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POST UTME RHEMA UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

Let X be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.

Correct A. \(P X > 0.5 \\) = \(\frac{1}{2}\)\) )

B. \(P X > 0.5 \\) = \(\frac{1}{4}\)\) )

C. \(P X > 0.5 \\) = \(\frac{3}{4}\)\) )

D. \(P X > 0.5 \\) = \(\frac{1}{3}\)\) )

Correct Answer: A

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Question 2 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'\((x) =\)\(\frac{2}{x^2 + 1\) ^2}\)\) )

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

Correct Answer: A

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Question 3 View Details

A rectangular prism has dimensions 3 cm, 4 cm, and 5 cm. Find the volume of the prism.

Correct A. \(V = 60 \text{cm}^3\)

B. \(V = 120 \text{cm}^3\)

C. \(V = 180 \text{cm}^3\)

D. \(V = 240 \text{cm}^3\)

Correct Answer: A

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Question 4 View Details

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

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

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

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

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

Correct Answer: A

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Question 5 View Details

Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\) for ( x ) in the interval ( [0, 2pi] ).

Correct A. \(x = \frac{\pi}{4}, \frac{3\pi}{4}\)

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

C. \(x = \frac{\pi}{4}, \frac{7\pi}{4}\)

D. \(x = \frac{\pi}{4}, \frac{9\pi}{4}\)

Correct Answer: A

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Question 6 View Details

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

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 7 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 8 View Details

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

Correct A. 6x + 2

B. 6x + 2 + 2x

C. 6x + 2 - 5

D. 6x + 2x - 5

Correct Answer: A

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Question 9 View Details

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

A. 0

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

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

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

Correct Answer: C

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Question 10 View Details

A circle has a radius of 4 cm. Find its circumference.

Correct A. 8\pi

B. 10\pi

C. 12\pi

D. 16\pi

Correct Answer: A

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Question 11 View Details

Find the equation of the circle passing through the points (2, 3), (4, 1), and \(-1, 2\).

Correct A. \(x^2\) + \\((y^2 - 6x - 2y + 12\)\(= 0\)\)

B. \(x^2\) + \\((y^2 - 4x + 2y + 8\)\(= 0\)\)

C. \(x^2\) + \\((y^2 + 2x - 4y + 4\)\(= 0\)\)

D. \(x^2\) + \\((y^2 - 2x + 4y - 8\)\(= 0\)\)

Correct Answer: A

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Question 12 View Details

Solve the equation \(\sin^2 x + \cos^2 x = \frac{3}{4}\) for x in the interval [0, 2\pi].

Correct A. \(x = \frac{\pi}{6}, \frac{5\pi}{6}\)

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

C. \(x = \frac{\pi}{3}, \frac{2\pi}{3}\)

D. \(x = \frac{\pi}{2}, \frac{3\pi}{2}\)

Correct Answer: A

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Question 13 View Details

Find the volume of the solid formed by revolving the region bounded by the curves \(y = x\^2\), \(y = 0\), and \(x = 2\) about the x-axis.

A. \(\frac{32\pi}{3}\)

B. \(\frac{64\pi}{3}\)

Correct C. \(\frac{128\pi}{3}\)

D. \(\frac{256\pi}{3}\)

Correct Answer: C

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Question 14 View Details

Solve the matrix equation \(\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}\) for x and y.

Correct A. \(x = 1, y = 2\)

B. \(x = 2, y = 1\)

C. \(x = 3, y = 4\)

D. \(x = 4, y = 3\)

Correct Answer: A

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Question 15 View Details

Find the equation of the line passing through the points (1, 2) and (3, 4).

Correct A. \(y = 2x - 1\)

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

C. \(y = x + 1\)

D. \(y = x - 1\)

Correct Answer: A

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Question 16 View Details

Determine the value of x in the equation \(\frac{x}{2} + \frac{1}{3} = \frac{7}{12}\).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 17 View Details

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

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 18 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, 1\) ∪ (3, ∞)

C. \(-∞, -1\) ∪ (1, ∞)

D. \(-∞, 3\) ∪ (1, ∞)

Correct Answer: A

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Question 19 View Details

A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?

A. 8

B. 10

Correct C. 12

D. 14

Correct Answer: C

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Question 20 View Details

In a geometric sequence, the first term is 2 and the common ratio is 3. Find the 5th term.

Correct A. 243

B. 2430

C. 24300

D. 243000

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 the inequality \(2x - 5 > 3\).

Correct A. \(x > 4\)

B. \(x < 4\)

C. \(x > 2\)

D. \(x < 2\)

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

Correct A. \(x = 3\), \(y = 1\)

B. \(x = 1\), \(y = 3\)

C. \(x = 2\), \(y = 2\)

D. \(x = 4\), \(y = 0\)

Correct Answer: A

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Question 25 View Details

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

Correct A. f'\((x) = 6x + 2\)

B. f'\((x) = 6x - 2\)

C. f'\((x) =\)\(3x^2 + 2\)

D. f'\((x) =\)\(3x^2 - 2\)

Correct Answer: A

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