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POST UTME KSU 2018 Mathematics | Objective

Are you preparing for POST UTME KSU 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.

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Question 1

Determine the value of \( int_{0}^{1} \frac{1}{x^2 + 1} dx \) u\sing the method of substitution.

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{6}

D. \frac{\pi}{8}

Correct Answer: A

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Question 2

A circle has equation \( x - 1 \ \)^2 + \( y - 2 \)^2 = 4 ). Find the equation of the \tangent line at point ( (3, 5) ).

Correct A. y = -\frac{1}{2}x + \frac{13}{2}

B. y = \frac{1}{2}x + \frac{13}{2}

C. y = -\frac{1}{2}x + \frac{9}{2}

D. y = \frac{1}{2}x + \frac{9}{2}

Correct Answer: A

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Question 3

A random variable ( X ) has probability distribution \( P\( X = 1 \ \) = \frac{1}{2} ) and \( P\( X = 2 \ \) = \frac{1}{2} ). Find the probability that ( X ) is greater than 1.

A. \frac{1}{2}

B. \frac{1}{4}

Correct C. \frac{3}{4}

D. \frac{1}{4} + \frac{1}{2}

Correct Answer: C

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Question 4

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

Correct A. f'(x) = \frac{-2x}{\( x^2 + 1 \)^2}

B. f'(x) = \frac{2x}{\( x^2 + 1 \)^2}

C. f'(x) = \frac{-2}{\( x^2 + 1 \)^2}

D. f'(x) = \frac{2}{\( x^2 + 1 \)^2}

Correct Answer: A

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Question 5

Solve the inequality \( 2^x + 2^{x+1} > 2^{x+2} \).

A. x < -2

Correct B. x > -2

C. x < -1

D. x > -1

Correct Answer: B

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Question 6

Find the volume of the solid formed by revolving the region bounded by the curve \( y = \frac{1}{2}x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.

Correct A. \( \frac{16pi}{3} \)

B. \( \frac{32pi}{3} \)

C. \( \frac{64pi}{3} \)

D. \( \frac{128pi}{3} \)

Correct Answer: A

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Question 7

Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. \( x = 10^2 \)

Correct B. \( x = 10^4 \)

C. \( x = 10^{-4} \)

D. \( x = 10^{-2} \)

Correct Answer: B

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Question 8

Find the area of the triangle formed by the points ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).

A. ( 6 )

B. ( 12 )

Correct C. ( 18 )

D. ( 24 )

Correct Answer: C

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Question 9

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. \( x = -1, y = 3 \)

Correct Answer: A

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Question 10

Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. ( 0 )

B. ( 1 )

C. \( -1 \)

D. ( 2 )

Correct Answer: A

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Question 11

Solve the inequality \( \frac{x-2}{x+1} > 0 \) for \( x in \( -infty, -1 \ \) cup \( -1, 2 \) cup (2, infty) ).

Correct A. \( x < -1 \) or \( x > 2 \)

B. \( x > -1 \) and \( x < 2 \)

C. \( x < -1 \) or \( x = 2 \)

D. \( x > -1 \) and \( x > 2 \)

Correct Answer: A

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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

Solve the equation \( 2^x + 2^{x+1} = 2^{x+2} + 2^{x+3} \).

Correct A. \( x = -1 \)

B. \( x = 0 \)

C. \( x = 1 \)

D. \( x = 2 \)

Correct Answer: A

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Question 14

Find the value of \( sum_{n=1}^{10} n^2 \).

A. ( 385 )

Correct B. ( 3850 )

C. ( 38500 )

D. ( 385000 )

Correct Answer: B

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Question 15

Solve the inequality \( \frac{x-1}{x+2} leq 0 \) for \( x in \( -infty, -2 \ \) cup \( -2, 1 \) cup (1, infty) ).

Correct A. \( x < -2 \) or \( x > 1 \)

B. \( x > -2 \) and \( x < 1 \)

C. \( x < -2 \) or \( x = 1 \)

D. \( x > -2 \) and \( x > 1 \)

Correct Answer: A

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Question 16

Determine the mean of the following dataset: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. If the mean is increased by 2, what is the new mean?

A. 22

Correct B. 24

C. 26

D. 28

Correct Answer: B

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Question 17

A circle has a diameter of 10 cm. If a chord is drawn from the center of the circle to a point on the circumference, what is the length of the chord?

A. 5 cm

Correct B. 7.07 cm

C. 10 cm

D. 15 cm

Correct Answer: B

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Question 18

Solve the inequality: 2x^2 + 5x - 3 > 0. What is the solution set?

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 19

Find the sum of the first 10 terms of the arithmetic progression: 2, 5, 8, 11, ...

A. 55

B. 60

Correct C. 65

D. 70

Correct Answer: C

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Question 20

A random experiment has two indep\endent events: A and B. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?

A. 0.24

Correct B. 0.36

C. 0.48

D. 0.60

Correct Answer: B

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Question 21

Determine the mean of the following dataset: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 6

B. 8

C. 10

Correct D. 12

Correct Answer: D

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Question 22

Find the area under the curve of the function ( f(x) = \frac{1}{x} ) from \( x = 1 \) to \( x = 2 \).

Correct A. 0.693

B. 0.693

C. 0.693

D. 0.693

Correct Answer: A

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Question 23

Solve the system of equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).

Correct A. x = 1, y = 2

B. x = 2, y = 3

C. x = 3, y = 4

D. x = 4, y = 5

Correct Answer: A

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Question 24

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

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 25

Convert the \fraction \( \frac{3}{4} \) to its equivalent in base 8.

A. 3

B. 4

C. 5

Correct D. 6

Correct Answer: D

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