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POST UTME UNIOSUN 2018 Mathematics | Objective

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Question 1 View Details

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

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

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

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

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

Correct Answer: A

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Question 2 View Details

A set of 10 students scored the following marks in a mathematics test: 85, 90, 78, 92, 88, 76, 95, 89, 91, 84. Calculate the mean and standard deviation of the scores.

Correct A. Mean: 87.5, Standard Deviation: 5.5

B. Mean: 88.5, Standard Deviation: 6.5

C. Mean: 89.5, Standard Deviation: 7.5

D. Mean: 90.5, Standard Deviation: 8.5

Correct Answer: A

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Question 3 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9} > 0\).

Correct A. x in \(-\infty, -3 \ cup -3, 2\) cup (2, infty) )

B. x in \( -infty, -3 \ cup (2, infty) )

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

D. x in \( -infty, -3 \ cup (2, infty) )

Correct Answer: A

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Question 4 View Details

A geometric sequence has first term \(a = 2\) and common ratio \(r = 3\). Find the sum of the first 5 terms.

Correct A. \(2 + 6 + 18 + 54 + 162 = 242\)

B. \(2 + 6 + 18 + 54 + 162 = 242\)

C. \(2 + 6 + 18 + 54 + 162 = 242\)

D. \(2 + 6 + 18 + 54 + 162 = 242\)

Correct Answer: A

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Question 5 View Details

A histogram of exam scores is shown below. What is the mode of the scores?

Correct A. 60

B. 70

C. 80

D. 90

Correct Answer: A

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Question 6 View Details

Find the value of \(\frac{d}{dx}\left \frac{1}{x^2}\right\)\).

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

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

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

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

Correct Answer: A

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Question 7 View Details

Solve the inequality \(\log_2 x-1\)\(> 2\)\).

Correct A. \(4, \infty\)

B. \(2, \infty\)

C. \(1, \infty\)

D. \(0, \infty\)

Correct Answer: A

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Question 8 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 9 View Details

A set \(A\) contains \(5\) elements, and a set \(B\) contains \(3\) elements. What is the number of elements in the set \(A \cup B\)?

A. 8

Correct B. 7

C. 6

D. 5

Correct Answer: B

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Question 10 View Details

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

A. 30

Correct B. 35

C. 40

D. 45

Correct Answer: B

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Question 11 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 104,783

B. 104,783

C. 104,783

D. 104,783

Correct Answer: A

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Question 12 View Details

Solve the inequality \(\frac{x^2 - 4}{x + 2}\)\)\\() > 0.\)

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

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

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

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

Correct Answer: A

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Question 13 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 + \(y - 3\)^\(2 = 25\)

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

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

Correct Answer: A

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Question 14 View Details

Evaluate the definite integral \int_\(0^1\) \(x^2\) dx.

Correct A. \(\frac{1}{3}\)\)

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

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

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

Correct Answer: A

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Question 15 View Details

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

Correct A. 6x + 2

B. 6x + 2

C. 6x + 2

D. 6x + 2

Correct Answer: A

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Question 16 View Details

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

Correct A. \(\frac{1}{6}\)\)\(4^3 + 12 \cdot 4^2 - 8 \cdot 4\) + 3 cdot \(4^2 - 2\) cdot 4

B. \(\frac{1}{6}\)\)\(4^3 + 12 \cdot 4^2 - 8 \cdot 4\) + 3 cdot \(4^2 - 2\) cdot 4 + 2

C. \(\frac{1}{6}\)\)\(4^3 + 12 \cdot 4^2 - 8 \cdot 4\) + 3 cdot \(4^2 - 2\) cdot 4 - 2

D. \(\frac{1}{6}\)\)\(4^3 + 12 \cdot 4^2 - 8 \cdot 4\) + 3 cdot \(4^2 - 2\) cdot 4 + 4

Correct Answer: A

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Question 17 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.

Correct A. 6 cdot 4 cdot 3

B. 6 cdot 4 cdot 3 + 2

C. 6 cdot 4 cdot 3 - 2

D. 6 cdot 4 cdot 3 + 4

Correct Answer: A

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Question 18 View Details

Solve the inequality \(|x - 2| \geq 3\).

Correct A. x leq -1 \text{ or } x geq 5

B. x leq 1 \text{ or } x geq 5

C. x leq -1 \text{ or } x geq 4

D. x leq -1 \text{ or } x geq 3

Correct Answer: A

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Question 19 View Details

Find the determinant of the matrix [egin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{pmatrix}].

Correct A. 2 cdot \(2 \cdot 2 - 1 \cdot 1\) - 1 cdot \(4 \cdot 2 - 1 \cdot 3\) + 3 cdot \(4 \cdot 1 - 2 \cdot 3\)

B. 2 cdot \(2 \cdot 2 - 1 \cdot 1\) - 1 cdot \(4 \cdot 2 - 1 \cdot 3\) - 3 cdot \(4 \cdot 1 - 2 \cdot 3\)

C. 2 cdot \(2 \cdot 2 - 1 \cdot 1\) + 1 cdot \(4 \cdot 2 - 1 \cdot 3\) + 3 cdot \(4 \cdot 1 - 2 \cdot 3\)

D. 2 cdot \(2 \cdot 2 - 1 \cdot 1\) + 1 cdot \(4 \cdot 2 - 1 \cdot 3\) - 3 cdot \(4 \cdot 1 - 2 \cdot 3\)

Correct Answer: A

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Question 20 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 + \(y - 3\)^\(2 = 4\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 9\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 25\)

Correct Answer: A

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Question 21 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pi \(cm^3\)

Correct B. 48\pi \(cm^3\)

C. 64\pi \(cm^3\)

D. 96\pi \(cm^3\)

Correct Answer: B

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Question 22 View Details

A circle passes through the points (2, 3) and (4, 5). Find the equation of the circle.

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

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

C. \(x - 4\)^2 + \(y - 5\)^\(2 = 25\)

D. \(x - 3\)^2 + \(y - 5\)^\(2 = 25\)

Correct Answer: B

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Question 23 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 > -1 or \(x < 3/2\)\)

D. x > -1 or \(x > 3/2\)\)

Correct Answer: A

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Question 24 View Details

Find the mean of the following data: 2, 4, 6, 8, 10.

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 25 View Details

A polynomial function f(x) has zeros at x = -2, \(x = 1\), and \(x = 3\). Write the function in factored form.

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

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

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

D. \(f(x) = a\)\(x + 2\), x - 1\)\(x - 3\) + 2

Correct Answer: B

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