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POST UTME SUMMIT UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 2 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 or tea?

A. 0.7

Correct B. 0.75

C. 0.8

D. 0.85

Correct Answer: B

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Question 3 View Details

The volume of a rectangular prism is given by \(V = lwh\). If the length is tripled, the width is doubled, and the height is halved, what is the new volume?

A. \(l/2\), \(w/3\)\)\(h/3\)

B. (3l)\(2w) h/2 \\)

Correct C. (3l)\(2w) h/2 \\)

D. \(l/3\), \(w/2\)\)\(h/6\)

Correct Answer: C

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Question 4 View Details

Solve for x in the equation: \(2^x\) + \\((5^x\)\(= 10\)\\()^x\).

A. \(x = 2\)

Correct B. \(x = 3\)

C. \(x = 4\)

D. \(x = 5\)

Correct Answer: B

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Question 5 View Details

A right triangle has a hypotenuse of length 10 and one leg of length 6. What is the length of the other leg?

Correct A. 8

B. 10

C. 12

D. 14

Correct Answer: A

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Question 6 View Details

In a certain number base, the number 1011 is equivalent to 11 in base 10. What is the value of the number base?

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 7 View Details

A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. What is the volume of the prism?

A. 400 \(cm^3\)

B. 500 \(cm^3\)

Correct C. 600 \(cm^3\)

D. 800 \(cm^3\)

Correct Answer: C

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Question 8 View Details

Two events, A and B, are independent. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. What is the probability that both events occur?

A. 0.2

Correct B. 0.24

C. 0.3

D. 0.36

Correct Answer: B

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Question 9 View Details

Simplify the expression \(\sqrt{48}\).

A. \(4√3\)

B. \(6√2\)

Correct C. \(8√3\)

D. \(12√2\)

Correct Answer: C

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Question 10 View Details

Solve the equation \(x^2 + 5x - 6 = 0\).

Correct A. -6, 1

B. -3, 2

C. -2, 3

D. -1, 6

Correct Answer: A

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Question 11 View Details

Find the area under the curve \(y = \frac{1}{2}x^2\) from \(x = 0\) to \(x = 4\).

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 12 View Details

Solve for ( x ) in the equation \(\sin^2 x + \cos^2 x = 1\).

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

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

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

D. \(x =\)\(\frac{5\pi}{4}\)\)

Correct Answer: A

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Question 13 View Details

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

A. \(\frac{1}{3}\)\)

B. \(\frac{1}{2}\)\)

Correct C. \(\frac{2}{3}\)\)

D. \(\frac{5}{6}\)\)

Correct Answer: C

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Question 14 View Details

Find the volume of the solid formed by revolving the region bounded by the curves \(y = x^2\) and \(y = x\) about the x-axis.

A. \(\frac{1}{6}\)\)

Correct B. \(\frac{1}{3}\)\)

C. \(\frac{1}{2}\)\)

D. \(\frac{2}{3}\)\)

Correct Answer: B

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Question 15 View Details

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. \(\frac{1}{2}\)\)

Correct B. \(\frac{2}{5}\)\)

C. \(\frac{3}{5}\)\)

D. \(\frac{4}{5}\)\)

Correct Answer: B

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Question 16 View Details

Determine the value of (x\) in the equation \(\\((x) in the equation \left \frac{1}{2} \right\)\\((^x\) =\)\(\frac{1}{64}\)\)\).

A. 2

B. 3

C. 4

Correct D. 5

Correct Answer: D

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Question 17 View Details

Find the sum of the first (n\) terms of the geometric series \(\\((n) terms of the geometric series \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots\).

Correct A. 1 - \(\frac{1}{2^n}\)\)\)

B. 1 - \(\frac{1}\){\(2^{n+1}}\)\)

C. 1 + \(\frac{1}{2^n}\)\)\)

D. 1 + \(\frac{1}\){\(2^{n+1}}\)\)

Correct Answer: A

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Question 18 View Details

Solve the inequality \(\log_2 x^2 - 4\)\(> 2\)\).

A. \(x > 2\)

B. \(x < -2\)

Correct C. \(x > 2\) or \(x < -2\)

D. \(x > 4\)

Correct Answer: C

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Question 19 View Details

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. \(-\frac{2}{x^2 + 1 ^2}\)

D. \(\frac{2}{x^2 + 1 ^2}\)

Correct Answer: A

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Question 20 View Details

Solve the system of equations \(\begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases}\).

A. \(x = 1, y = 2\)

Correct B. \(x = 2, y = 1\)

C. \(x = -1, y = 3\)

D. \(x = 3, y = -1\)

Correct Answer: B

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Question 21 View Details

Find the area under the curve \(y = \frac{1}{2}x^2\) from \(x = 0\) to \(x = 4\).

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 22 View Details

Solve the matrix equation \(\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}\).

Correct A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \\ 1 \end{bmatrix}

C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \\ 3 \end{bmatrix}

Correct Answer: A

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Question 23 View Details

Find the sum of the first 5 terms of the geometric progression ( 2, 6, 18, 54, ... ).

Correct A. 190

B. 210

C. 230

D. 250

Correct Answer: A

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Question 24 View Details

Find the mean deviation of the data set ( 2, 4, 6, 8, 10 ).

Correct A. 4

B. 6

C. 8

D. 10

Correct Answer: A

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Question 25 View Details

Solve the system of linear equations \(2x + 3y = 7\) and \(x - 2y = -3\).

Correct A. \begin{bmatrix} \(x = 1\) \ \(y = 2\) \end{bmatrix}

B. \begin{bmatrix} \(x = 2\) \ \(y = 1\) \end{bmatrix}

C. \begin{bmatrix} \(x = 3\) \ \(y = 4\) \end{bmatrix}

D. \begin{bmatrix} \(x = 4\) \ \(y = 3\) \end{bmatrix}

Correct Answer: A

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