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POST UTME MOUNTAIN TOP UNIVERSITY 2020 Mathematics | Objective

Are you preparing for POST UTME MOUNTAIN TOP UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Determine the value of x in the equation \( \frac{1}{2}x^2 + 3x - 2 = 0 \) u\sing the quadratic formula.

A. \( x = -6 \pm \sqrt{6^2 - 4 \cdot \frac{1}{2} \cdot \( -2 \ \)} \)

B. \( x = -6 \pm \sqrt{6^2 - 4 \cdot \frac{1}{2} \cdot 2} \ \)

Correct C. \( x = -6 \pm \sqrt{6^2 - 4 \cdot \frac{1}{2} \cdot 3} \ \)

D. \( x = -6 \pm \sqrt{6^2 - 4 \cdot \frac{1}{2} \cdot \( -3 \ \)} \)

Correct Answer: C

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Question 2

A random variable X has a probability distribution given by ( P(X) = \begin{cases} 0.2 & \text{if } x = 1 \ 0.3 & \text{if } x = 2 \ 0.5 & \text{if } x = 3 \end{cases} \). Find the expected value of X.

Correct A. ( E(X) = 1 \cdot 0.2 + 2 \cdot 0.3 + 3 \cdot 0.5 \)

B. ( E(X) = 1 \cdot 0.3 + 2 \cdot 0.2 + 3 \cdot 0.5 \)

C. ( E(X) = 1 \cdot 0.5 + 2 \cdot 0.3 + 3 \cdot 0.2 \)

D. ( E(X) = 1 \cdot 0.2 + 2 \cdot 0.5 + 3 \cdot 0.3 \)

Correct Answer: A

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Question 3

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

Correct A. \( x = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4} \ \)

B. \( x = \frac{\pi}{2}, \frac{3\pi}{2} \ \)

C. \( x = \frac{\pi}{4}, \frac{3\pi}{4} \ \)

D. \( x = \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2} \ \)

Correct Answer: A

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Question 4

A vector \( \mathbf{a} \ \) has components \( a_x = 2 \ \) and \( a_y = 3 \ \). A vector \( \mathbf{b} \ \) has components \( b_x = -1 \ \) and \( b_y = 4 \ \). Find the magnitude of the sum of these two vectors.

Correct A. \( \sqrt{\( 2 - 1 \ \)^2 + \( 3 + 4 \)^2} \)

B. \( \sqrt{\( 2 + 1 \ \)^2 + \( 3 - 4 \)^2} \)

C. \( \sqrt{\( 2 - 1 \ \)^2 + \( 3 - 4 \)^2} \)

D. \( \sqrt{\( 2 + 1 \ \)^2 + \( 3 + 4 \)^2} \)

Correct Answer: A

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Question 5

A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 80.

Correct A. \( P\( X > 80 \ \) = 0.1587 \)

B. \( P\( X > 80 \ \) = 0.3413 \)

C. \( P\( X > 80 \ \) = 0.5 \)

D. \( P\( X > 80 \ \) = 0.8413 \)

Correct Answer: A

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Question 6

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

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 7

A rec\tangular solid has dimensions 5 cm, 8 cm, and 3 cm. Find its surface area.

A. 154 cm^2

Correct B. 156 cm^2

C. 158 cm^2

D. 160 cm^2

Correct Answer: B

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Question 8

Evaluate the definite integral \[ \int_0^1 \( 2x^2 + 3x - 1 \) dx \].

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 9

Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P\( A \cap B \).

A. 0.2

B. 0.24

C. 0.3

Correct D. 0.36

Correct Answer: D

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Question 10

Solve the 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 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 12

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

A. 50

B. 60

Correct C. 70

D. 80

Correct Answer: C

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Question 13

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, 1 \) ∪ (3, ∞)

C. \( -∞, -1 \) ∪ (1, ∞)

D. \( -∞, 3 \) ∪ (1, ∞)

Correct Answer: A

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Question 14

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).

Correct A. 6x + 2

B. 3x^2 + 2

C. 2x^2 + 6

D. x^2 + 2

Correct Answer: A

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Question 15

A survey of 100 students found that 60 students preferred coffee, 30 students preferred tea, and 10 students preferred both. What is the probability that a randomly selected student prefers coffee?

Correct A. 0.6

B. 0.7

C. 0.8

D. 0.9

Correct Answer: A

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Question 16

Find the area under the curve \( y = x^2 + 2x + 1 \) from \( x = 0 \) to \( x = 2 \).

A. 7

B. 9

Correct C. 11

D. 13

Correct Answer: C

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Question 17

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 18

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 19

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

Correct A. 240

B. 242

C. 244

D. 246

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. \( x - 3 \)^2 + \( y - 2 \)^2 = 16

C. \( x - 2 \)^2 + \( y - 3 \)^2 = 9

D. \( x - 3 \)^2 + \( y - 2 \)^2 = 9

Correct Answer: A

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Question 21

Let ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ). Find the value of \( f\( -2 \ \) ).

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 22

A circle with center ( C ) and radius ( 4 ) has equation \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 ). Find the equation of the line pas\sing through ( C ) and perp\endicular to the line \( y = x + 1 \).

Correct A. y = -x + 5

B. y = x - 5

C. y = -x - 5

D. y = x + 5

Correct Answer: A

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Question 23

A box with a square base of side length ( 6 ) and height ( 8 ) has a square hole cut out of one of its sides. The hole has a side length of ( 2 ) and is centered on the side of the box. Find the volume of the box with the hole cut out.

Correct A. 48

B. 50

C. 52

D. 54

Correct Answer: A

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Question 24

A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers rolled is greater than 7?

A. \frac{1}{3}

B. \frac{1}{2}

Correct C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: C

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Question 25

A circle with center ( C ) and radius ( 5 ) has equation \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 ). Find the equation of the line pas\sing through ( C ) and perp\endicular to the line \( y = x - 2 \).

Correct A. y = -x + 7

B. y = x + 7

C. y = -x - 7

D. y = x - 7

Correct Answer: A

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