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POST UTME SKYLINE UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix}\).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 2 View Details

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

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 3 View Details

Solve the system of equations \(egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases}\).

Correct A. (1, 3)

B. (2, 2)

C. (3, 1)

D. (4, 0)

Correct Answer: A

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Question 4 View Details

Find the derivative of the function ( f(x) = \(\sqrt{3x + 2}\) ) using the chain rule.

Correct A. \(\frac{3}{2\sqrt{3x + 2}}\)

B. \(\frac{3}{2 3x + 2 \}\)\) )

C. \(\frac{3}{2\sqrt{3x + 2}} + \frac{1}{2\sqrt{3x + 2}}\)

D. \(\frac{3}{2 3x + 2 \}\)\) - \(\frac{1}{2 3x + 2}\)\) )

Correct Answer: A

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Question 5 View Details

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

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 6 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.3\), P\(X = 2 = 0.4\), and P(X = 3 = 0.3\). If two independent random variables X and Y have the same probability distribution, what is the probability that \(X + Y = 4\\((X = 3 = 0.3). If two independent random variables X and Y have the same probability distribution, what is the probability that\)?

A. 0.1

B. 0.2

Correct C. 0.3

D. 0.4

Correct Answer: C

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Question 7 View Details

Solve for 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 8 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 - 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 9 View Details

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 10 View Details

If \(\(1x \\) = \(frac{1}{2}\)\) ), find the value of \\(frac{1}{2})\(\)1x \\) ).

Correct A. \(\frac{\sqrt{3}}{2}\)

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

C. \(\frac{\sqrt{5}}{2}\)

D. \(\frac{1}{\sqrt{2}}\)

Correct Answer: A

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Question 11 View Details

Let ( f(x) = \(\frac{x^2 - 4}{x - 2}\)\)\) ). Find the derivative of ( f(x) ) using the quotient rule.

A. \(\frac{2x x - 2 - x^2 - 4\) }{ x - 2 ^2}\)\)

B. \(\frac{2x x - 2 + x^2 - 4\) }{ x - 2 ^2}\)\)

Correct C. \(\frac{2x x - 2 - x^2 - 4\) }{ x - 2 ^2}\)\)

D. \(\frac{2x x - 2 + x^2 - 4\) }{ x - 2 ^2}\)\)

Correct Answer: C

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Question 12 View Details

A set ( A ) contains 5 elements. If ( A ) is a subset of a set ( B ), and ( B ) has 8 elements, what is the number of elements in the power set of ( B )?

A. 32

Correct B. 64

C. 128

D. 256

Correct Answer: B

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Question 13 View Details

A sequence is defined as \(a_n = 2n + 1\). Find the sum of the first 5 terms of the sequence.

A. 15

Correct B. 25

C. 35

D. 45

Correct Answer: B

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Question 14 View Details

A histogram is shown below. What is the mean of the data set?

A. 10

Correct B. 20

C. 30

D. 40

Correct Answer: B

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Question 15 View Details

A vector ( mathbf{a} ) is defined as \(\mathbf{a} = 2\mathbf{i} + 3\mathbf{j}\). Find the magnitude of ( mathbf{a} ).

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 16 View Details

Determine the value of (x\) in the equation \(2^x + 5^x = 7^x\\((x) in the equation\).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 17 View Details

Solve the inequality \(\frac{x^2 - 4}{x + 2} > 0\).

Correct A. \(x > -2\)

B. \(x < -2\)

C. \(x > 2\)

D. \(x < 2\)

Correct Answer: A

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Question 18 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. \(\frac{3}{8}\)\)

D. \(\frac{4}{9}\)\)

Correct Answer: B

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Question 19 View Details

Solve the quadratic 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 20 View Details

A company produces 200 units of a product per day. If the production rate is increased by 20% per day, how many units will be produced in 5 days?

A. 1200

B. 1500

Correct C. 1800

D. 2000

Correct Answer: C

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Question 21 View Details

Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{array} ].

Correct A. -2

B. 2

C. 4

D. 6

Correct Answer: A

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Question 22 View Details

A rectangular solid has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Find its surface area.

A. 120 \(cm^2\)

Correct B. 150 \(cm^2\)

C. 180 \(cm^2\)

D. 200 \(cm^2\)

Correct Answer: B

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Question 23 View Details

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

Correct A. x \leq -1 \text{ or } x \geq \(\frac{3}{2}\)\)

B. x \leq -1 \text{ or } x \geq 1

C. x \leq 1 \text{ or } x \geq -1

D. x \leq -1 \text{ or } x \geq -\(\frac{3}{2}\)\)

Correct Answer: A

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Question 24 View Details

Find the mean of the numbers 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

A. 10

B. 12

C. 14

Correct D. 16

Correct Answer: D

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Question 25 View Details

A histogram shows that the heights of 20 students are normally distributed with a mean of 160 cm and a standard deviation of 10 cm. Find the probability that a randomly selected student is less than 170 cm tall.

A. 0.25

Correct B. 0.5

C. 0.75

D. 0.9

Correct Answer: B

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