the points (2, 3) and (4, 5).

Correct A. y = 2x + 1

B. y = 2x - 1

C. y = -2x + 1

D. y = -2x - 1

Correct Answer: A

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Question 25

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

Correct A. 30

B. 31

C. 32

D. 33

Correct Answer: A

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