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POST UTME MADONNA UNIVERSITY 2022 Mathematics | Objective

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Question 1

Find the value of x in the equation \( 2^x + 5^x = 3^x \).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 2

Solve for y in the equation \( y = \frac{1}{2} \log_{10} \( x^2 \ \) ).

A. \log_{10} (x)

Correct B. \frac{1}{2} \log_{10} (x)

C. \log_{10} \( x^2 \)

D. 2 \log_{10} (x)

Correct Answer: B

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Question 3

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 4

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

Correct A. \( x < -1 \) or \( x > \frac{3}{2} \)

B. \( x < -\frac{3}{2} \) or \( x > 1 \)

C. \( x < -\frac{1}{2} \) or \( x > 3 \)

D. \( x < 1 \) or \( x > -\frac{3}{2} \)

Correct Answer: A

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Question 5

Find the value of x in the equation \( \sin \( 2x \ \) = \frac{1}{2} ).

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

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

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

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

Correct Answer: A

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Question 6

Determine the mean of the following dataset: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

A. 5

Correct B. 6

C. 7

D. 10

Correct Answer: B

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Question 7

A histogram is a graphical representation of a dataset. What is the primary purpose of a histogram?

Correct A. To show the distribution of data

B. To calculate the mean of a dataset

C. To determine the median of a dataset

D. To create a scatter plot

Correct Answer: A

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Question 8

Given the vectors α = ¯(1, 2) and β = ¯(3, 4), find the magnitude of the vector α + β.

A. √10

B. √14

Correct C. √18

D. √22

Correct Answer: C

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Question 9

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 occur?

A. 0.2

Correct B. 0.4

C. 0.6

D. 0.8

Correct Answer: B

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Question 10

Find the area under the curve y = x^2 from x = 0 to x = 4.

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 11

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 12

Solve the equation \( \tan x = \frac{1}{3} \ \) for ( x ) in the interval \( \left[ \frac{\pi}{2}, \frac{5\pi}{2} \right] \).

A. \frac{\pi}{6}

B. \frac{\pi}{3}

C. \frac{\pi}{2}

Correct D. \frac{5\pi}{6}

Correct Answer: D

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Question 13

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 14

Find the equation of the circle with center ( (2, 3) ) and radius 4.

Correct A. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16

B. \left\( x - 3 \right \)^2 + \left\( y - 2 \right \)^2 = 16

C. \left\( x - 4 \right \)^2 + \left\( y - 3 \right \)^2 = 16

D. \left\( x - 2 \right \)^2 + \left\( y - 4 \right \)^2 = 16

Correct Answer: A

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Question 15

Solve the system of equations u\sing matrices:

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ 1 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 16

Determine the sum of the infinite geometric series - 3 + 6 + 12 + …, where the first term is - 3 and the common ratio is 2.

Correct A. 9

B. -3

C. -9

D. 27

Correct Answer: A

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Question 17

A solid cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone.

A. 256\pi

B. 512\pi

Correct C. 1024\pi

D. 2048\pi

Correct Answer: C

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Question 18

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

Correct A. 6x + 2

B. 6x^2 + 2x - 5

C. 6x + 2x - 5

D. 6x^2 + 2

Correct Answer: A

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Question 19

Solve the system of linear equations u\sing the method of substitution: 2x + 3y = 7 and x - 2y = -3.

Correct A. x = 2, y = 1

B. x = 1, y = 2

C. x = -1, y = 2

D. x = 2, y = -1

Correct Answer: A

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Question 20

A vector ℓ has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x and y components of the vector.

Correct A. x = 4, y = 3

B. x = 3, y = 4

C. x = 4, y = -3

D. x = -3, y = 4

Correct Answer: A

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Question 21

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

Correct A. 5 cm

B. 10 cm

C. 15 cm

D. 20 cm

Correct Answer: A

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Question 22

A vector \overrightarrow{a} has a magnitude of 6 units and makes an angle of 60° with the positive x-axis. Find the x and y components of the vector.

Correct A. x = 3, y = 3\sqrt{3}

B. x = 3, y = 3

C. x = 6, y = 6

D. x = 6, y = 6\sqrt{3}

Correct Answer: A

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Question 23

A histogram is shown below. Find the mean of the data.

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 24

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 25

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

A. 15

Correct B. 30

C. 45

D. 60

Correct Answer: B

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