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POST UTME RSU 2019 Mathematics | Objective

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Question 1 View Details

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

Correct A. 40

B. 42

C. 44

D. 46

Correct Answer: A

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Question 2 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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Question 3 View Details

Find the value of ( x ) in the equation \(x^3 - 6x^2 + 11x - 6 = 0\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 4 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \(1/6\)

B. \(1/3\)

C. \(1/2\)

Correct D. \(2/3\)

Correct Answer: D

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Question 5 View Details

In the circuit below, what is the equivalent resistance between points A and B?

A. 2Ω

B. 4Ω

Correct C. 6Ω

D. 8Ω

Correct Answer: C

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Question 6 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. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 7 View Details

A die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. \(1/6\)

B. \(1/3\)

Correct C. \(1/2\)

D. \(2/3\)

Correct Answer: C

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Question 8 View Details

Find the derivative of the function f(x) = \(2x^2 + 3x - 1\) / \(x^2 - 4x + 3\) using the quotient rule.

Correct A. \(4x + 3\) / \(x^2 - 4x + 3\)²

B. \(4x + 3\) / \(x^2 - 4x + 3\)

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

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

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 union of sets A and B?

A. 8

Correct B. 10

C. 12

D. 15

Correct Answer: B

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Question 10 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio \(1/2\).

A. 1.9375

B. 1.96875

Correct C. 1.984375

D. 2.000000

Correct Answer: C

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Question 11 View Details

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

A. 40

B. 60

Correct C. 80

D. 100

Correct Answer: C

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Question 12 View Details

Solve the matrix equation \(\begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 4 \end{bmatrix}\).

Correct A. \begin{bmatrix} 1 \ 1 \end{bmatrix}

B. \begin{bmatrix} 2 \ 2 \end{bmatrix}

C. \begin{bmatrix} 3 \ 3 \end{bmatrix}

D. \begin{bmatrix} 4 \ 4 \end{bmatrix}

Correct Answer: A

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Question 13 View Details

Find the equation of the line passing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. \(y = x + 1\)

B. \(y = x - 1\)

C. \(y = 2x - 1\)

D. \(y = 2x + 1\)

Correct Answer: A

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Question 14 View Details

Find the area of the circle \(x^2 + y^2 = 4\).

Correct A. 4\pi

B. 8\pi

C. 16\pi

D. 32\pi

Correct Answer: A

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Question 15 View Details

Solve the system of equations \(x + y = 4\) and \(x - y = 2\).

Correct A. \begin{bmatrix} 3 \ 1 \end{bmatrix}

B. \begin{bmatrix} 1 \ 3 \end{bmatrix}

C. \begin{bmatrix} 2 \ 2 \end{bmatrix}

D. \begin{bmatrix} 4 \ 0 \end{bmatrix}

Correct Answer: A

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Question 16 View Details

Solve the inequality (\(\frac{\(x^2 - 4x - 5}{x + 1}\)\(> 0\)\) for x in \\((frac{\(x^2 - 4x - 5}{x + 1}\)\(> 0\)\(-infty\), infty \ ).

Correct A. \(-\infty, -1\) \cup (5, infty)

B. \(-\infty, -1\) \cup \(-1, 5\)

C. \(-\infty, 5\)

D. (5, infty)

Correct Answer: A

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Question 17 View Details

Find the area under the curve \(y = \sin^2 x\) from \(x = 0\) to \(x = \frac{\pi}{2}\).

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

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

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

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

Correct Answer: A

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Question 18 View Details

Solve the system of equations \(x^2 + y^2 = 4\) and \(x + y = 2\).

A. (0, 2)

Correct B. (1, 1)

C. (2, 0)

D. (1, 2)

Correct Answer: B

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Question 19 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. \(x - 3\)^2 + \(y - 2\)^\(2 = 16\)

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

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

Correct Answer: A

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Question 20 View Details

Solve the equation \(x^3 - 6x^2 + 11x - 6 = 0\).

Correct A. (1, 2, 3)

B. (1, 2, 6)

C. (1, 3, 6)

D. (2, 3, 6)

Correct Answer: A

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Question 21 View Details

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

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

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

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

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

Correct Answer: A

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Question 22 View Details

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

Correct A. \(x < -1\) or \(x > 5\)

B. \(x > -1\) or \(x < 5\)

C. \(x < 1\) or \(x > 5\)

D. \(x > 1\) or \(x < 5\)

Correct Answer: A

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Question 23 View Details

A set ( A ) contains 5 elements. If 3 elements are randomly selected from set ( A ), find the probability that the selected elements are distinct.

Correct A. \(\frac{3}{10}\)

B. \(\frac{3}{20}\)

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

D. \(\frac{3}{15}\)

Correct Answer: A

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Question 24 View Details

Find the sum of the first 10 terms of the geometric series \(2x + 3x^2 + 4x^3 + ldots\).

Correct A. \(\frac{2x 1 - x^{10}\)\( 1 + x \ }{ 1 - x ^2} )

B. \(\frac{2x 1 - x^{10}\) \ }{ 1 - x ^2}\) )

C. \(\frac{2x 1 - x^{10}\)\(1 + x \\)^2}{ 1 - x ^2} )

D. \(\frac{2x 1 - x^{10}\) \ }{ 1 - x ^3}\) )

Correct Answer: A

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Question 25 View Details

A box contains 5 red balls and 3 blue balls. If 2 balls are randomly selected, find the probability that both balls are red.

Correct A. \(\frac{5}{8}\)

B. \(\frac{5}{14}\)

C. \(\frac{3}{14}\)

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

Correct Answer: A

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