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POST UTME SKYLINE UNIVERSITY 2024 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 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

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

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

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

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

Correct Answer: B

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Question 2

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{5}{4} $ or $ x < \frac{3}{2} $

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

Correct Answer: A

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Question 3

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

Correct A. $ \frac{pi}{4} $

B. $ \frac{pi}{2} $

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

D. $ \frac{pi}{6} $

Correct Answer: A

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Question 4

Find the determinant of the matrix $ egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} $.

Correct A. ( 2 )

B. $ -2 $

C. ( 0 )

D. ( 1 )

Correct Answer: A

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Question 5

Solve the system of equations $ egin{cases} x + y = 2 \ 2x - y = 3 \end{cases} $.

Correct A. $ x = 1, y = 1 $

B. $ x = 2, y = 0 $

C. $ x = 0, y = 2 $

D. $ x = 1, y = 2 $

Correct Answer: A

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Question 6

Find the value of k such that the equation $ x^2 + kx + 16 = 0 $ has exactly one solution.

A. 4

Correct B. -4

C. 8

D. -8

Correct Answer: B

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Question 7

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

Correct A. 78.5

B. 31.4

C. 314

D. 785

Correct Answer: A

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Question 8

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

Correct A. x > 4

B. x < 4

C. x > 1

D. x < 1

Correct Answer: A

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Question 9

A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. Find the average speed for the round trip.

A. 48

Correct B. 52

C. 56

D. 60

Correct Answer: B

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Question 10

Solve the equation $ x^2 - 4x + 4 = 0 $.

Correct A. x = 2

B. x = 1

C. x = 0

D. x = -2

Correct Answer: A

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Question 11

Solve for x in the equation $ \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2} $.

A. $ x = -1 \ $

Correct B. $ x = 2 \ $

C. $ x = -2 \ $

D. $ x = 1 \ $

Correct Answer: B

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Question 12

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

Correct A. $ \frac{32}{3} \pi \ $

B. $ \frac{64}{3} \pi \ $

C. $ \frac{16}{3} \pi \ $

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

Correct Answer: A

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Question 13

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 14

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 = 4 \)

C. $ x - 2 \ $^2 + $ y - 3 $^2 = 9 \)

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

Correct Answer: A

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Question 15

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).

Correct A. $ 6 \ $

B. $ 12 \ $

C. $ 18 \ $

D. $ 24 \ $

Correct Answer: A

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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. 32\pi cm^3

B. 64\pi cm^3

Correct C. 96\pi cm^3

D. 128\pi cm^3

Correct Answer: C

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Question 17

Evaluate the definite integral \int_0^1 x^2 \sin x dx.

A. -1

Correct B. 0

C. 1

D. 2

Correct Answer: B

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Question 18

Solve the inequality x^2 - 4x - 5 > 0.

Correct A. $ -\infty, -1 $ \cup $ 5, \infty $

B. $ -\infty, -5 $ \cup $ 0, \infty $

C. $ -\infty, 1 $ \cup $ 5, \infty $

D. $ -\infty, -1 $ \cup $ 0, \infty $

Correct Answer: A

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Question 19

Express the number 240 in base 8.

A. 360

Correct B. 400

C. 420

D. 440

Correct Answer: B

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Question 20

Find the vector projection of \vec{a} = 2\hat{i} + 3\hat{j} onto \vec{b} = \hat{i} + \hat{j}.

Correct A. \frac{5}{2}\hat{i} + \frac{5}{2}\hat{j}

B. \frac{5}{3}\hat{i} + \frac{5}{3}\hat{j}

C. \frac{5}{4}\hat{i} + \frac{5}{4}\hat{j}

D. \frac{5}{6}\hat{i} + \frac{5}{6}\hat{j}

Correct Answer: A

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Question 21

Determine the value of $x$ in the equation [ 2x + 5 = 11 ].

Correct A. 4

B. 5

C. 6

D. 7

Correct Answer: A

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Question 22

A cylindrical \tank has a height of 10m and a radius of 4m. If the \tank is filled with water to a height of 6m, calculate the volume of water in the \tank.

A. 1200\pi

Correct B. 1500\pi

C. 1800\pi

D. 2000\pi

Correct Answer: B

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Question 23

Solve the inequality [ 2x - 5 > 3x + 2 \].

A. x < -1

Correct B. x > -1

C. x < 1

D. x > 1

Correct Answer: B

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Question 24

A car travels from city A to city B at an average speed of 60km/h and returns at an average speed of 40km/h. If the dis\tance between the two cities is 240km, calculate the average speed for the entire trip.

A. 48

B. 50

Correct C. 52

D. 54

Correct Answer: C

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Question 25

A right-angled triangle has a hypotenuse of length 10cm and one of the other sides has a length of 6cm. Calculate the length of the third side.

A. 8cm

B. 10cm

Correct C. 12cm

D. 14cm

Correct Answer: C

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