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POST UTME MOUNTAIN TOP UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation \(\frac{1}{2}x^2 + 3x - 2 = 0\) using 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 View Details

A random variable X has a probability distribution given by ( P(X) = begin{cases} 0.2 & \text{if } \(x = 1\\(begin{cases} 0.2 & text{if}\) 0.3 & \text{if } \(x = 2\\( 0.3 & text{if}\) 0.5 & \text{if } \(x = 3\\( 0.5 & text{if}\) \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 View Details

Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\) for \(x \\\() 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 View Details

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 View Details

A histogram of exam scores has a mean of 70 and a standard 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 View Details

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 View Details

A rectangular 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 View Details

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 View Details

Two events, A and B, are independent. 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 22 View Details

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

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 View Details

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 View Details

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 View Details

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

Correct A. \(y = -x + 7\)

B. \(y = x + 7\)

C. \(y = -x - 7\)

D. \(y = x - 7\)

Correct Answer: A

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