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POST UTME OSUSTECH 2019 Mathematics | Objective

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Question 1 View Details

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 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{x^2}\)\)\) ) using 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 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using 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 View Details

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 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 2\) using 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 View Details

A rectangular 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Let X and Y be independent 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 View Details

A histogram of exam scores has a mean of 75 and a standard 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 View Details

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

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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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