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POST UTME REDEEMERS UNIVERSITY 2024 Mathematics | Objective

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Question 1

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^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

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

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

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

Find the equation of the \tangent line to the curve y = x^2 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

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

Solve the system of equations u\sing 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

Find the derivative of the function ( f(x) = 2x^3 - 5x^2 + 3x - 1 ) u\sing 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

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

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

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

A. x > 4

Correct B. x > 6

C. x < 4

D. x < 6

Correct Answer: B

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Question 12

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

A histogram of exam scores has a mean of 70 and a s\tandard 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

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

Solve the system of equations u\sing 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

In a random experiment, two events A and B are indep\endent. 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

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

A rec\tangular 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

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

A set of exam scores has a mean of 75 and a s\tandard 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

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

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

A set of exam scores has a mean of 80 and a s\tandard 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

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

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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