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POST UTME UNIBEN 2017 Mathematics | Objective

Prepare for your exams with POST UTME UNIBEN questions? Reviewing past/model 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 View Details

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

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

B. ( 3 )

C. ( 4 )

D. ( 6 )

Correct Answer: A

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Question 2 View Details

A set of 10 numbers has a mean of 20 and a standard deviation of 5. What is the probability that a randomly selected number from this set will be greater than 25?

A. 0.25

B. 0.5

Correct C. 0.75

D. 0.9

Correct Answer: C

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Question 3 View Details

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

Correct A. \(x < -1\) or \(x > 3\)

B. \(x < -3\) or \(x > 1\)

C. \(x < -2\) or \(x > 2\)

D. \(x < -4\) or \(x > 4\)

Correct Answer: A

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Question 4 View Details

Find the sum of the first 10 terms of the geometric series \(2 + 6 + 18 + ldots\).

A. \(2 + 6 + 18 + ldots + 972\)

B. \(2 + 6 + 18 + ldots + 1024\)

Correct C. \(2 + 6 + 18 + ldots + 1026\)

D. \(2 + 6 + 18 + ldots + 1028\)

Correct Answer: C

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Question 5 View Details

A polynomial function has a degree of 4 and has zeros at \(x = -2\), \(x = 1\)\), and \(x = 3\). Find the polynomial function.

A. \(x + 2\), x - 1\)\(x - 3 \\) )

Correct B. \(x + 2\), x - 1\)\(x - 3\), x + 1 \\) )

C. \(x + 2\), x - 1\)\(x - 3\), x - 4 \\) )

D. \(x + 2\), x - 1\)\(x - 3\), x + 4 \\) )

Correct Answer: B

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Question 6 View Details

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

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

B. \(-\infty, 2\) \cap \(2, \infty\)

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

D. \(-\infty, 2\) \cap \(2, \infty\)

Correct Answer: A

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Question 7 View Details

Find the value of ( x ) in the equation \(2x^2 + 5x - 3 = 0\) using the quadratic formula.

Correct A. -\(\frac{5}{4}\)\)

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

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

D. \(\frac{5}{4}\)\)

Correct Answer: A

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Question 8 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. What is the z-score of a score of 70?

A. 0.5

B. 1.0

Correct C. 1.5

D. 2.0

Correct Answer: C

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Question 9 View Details

Find the derivative of the function ( f(x) = \(3x^2 + 2x - 5\) ) using the power rule.

Correct A. 6x + 2

B. 6x - 2

C. \(3x^2 + 2\)

D. \(3x^2 - 2\)

Correct Answer: A

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Question 10 View Details

A circle has a radius of 4 cm. What is the area of the circle?

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 11 View Details

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

Correct A. \(x =\)\(\frac{\pi}{4}\)\)

B. \(x =\)\(\frac{3\pi}{4}\)\)

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

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

Correct Answer: A

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Question 12 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using 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'\((x) =\)\(\frac{-1}{x^2 + 1\) ^2}\)\)

Correct Answer: A

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Question 13 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\) using the quadratic formula.

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 14 View Details

Find the mean and standard deviation of the data set {1, 2, 3, 4, 5} using the formulas \(\bar{x} = \frac{\(1x_i}{n}\) and \(s = \sqrt{\frac{\)1x_i - \bar{x} \\\()^2}{n - 1}}\) ).

Correct A. \bar{x}\(= 3\), \(s = 1.414\)

B. \bar{x}\(= 3\), \(s = 1.732\)

C. \bar{x}\(= 2\), \(s = 1.414\)

D. \bar{x}\(= 2\), \(s = 1.732\)

Correct Answer: A

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Question 15 View Details

Graph the function (y = \(1x\) over the interval \([0, 2\\((y =\)1x) over the interval \pi]\) using the unit circle.

A. A graph of the function y = \sin x over the interval [0, 2π] showing the unit circle.

B. A graph of the function y = \sin x over the interval [0, 2π] showing the \sine wave.

Correct C. A graph of the function y = \sin x over the interval [0, 2π] showing the unit circle and the \sine wave.

D. A graph of the function y = \sin x over the interval [0, 2π] showing only the unit circle.

Correct Answer: C

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Question 16 View Details

If ( f(x) = \(\frac{1}{x^2 + 1}\)\)) ), find lim_{x \to infty} f\( x \\() ), find lim_{x to infty} f\ ).

Correct A. 0

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

C. \(\frac{1}{\infty}\)\)

D. \(\frac{\infty}{\infty}\)\)

Correct Answer: A

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Question 17 View Details

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

Correct A. \(-\infty, -1\) \cup \(3, \infty\)

B. \(-\infty, -3\) \cup \(1, \infty\)

C. \(-\infty, 1\) \cup \(3, \infty\)

D. \(-\infty, -3\) \cup \(1, \infty\)

Correct Answer: A

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Question 18 View Details

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

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

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

Correct C. \(\frac{2}{5}\)\)

D. \(\frac{3}{5}\)\)

Correct Answer: C

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Question 19 View Details

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

Correct A. \(\frac{32\pi}{5}\)\)

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

C. \(\frac{8\pi}{3}\)\)

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

Correct Answer: A

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Question 20 View Details

If ( f(x) = \sin x ), find ( f'(x) ).

Correct A. \cos x

B. \sin x

C. \tan x

D. \csc x

Correct Answer: A

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Question 21 View Details

Find the derivative of the function ( f(x) = \(\frac{x^2 + 2x - 3}{x^2 - 4}\)\)\) ) using the quotient rule.

A. \(\frac{x^2 - 4\) 2x + 2 \ - \(x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

B. \(\frac{x^2 - 4\) 2x + 2 \ + \(x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

Correct C. \(\frac{x^2 - 4\) 2x + 2 \ - \(x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

D. \(\frac{x^2 - 4\) 2x + 2 \ + \(x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

Correct Answer: C

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Question 22 View Details

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

Correct A. \(x < -\frac{5}{4}\) or \(x > \frac{3}{2}\)

B. \(x > -\frac{5}{4}\) or \(x < \frac{3}{2}\)

C. \(x < -\frac{5}{4}\) or \(x < \frac{3}{2}\)

D. \(x > -\frac{5}{4}\) or \(x > \frac{3}{2}\)

Correct Answer: A

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Question 23 View Details

Find the sum of the first 10 terms of the arithmetic progression ( 2, 5, 8, ldots ).

Correct A. ( 55 )

B. ( 65 )

C. ( 75 )

D. ( 85 )

Correct Answer: A

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Question 24 View Details

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

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

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

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

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

Correct Answer: B

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Question 25 View Details

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