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Subject

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POST UTME SKYLINE UNIVERSITY 2023 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 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 2

Solve for y in the equation \( y = \frac{1}{2} \left\( \frac{1}{x} + \frac{1}{x^2} \right \ \) ).

Correct A. x^2 + 2x + 1

B. x^2 - 2x + 1

C. x^2 + x + 1

D. x^2 - x + 1

Correct Answer: A

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Question 3

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

A. 50π

Correct B. 100π

C. 150π

D. 200π

Correct Answer: B

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Question 4

Find the value of x in the equation \( x^2 + 4x + 4 = 0 \).

A. 0

Correct B. -2

C. 2

D. -4

Correct Answer: B

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Question 5

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

A. 4

B. 6

Correct C. 8

D. 12

Correct Answer: C

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Question 6

Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 3x - 1} ) u\sing the quotient rule.

Correct A. \frac{-4x + 3}{\( 2x^2 + 3x - 1 \)^2}

B. \frac{4x + 3}{\( 2x^2 + 3x - 1 \)^2}

C. \frac{4x - 3}{\( 2x^2 + 3x - 1 \)^2}

D. \frac{-4x - 3}{\( 2x^2 + 3x - 1 \)^2}

Correct Answer: A

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Question 7

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

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

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

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

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

Correct Answer: A

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Question 8

A binary operation \( \ast \) is defined as \( a \ast b = a^2 + b^2 \). Find the value of \( 2 \ast 3 \).

Correct A. 13

B. 14

C. 15

D. 16

Correct Answer: A

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Question 9

Find the value of ( x ) in the equation \( 2^x + 3^x = 10 \).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 10

Solve the inequality \( 2x^2 + 3x - 1 > 0 \).

A. x < -1

Correct B. x > -1

C. x < 1

D. x > 1

Correct Answer: B

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Question 11

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

Correct A. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

B. \( \frac{\( x^2 + 2x - 3 \)\( 2x + 2 \ \) - \( x^2 - 4 \)(2x)}{\( x^2 - 4 \)^2} )

C. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

D. \( \frac{\( x^2 + 2x - 3 \)\( 2x + 2 \ \) + \( x^2 - 4 \)(2x)}{\( x^2 - 4 \)^2} )

Correct Answer: A

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Question 12

A right circular cylinder has a height of 10 cm and a radius of 4 cm. Find the volume of the cylinder.

A. ( 40pi ) cm^3

B. ( 80pi ) cm^3

Correct C. ( 160pi ) cm^3

D. ( 320pi ) cm^3

Correct Answer: C

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Question 13

Find the equation of the circle with center \( -2, 3 \) and radius 5.

Correct A. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 25 )

B. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 25 )

C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 25 )

D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )

Correct Answer: A

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Question 14

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

Correct A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)

B. \( x < -\frac{3}{2} \) or \( x > \frac{5}{4} \)

C. \( x < -\frac{3}{2} \) or \( x < \frac{5}{4} \)

D. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)

Correct Answer: A

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Question 15

Find the value of ( x ) in the equation \( 2^x + 3^x = 5^x \).

A. \( x = 2 \)

Correct B. \( x = 3 \)

C. \( x = 4 \)

D. \( x = 5 \)

Correct Answer: B

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Question 16

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 64\pi cm^3

Correct B. 128\pi cm^3

C. 256\pi cm^3

D. 512\pi cm^3

Correct Answer: B

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Question 17

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 18

Solve for x in the equation \( 2^x + 3^x = 5^x \).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 19

In the triangle ABC, the length of side AB is 5 cm, the length of side BC is 7 cm, and the length of side AC is 9 cm. What is the measure of angle A in degrees?

A. 30

B. 45

Correct C. 60

D. 90

Correct Answer: C

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Question 20

A circle has a radius of 4 cm. What is the area of the circle?

Correct A. 16\pi cm^2

B. 32\pi cm^2

C. 64\pi cm^2

D. 128\pi cm^2

Correct Answer: A

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Question 21

Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].

A. -120

B. 120

Correct C. 0

D. -60

Correct Answer: C

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Question 22

A histogram is constructed u\sing the following data: [ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ]. The width of each bar is 1 unit. Find the mean of the data.

A. 6

Correct B. 7

C. 8

D. 9

Correct Answer: B

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Question 23

Find the volume of the solid formed by revolving the region bounded by the curve [ y = x^2 ] and the line [ y = 4 ] about the x-axis.

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 24

A sequence is defined by [ a_n = 2n + 1 ]. Find the sum of the first 5 terms of the sequence.

A. 15

B. 25

C. 35

Correct D. 45

Correct Answer: D

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Question 25

A set of 5 numbers has a mean of 10. If 2 more numbers are added to the set, the mean becomes 12. Find the sum of the original 5 numbers.

A. 40

Correct B. 50

C. 60

D. 70

Correct Answer: B

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