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POST UTME SKYLINE UNIVERSITY 2019 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 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

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

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

Find the derivative of the function ( f(x) = \sqrt{3x + 2} ) u\sing 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

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{3pi}{4} $

D. $ x = \frac{5pi}{4} $

Correct Answer: A

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Question 6

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 indep\endent random variables X and Y have the same probability distribution, what is the probability that X + Y = 4?

A. 0.1

B. 0.2

Correct C. 0.3

D. 0.4

Correct Answer: C

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Question 7

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

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

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

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

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

Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing 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

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

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

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

A vector ( mathbf{a} ) is defined as $ mathbf{a} = 2mathbf{i} + 3mathbf{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

Determine the value of $x$ in the equation $2^x + 5^x = 7^x$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 17

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

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

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

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

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

A rec\tangular 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

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

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

A histogram shows that the heights of 20 students are normally distributed with a mean of 160 cm and a s\tandard 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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