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POST UTME REDEEMERS UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.4\), P\(X = 2 = 0.3\),\(P(X = 3\)= 0.3\). If \(Y = X\\((X = 3 = 0.3). If \^2\), find E[Y].

A. 1.4

B. 2.1

Correct C. 2.7

D. 3.2

Correct Answer: C

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Question 2 View Details

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

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 3 View Details

If f(x) = \(3x^2 + 2x - 5\) and g(x) = \(2x^2 - 3x + 1\), find \(f \circ g\)(x).

Correct A. \(12x^4 - 36x^3 + 36x^2 + 4x - 3\)

B. \(12x^4 - 36x^3 + 36x^2 + 2x - 3\)

C. \(12x^4 - 36x^3 + 36x^2 - 4x - 3\)

D. \(12x^4 - 36x^3 + 36x^2 - 2x - 3\)

Correct Answer: A

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Question 4 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 5 View Details

Find the equation of the tangent line to the curve \(y = x\^2\\(tangent line to the curve (y = x\) at the point (1, 1).

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 6 View Details

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

Correct A. ( 28 )

B. ( 32 )

C. ( 36 )

D. ( 40 )

Correct Answer: A

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Question 7 View Details

Solve the system of equations using matrices: \(\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}\).

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 8 View Details

Find the derivative of the function ( f(x) = \(2x^3 - 5x^2 + 3x - 1\) ) using the chain rule.

Correct A. ( f'\((x) =\)\(6x^2 - 10x + 3\) \)

B. ( f'\((x) =\)\(12x^2 - 20x + 6\) \)

C. ( f'\((x) =\)\(18x^2 - 30x + 9\) \)

D. ( f'\((x) =\)\(24x^2 - 40x + 12\) \)

Correct Answer: A

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Question 9 View Details

Solve the vector equation \(\begin{bmatrix} 2 \ 3 \end{bmatrix} \cdot \begin{bmatrix} 4 \ 5 \end{bmatrix} = \begin{bmatrix} 1 \ 2 \end{bmatrix} \cdot \begin{bmatrix} 6 \ 7 \end{bmatrix}\).

A. \(10 = 42 \\)

Correct B. \(12 = 48 \\)

C. \(14 = 54 \\)

D. \(16 = 60 \\)

Correct Answer: B

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Question 10 View Details

Convert the \fraction \(\frac{3}{4}\) to a decimal in base 10.

Correct A. \(0.75 \\)

B. \(0.25 \\)

C. \(0.50 \\)

D. \(0.33 \\)

Correct Answer: A

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Question 11 View Details

Solve the inequality (\(\frac{x}{x-2}\(> 2\)\) for \\((frac{x}{x-2} > 2\(x > 2\)\).

A. \(x > 4\)

Correct B. \(x > 6\)

C. \(x < 4\)

D. \(x < 6\)

Correct Answer: B

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Question 12 View Details

Find the value of ( x ) in the equation \(x^2 + 5x - 6 = 0\).

A. \(x = 1\)

B. \(x = -1\)

Correct C. \(x = 2\)

D. \(x = -2\)

Correct Answer: C

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Question 13 View Details

A histogram of exam scores has a mean of 70 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 85?

A. 0.16

B. 0.32

C. 0.68

Correct D. 0.84

Correct Answer: D

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Question 14 View Details

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

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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Question 15 View Details

Solve the system of equations using matrices: \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}\).

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 16 View Details

In a random experiment, two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events A and B occur?

Correct A. 0.24

B. 0.24

C. 0.48

D. 0.64

Correct Answer: A

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Question 17 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 18 View Details

A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Find its volume.

Correct A. 120 \(cm^3\)

B. 1200 \(cm^3\)

C. 12000 \(cm^3\)

D. 120000 \(cm^3\)

Correct Answer: A

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Question 19 View Details

Find the determinant of the matrix [egin{pmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{pmatrix}].

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 20 View Details

A set of exam scores has a mean of 75 and a standard deviation of 10. If a student scores 90, what is his z-score?

A. -1.5

Correct B. 1.5

C. 2.5

D. 3.5

Correct Answer: B

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Question 21 View Details

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

Correct A. 12

B. 16

C. 20

D. 24

Correct Answer: A

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Question 22 View Details

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

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

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

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

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

Correct Answer: A

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Question 23 View Details

A set of exam scores has a mean of 80 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 70 and 90?

A. 0.34

Correct B. 0.68

C. 0.85

D. 0.95

Correct Answer: B

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Question 24 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). Find the sum of the first 10 terms of the sequence.

A. 110

B. 120

Correct C. 130

D. 140

Correct Answer: C

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Question 25 View Details

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

A. 0.2

Correct B. 0.3

C. 0.4

D. 0.5

Correct Answer: B

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