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POST UTME SKYLINE UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details

Solve for x in the quadratic equation \(x^2 + 5x + 6 = 0\)

Correct A. \(x = -2\)

B. \(x = -3\)

C. \(x = 2\)

D. \(x = 3\)

Correct Answer: A

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Question 2 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?

A. \(1/2\)

B. \(1/3\)

C. \(2/3\)

Correct D. \(1/6\)

Correct Answer: D

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Question 3 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\)

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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Question 4 View Details

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

Correct A. x < -1 or \(x > 3/2\)\)

B. \(x < 1\) or x > \(-3/2\)

C. \(x <\)\(-3/2\) or \(x > 1\)

D. \(x < 3/2\)\) or x > -1

Correct Answer: A

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Question 5 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. \(1/2\)

Correct B. \(1/3\)

C. \(2/3\)

D. \(3/4\)

Correct Answer: B

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Question 6 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{1 - \(x^2}}\)\) ) using the chain rule.

Correct A. \(\frac{x}\){ 1 - \(x^2\) \)^{\(3/2\)}}\)

B. \(\frac{-x}\){ 1 - \(x^2\) \)^{\(3/2\)}}\)

C. \(\frac{1}\){ 1 - \(x^2\) \)^{\(3/2\)}}\)

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

Correct Answer: A

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Question 7 View Details

A circle has equation \((x^2 + y^2\) = 4\). Find the equation of the \tangent line at point \\((x^2 + y^2 = 4). Find the equation of the \(1, \sqrt{3} \\) ).

A. \(y = -\)\(\sqrt{3}\) x + 4

Correct B. \(y =\)\(\sqrt{3}\) x + 4

C. \(y = -\)\(\sqrt{3}\) x - 4

D. \(y =\)\(\sqrt{3}\) x - 4

Correct Answer: B

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Question 8 View Details

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

Correct A. 0.2

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 9 View Details

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

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 10 View Details

A line passes through points ( (1, 2) ) and ( (3, 4) ). Find the equation of the line.

Correct A. \(y = x + 1\)

B. \(y = x - 1\)

C. \(y = -x + 3\)

D. \(y = x - 3\)

Correct Answer: A

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Question 11 View Details

A random variable X follows a binomial distribution with parameters \(n = 10\) and \(p = 0.4\). Find the probability that X is greater than 7.

Correct A. 0.032

B. 0.064

C. 0.128

D. 0.256

Correct Answer: A

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Question 12 View Details

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

A. \(y = x + 1\)

B. \(y = x - 1\)

C. \(y = 2x - 1\)

Correct D. \(y = 2x + 1\)

Correct Answer: D

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Question 13 View Details

A circle has a radius of 5 units. Find the area of the circle.

Correct A. 25π

B. 50π

C. 75π

D. 100π

Correct Answer: A

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Question 14 View Details

A rectangular prism has a length of 6 units, a width of 4 units, and a height of 3 units. Find the volume of the prism.

A. 72

Correct B. 96

C. 120

D. 144

Correct Answer: B

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Question 15 View Details

A vector has a magnitude of 10 units and an angle of 30 degrees with the positive x-axis. Find the x-component of the vector.

A. 5

Correct B. \(5√3\)

C. 10

D. \(10√3\)

Correct Answer: B

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Question 16 View Details

Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 4 \ 5 end{pmatrix}\). Find the vector \(\\(end{pmatrix}). Find the vector \mathbf{a} \times \mathbf{b}\) using the determinant method.

Correct A. \begin{pmatrix} -15 \ 12 \end{pmatrix}

B. \begin{pmatrix} 12 \ -15 \end{pmatrix}

C. \begin{pmatrix} 15 \ -12 \end{pmatrix}

D. \begin{pmatrix} -12 \ 15 \end{pmatrix}

Correct Answer: A

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Question 17 View Details

A random experiment has two independent events, A and B, with probabilities 0.4 and 0.6, respectively. Find the probability that both events occur.

Correct A. 0.24

B. 0.48

C. 0.64

D. 0.76

Correct Answer: A

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Question 18 View Details

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

A. \(\frac{\pi}{4}\)\)

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

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

D. \pi

Correct Answer: B

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Question 19 View Details

Convert the number 1011 from base 2 to base 10.

A. 3

Correct B. 5

C. 7

D. 9

Correct Answer: B

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Question 20 View Details

Find the volume of the frustum of a cone with radii 6 and 4 and height 10.

A. 120\pi

Correct B. 150\pi

C. 180\pi

D. 200\pi

Correct Answer: B

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Question 21 View Details

Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 1 \ -2 end{pmatrix}\). Find the vector \(\\(end{pmatrix}). Find the vector \mathbf{a} \times \mathbf{b}\) using the cross product formula.

A. \(egin{pmatrix} 0 \ 0 \ 0 \end{pmatrix}\)

Correct B. \(egin{pmatrix} 6 \ -4 \ 0 \end{pmatrix}\)

C. \(egin{pmatrix} 0 \ 0 \ 6 \end{pmatrix}\)

D. \(egin{pmatrix} 0 \ 0 \ -6 \end{pmatrix}\)

Correct Answer: B

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Question 22 View Details

Solve the inequality \(\frac{2x + 3}{x - 1} > 0\) using the sign chart method.

Correct A. \(x < -1\) or \(x > 1\)

B. \(x < -1\) or \(x = 1\)

C. \(x > -1\) or \(x < 1\)

D. \(x < -1\) or \(x > 1\)

Correct Answer: A

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Question 23 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using the quotient rule.

Correct A. ( f'\((x) =\)\(\frac{-2x}{x^2 + 1\) ^2}\)\) )

B. ( f'\((x) =\)\(\frac{2x}{x^2 + 1\) ^2}\)\) )

C. ( f'\((x) =\)\(\frac{x^2}{\) \(x^2 + 1\) ^2}\)\) )

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

Correct Answer: A

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Question 24 View Details

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

Correct A. \(P X > 4 \\) = \(\frac{1}{6}\)\) )

B. \(P X > 4 \\) = \(\frac{1}{3}\)\) )

C. \(P X > 4 \\) = \(\frac{2}{3}\)\) )

D. \(P X > 4 \\) = \(\frac{5}{6}\)\) )

Correct Answer: A

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Question 25 View Details

Find the sum of the infinite geometric series \(sum_{n = 1}^{\infty} \frac{1}{2^n}\).

Correct A. \(S = \frac{1}{2}\)

B. \(S = \frac{1}{4}\)

C. \(S = \frac{1}{8}\)

D. \(S = \frac{1}{16}\)

Correct Answer: A

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