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POST UTME OSUSTECH 2019 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 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

A. 6

B. 8

C. 10

Correct D. 12

Correct Answer: D

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Question 2

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

Correct A. ( f'(x) = -\frac{2}{x^3} )

B. ( f'(x) = \frac{2}{x^3} )

C. ( f'(x) = -\frac{1}{x^3} )

D. ( f'(x) = \frac{1}{x^3} )

Correct Answer: A

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Question 3

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

Correct A. \( x = -2, -3 \)

B. \( x = 2, 3 \)

C. \( x = -3, 2 \)

D. \( x = 3, -2 \)

Correct Answer: A

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Question 4

A histogram is shown below. If the area under the curve is 20, what is the value of ( x )?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 5

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.

Correct A. \( \frac{8}{3} \)

B. \( \frac{16}{3} \)

C. \( \frac{24}{3} \)

D. \( \frac{32}{3} \)

Correct Answer: A

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Question 6

A rec\tangular box has dimensions 5cm x 8cm x 10cm. Find the volume of the box in cubic centimeters.

A. 40

B. 50

Correct C. 60

D. 80

Correct Answer: C

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Question 7

Solve for x in the equation \( 2^x = 32 \).

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 8

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

Correct A. 50.24

B. 50.27

C. 50.31

D. 50.35

Correct Answer: A

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Question 9

A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a different score range. The heights of the bars are 8, 12, 15, 10, and 5 units, respectively. Find the mean score of the class.

A. 12

Correct B. 13

C. 14

D. 15

Correct Answer: B

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Question 10

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

A. y = 1x + 1

Correct B. y = 2x + 1

C. y = 3x + 1

D. y = 4x + 1

Correct Answer: B

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Question 11

Let X and Y be indep\endent random variables with means 2 and 3, respectively. If E(XY) = 7, find the variance of X + Y.

Correct A. 10

B. 12

C. 15

D. 20

Correct Answer: A

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Question 12

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is between 60 and 90.

A. 0.9772

Correct B. 0.9849

C. 0.9915

D. 0.9986

Correct Answer: B

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Question 13

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

A. \frac{32\pi}{5}

Correct B. \frac{64\pi}{5}

C. \frac{128\pi}{5}

D. \frac{256\pi}{5}

Correct Answer: B

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Question 14

Let A = {1, 2, 3, 4, 5} and B = {2, 3, 4, 5, 6}. Find the number of elements in the set A \cup B.

A. 5

B. 6

C. 7

Correct D. 8

Correct Answer: D

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Question 15

Find the sum of the first 10 terms of the geometric series 2x^2 + 4x^3 + 8x^4 + ...

A. 2048x^{10}

B. 4096x^{10}

Correct C. 8192x^{10}

D. 16384x^{10}

Correct Answer: C

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Question 16

Find the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 8

B. 10

Correct C. 12

D. 14

Correct Answer: C

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Question 17

Solve the quadratic equation: x^2 + 5x + 6 = 0

A. -2

Correct B. -3

C. 1

D. 2

Correct Answer: B

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Question 18

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 19

Solve the inequality: 2x^2 + 5x - 3 > 0

Correct A. x < -1 or x > 3/2

B. x > -1 or x < 3/2

C. x < 3/2 or x > -1

D. x > 3/2 or x < -1

Correct Answer: A

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Question 20

Find the derivative of the function: f(x) = 3x^2 + 2x - 5

Correct A. 6x + 2

B. 3x^2 + 2

C. 2x - 5

D. x^2 + 2x

Correct Answer: A

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Question 21

Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 22

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

Correct A. y = \frac{1}{2} x^2 + 3x - 1

B. y = \frac{1}{2} x^2 + 3x + 1

C. y = \frac{1}{2} x^2 - 3x - 1

D. y = \frac{1}{2} x^2 - 3x + 1

Correct Answer: A

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Question 23

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 24

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 25

Find the area under the curve \( y = x^2 \) from x = 0 to x = 4.

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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