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POST UTME SKYLINE UNIVERSITY 2020 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 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the area under the curve $ y = \frac{1}{2}x^2 $ from $ x = 0 $ to $ x = 4 $.

Correct A. $ \frac{16}{3} $

B. $ \frac{32}{3} $

C. $ \frac{64}{3} $

D. $ \frac{128}{3} $

Correct Answer: A

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Question 2

Solve the equation $ 2x^2 + 5x - 3 = 0 $ u\sing the quadratic formula.

A. $ x = \frac{-5 pm \sqrt{109}}{4} $

B. $ x = \frac{-5 pm \sqrt{121}}{4} $

Correct C. $ x = \frac{-5 pm \sqrt{169}}{4} $

D. $ x = \frac{-5 pm \sqrt{225}}{4} $

Correct Answer: C

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Question 3

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. $ x - 3 \ $^2 + $ y - 4 $^2 = 25 )

B. $ x - 4 \ $^2 + $ y - 3 $^2 = 25 )

C. $ x - 5 \ $^2 + $ y - 3 $^2 = 25 )

D. $ x - 3 \ $^2 + $ y - 5 $^2 = 25 )

Correct Answer: A

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Question 4

Find the volume of the cylinder with radius ( 4 ) and height ( 6 ).

Correct A. ( 96pi )

B. ( 192pi )

C. ( 384pi )

D. ( 768pi )

Correct Answer: A

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Question 5

Solve the inequality $ x^2 - 4x + 3 > 0 $.

Correct A. $ x < -1 $ or $ x > 3 $

B. $ x < 1 $ or $ x > 3 $

C. $ x < -3 $ or $ x > 1 $

D. $ x < 3 $ or $ x > 1 $

Correct Answer: A

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Question 6

Find the area under the curve $ y = \frac{1}{2}x^2 + 3x - 2 $ from $ x = 0 $ to $ x = 4 $.

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 7

A circle has equation $ x - 2 \ $^2 + $ y - 3 $^2 = 4 ). Find the equation of the \tangent line at point ( (3, 5) ).

Correct A. y = -x + 7

B. y = x + 1

C. y = 2x - 3

D. y = -2x + 9

Correct Answer: A

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Question 8

Solve the inequality $ 2x^2 - 5x - 3 > 0 $.

A. x < -1 or x > 3

Correct B. x < 1 or x > 3

C. x < -3 or x > 1

D. x < 3 or x > 1

Correct Answer: B

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Question 9

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

Correct A. -\frac{2x}{$ x^2 + 1 $^2}

B. \frac{2x}{$ x^2 + 1 $^2}

C. -\frac{1}{$ x^2 + 1 $^2}

D. \frac{1}{$ x^2 + 1 $^2}

Correct Answer: A

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Question 10

A binary number is represented as $ 1011_2 $. Convert it to decimal.

A. 11

B. 13

Correct C. 15

D. 17

Correct Answer: C

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Question 11

Determine the value of $x$ in the equation $2^x + 5^x = 3^x$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 12

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 13

The mean of five numbers is $25$. If one of the numbers is $10$, find the sum of the other four numbers.

Correct A. 90

B. 100

C. 110

D. 120

Correct Answer: A

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Question 14

Solve the inequality $\log_{10} $ x^2 $ > 4$.

Correct A. $ x > 10 $

B. $ x < -10 $

C. $ x > 100 $

D. $ x < -100 $

Correct Answer: A

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Question 15

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

A. $ \frac{1}{6} $

B. $ \frac{1}{3} $

C. $ \frac{2}{3} $

Correct D. $ \frac{5}{6} $

Correct Answer: D

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Question 16

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pi\text{ cm}^3

B. 48\pi\text{ cm}^3

Correct C. 72\pi\text{ cm}^3

D. 96\pi\text{ cm}^3

Correct Answer: C

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Question 17

Solve the system of linear equations u\sing matrices: \begin{align*} x + 2y - z &= 3 \ 2x - 3y + 4z &= 2 \ 3x + y - 2z &= 1 \end{align*}

Correct A. \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}

B. \begin{pmatrix} 2 \ -1 \ 1 \end{pmatrix}

C. \begin{pmatrix} 3 \ 1 \ -2 \end{pmatrix}

D. \begin{pmatrix} 4 \ 2 \ 1 \end{pmatrix}

Correct Answer: A

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Question 18

Find the area under the curve \[ f(x) = \begin{cases} 2x + 1, & \text{if } x < 2 \ 3x - 2, & \text{if } x \geq 2 \end{cases} \] from x = 0 to x = 4.

A. 14

Correct B. 16

C. 18

D. 20

Correct Answer: B

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Question 19

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 = 20

C. $ x - 2 $^2 + $ y - 3 $^2 = 24

D. $ x - 2 $^2 + $ y - 3 $^2 = 28

Correct Answer: A

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Question 20

Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...

A. 124

B. 126

Correct C. 128

D. 130

Correct Answer: C

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Question 21

Find the determinant of the matrix $ egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} $.

A. 1

Correct B. -1

C. 5

D. 10

Correct Answer: B

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Question 22

A circle has a diameter of 10 cm. Find the area of the circle.

A. 50π

Correct B. 100π

C. 200π

D. 250π

Correct Answer: B

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Question 23

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

Correct A. 30

B. 50

C. 60

D. 70

Correct Answer: A

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Question 24

A line passes through the points (2, 3) and (4, 5). Find the equation of the line in slope-intercept form.

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 25

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experiment is a success. Find the probability of success.

Correct A. 1/2

B. 1/3

C. 2/3

D. 3/4

Correct Answer: A

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