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POST UTME SKYLINE UNIVERSITY 2018 Mathematics | Objective

Are you preparing for POST UTME SKYLINE UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

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

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

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

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

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing 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

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

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

Two events A and B are indep\endent. 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

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

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

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

Find the equation of the line pas\sing 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

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

A rec\tangular 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

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

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

A random experiment has two indep\endent 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

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

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

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

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing 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

Solve the inequality \( \frac{2x + 3}{x - 1} > 0 \) u\sing 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

Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing 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

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

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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