Exam Body

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

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Question 1

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

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

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

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

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

Correct Answer: A

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Question 2

A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?

A. \[ P\( \text{multiple of 3} \) = \frac{1}{3} \]

Correct B. \[ P\( \text{multiple of 3} \) = \frac{2}{6} \]

C. \[ P\( \text{multiple of 3} \) = \frac{1}{2} \]

D. \[ P\( \text{multiple of 3} \) = \frac{3}{6} \]

Correct Answer: B

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Question 3

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

Correct A. \[ x < -1 \text{ or } x > \frac{3}{2} \]

B. \[ x < -1 \text{ or } x < \frac{3}{2} \]

C. \[ x > -1 \text{ or } x > \frac{3}{2} \]

D. \[ x < -1 \text{ and } x > \frac{3}{2} \]

Correct Answer: A

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Question 4

Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{bmatrix} \).

Correct A. \[ 10 \]

B. \[ -10 \]

C. \[ 20 \]

D. \[ -20 \]

Correct Answer: A

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Question 5

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. \[ A = 16\pi \text{ cm}^2 \]

B. \[ A = 32\pi \text{ cm}^2 \]

C. \[ A = 64\pi \text{ cm}^2 \]

D. \[ A = 128\pi \text{ cm}^2 \]

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. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 7

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 8

Find the value of \( \log_{10} \( x^2 \ \) ) given that \( \log_{10} x = 2 \).

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 9

A particle moves in a straight line with a velocity ( v(t) = 2t + 5 ) m/s. Find the displacement of the particle from \( t = 0 \) to \( t = 3 \) seconds.

A. 21

B. 25

Correct C. 30

D. 35

Correct Answer: C

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Question 10

Solve the system of equations: \( x + y = 4 \) and \( xy = 5 \).

Correct A. 1, 3

B. 2, 2

C. 3, 1

D. 4, 0

Correct Answer: A

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Question 11

Let ( X ) and ( Y ) be indep\endent random variables with probability density functions \( f_X\( x \ \) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ) and \( f_Y\( y \ \) = egin{cases} 3y^2 & 0 leq y leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that \( X + Y leq 1 \).

Correct A. \( \frac{1}{2} \)

B. \( \frac{1}{3} \)

C. \( \frac{2}{3} \)

D. \( \frac{3}{4} \)

Correct Answer: A

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Question 12

Solve the inequality \( \log_{10} \( x^2 \ \) > 2 ).

Correct A. \( x > 10 \)

B. \( x < 10 \)

C. \( x > 100 \)

D. \( x < 100 \)

Correct Answer: A

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Question 13

Find the area under the curve \( y = \sin x \) from \( x = 0 \) to \( x = \frac{pi}{2} \).

Correct A. ( 1 )

B. \( \frac{1}{2} \)

C. \( \frac{pi}{2} \)

D. \( \frac{pi}{4} \)

Correct Answer: A

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Question 14

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

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

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

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

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

Correct Answer: A

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Question 15

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 16

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

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 17

Solve the system of equations: \( 2x + 3y = 7 \) and \( x - 2y = -3 \).

Correct A. x = 1, y = 2

B. x = 2, y = 1

C. x = 3, y = 4

D. x = 4, y = 3

Correct Answer: A

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Question 18

Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} \).

A. 0

Correct B. 2

C. 4

D. 6

Correct Answer: B

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Question 19

Find the sum of the infinite geometric series \( 1 + \frac{1}{2} + \frac{1}{4} + \cdots \).

Correct A. 2

B. 4

C. 6

D. 8

Correct Answer: A

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Question 20

Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

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Question 21

Solve the inequality \( \frac{x}{x-1} > 1 \) for \( x > 1 \).

Correct A. x > 2

B. x > 3

C. x > 4

D. x > 5

Correct Answer: A

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Question 22

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 = 25

C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49

Correct Answer: A

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Question 23

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \), with initial term \( a_1 = 3 \). Find the sum of the first five terms of the sequence.

Correct A. 3 + 7 + 15 + 31 + 63

B. 3 + 5 + 11 + 23 + 47

C. 3 + 7 + 15 + 31 + 63

D. 3 + 5 + 11 + 23 + 47

Correct Answer: A

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Question 24

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{2}{\( x^2 + 1 \)^2}

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

Correct Answer: A

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Question 25

Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ).

A. x = \frac{pi}{2}

Correct B. x = \frac{pi}{4}

C. x = \frac{3pi}{4}

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

Correct Answer: B

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