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POST UTME OSUSTECH 2017 Mathematics | Objective

Are you preparing for POST UTME OSUSTECH exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Let X be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.

Correct A. \( int_{0.5}^{1} 2x , dx \)

B. \( int_{0}^{0.5} 2x , dx \)

C. \( int_{0}^{1} 2x , dx \)

D. \( int_{0}^{1} 2x^2 , dx \)

Correct Answer: A

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Question 2

Find the derivative of the function ( 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{1}{\( x^2 + 1 \)^2} )

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

Correct Answer: A

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Question 3

A histogram of exam scores has a mean of 80 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 90.

Correct A. \( P\( X > 90 \ \) = 0.1587 )

B. \( P\( X > 90 \ \) = 0.8413 )

C. \( P\( X > 90 \ \) = 0.5 )

D. \( P\( X > 90 \ \) = 0.25 )

Correct Answer: A

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Question 4

Solve the system of equations u\sing matrices: \( egin{cases} 2x + 3y = 7 \ x - 2y = -3 \end{cases} \).

Correct A. \( egin{pmatrix} x \ y \end{pmatrix} = egin{pmatrix} 19/7 \ 2/7 \end{pmatrix} \)

B. \( egin{pmatrix} x \ y \end{pmatrix} = egin{pmatrix} 2/7 \ 19/7 \end{pmatrix} \)

C. \( egin{pmatrix} x \ y \end{pmatrix} = egin{pmatrix} 7/19 \ 2/19 \end{pmatrix} \)

D. \( egin{pmatrix} x \ y \end{pmatrix} = egin{pmatrix} 2/19 \ 7/19 \end{pmatrix} \)

Correct Answer: A

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Question 5

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

Correct A. \( V = \frac{8}{15} pi \)

B. \( V = \frac{8}{3} pi \)

C. \( V = \frac{4}{3} pi \)

D. \( V = \frac{16}{5} pi \)

Correct Answer: A

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Question 6

Find the equation of the circle with center at ((2,3)) and radius 4.

Correct A. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )

B. \( x-2 \ \)^2 + \( y-3 \)^2 = 32 )

C. \( x-2 \ \)^2 + \( y-3 \)^2 = 64 )

D. \( x-2 \ \)^2 + \( y-3 \)^2 = 256 )

Correct Answer: A

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Question 7

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

A. \( x = -1 \)

B. \( x = 0 \)

Correct C. \( x = 1 \)

D. \( x = 2 \)

Correct Answer: C

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Question 8

A fair six-sided die is rolled. What is the probability that the number rolled is even?

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

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

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

D. \( \frac{5}{6} \)

Correct Answer: A

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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. ( 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 10

A vector (mathbf{a}) has magnitude 5 and direction \( 30^circ \) counterclockwise from the positive x-axis. Find the vector (mathbf{a} cdot mathbf{b}) if \( mathbf{b} = egin{pmatrix} 2 \ 3 \end{pmatrix} \).

Correct A. ( 11 )

B. ( 13 )

C. ( 15 )

D. ( 17 )

Correct Answer: A

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Question 11

Find the value of x in the equation \( \frac{1}{x} + \frac{1}{2x} = \frac{3}{4x} \).

Correct A. 4

B. 2

C. 1

D. 0.5

Correct Answer: A

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Question 12

A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 13

A curve is defined by the equation \( y = x^2 - 4x + 3 \). Find the x-coordinate of the vertex of the curve.

Correct A. 2

B. 3

C. 4

D. 5

Correct Answer: A

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Question 14

A solid is formed by rotating the region bounded by the curve \( y = x^2 \) and the x-axis about the x-axis. Find the volume of the solid.

A. π/2

Correct B. π

C. 2π

D. 3π

Correct Answer: B

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Question 15

A triangle has sides of length 3, 4, and 5. Find the area of the triangle.

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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Question 16

Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the value of \( lim_{x \to 2} f\( x \ \) ).

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 17

A histogram of exam scores is shown below. If the mean score is 60, find the value of ( sigma ).

A. 5

B. 10

Correct C. 15

D. 20

Correct Answer: C

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Question 18

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

A. 0

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

C. \frac{\pi}{2}

D. \frac{3\pi}{4}

Correct Answer: B

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Question 19

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

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

B. \( x - 3 \)^2 + \( y - 4 \)^2 = 30

C. \( x - 3 \)^2 + \( y - 4 \)^2 = 35

D. \( x - 3 \)^2 + \( y - 4 \)^2 = 40

Correct Answer: A

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Question 20

Solve the inequality \( \frac{x - 2}{x + 1} > 0 \).

Correct A. \( -\infty, -1 \) \cup \( 2, \infty \)

B. \( -\infty, -1 \) \cup (1, 2)

C. \( -\infty, -1 \) \cup \( 2, \infty \)

D. \( -\infty, -1 \) \cup (1, 2)

Correct Answer: A

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Question 21

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

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

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

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

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

Correct Answer: A

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Question 22

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 23

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.

Correct A. \( x = -2 \)

B. \( x = -3 \)

C. \( x = 2 \)

D. \( x = 3 \)

Correct Answer: A

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Question 24

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 25

A box contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball first and then a blue ball?

A. \( \frac{1}{4} \)

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

Correct C. \( \frac{3}{4} \)

D. \( \frac{5}{6} \)

Correct Answer: C

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