Practice post utme futa mathematics 2021 Past Questions

Question 1

Let ( f(x) = \frac{1}{x^2 + 1} ). Find the derivative of ( f(x) ) u\sing 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{1}{\( x^2 + 1 \)^2} \)

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

Correct Answer: A

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Question 2

A histogram of exam scores is shown below. Find the mean of the scores.

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 3

Let ( P(x) = 2x^3 - 5x^2 + x - 1 ). Find the derivative of ( P(x) ) u\sing the power rule.

Correct A. ( P'(x) = 6x^2 - 10x + 1 \)

B. ( P'(x) = 6x^2 - 10x - 1 \)

C. ( P'(x) = 6x^2 + 10x - 1 \)

D. ( P'(x) = 6x^2 + 10x + 1 \)

Correct Answer: A

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Question 4

A random experiment consists of rolling a fair six-sided die. What is the probability that the number rolled is greater than 4?

A. \frac{1}{6}

B. \frac{1}{3}

C. \frac{2}{3}

Correct D. \frac{5}{6}

Correct Answer: D

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Question 5

Let ( f(x) = \sin^2 x ). Find the derivative of ( f(x) ) u\sing the chain rule.

Correct A. ( f'(x) = 2 \sin x \cos x \)

B. ( f'(x) = 2 \cos x \)

C. ( f'(x) = 2 \sin x \)

D. ( f'(x) = 2 \sin^2 x \)

Correct Answer: A

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Question 6

In a circle of radius 8 cm, a chord of length 12 cm subt\ends an angle of 60° at the centre. Find the area of the sector formed by the chord and the radii drawn to the \ends of the chord.

A. 48\pi cm^2

Correct B. 64\pi cm^2

C. 72\pi cm^2

D. 80\pi cm^2

Correct Answer: B

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Question 7

A right-angled triangle has sides of length 3 cm, 4 cm, and 5 cm. Find the area of the triangle.

Correct A. 6 cm^2

B. 8 cm^2

C. 10 cm^2

D. 12 cm^2

Correct Answer: A

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Question 8

A solid cylinder has a height of 10 cm and a radius of 4 cm. Find the volume of the cylinder.

Correct A. 160\pi cm^3

B. 200\pi cm^3

C. 240\pi cm^3

D. 280\pi cm^3

Correct Answer: A

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Question 9

A right-angled triangle has sides of length 6 cm, 8 cm, and 10 cm. Find the area of the triangle.

Correct A. 24 cm^2

B. 30 cm^2

C. 36 cm^2

D. 40 cm^2

Correct Answer: A

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Question 10

A solid sphere has a radius of 6 cm. Find the volume of the sphere.

Correct A. 904.32 cm^3

B. 1000 cm^3

C. 1200 cm^3

D. 1400 cm^3

Correct Answer: A

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Question 11

Find the value of ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 12

A circle with center ( C(2,3) ) and radius \( r = 4 \) has equation \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). Find the equation of the circle.

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

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

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

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

Correct Answer: A

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Question 13

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing the definite integral.

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 14

A histogram shows the distribution of exam scores with a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is between 50 and 70.

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 15

Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 16

A circle with center ( C(2,3) ) and radius \( r = 4 \) has equation \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). Find the equation of the circle.

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

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

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

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

Correct Answer: A

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Question 17

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing the definite integral.

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 18

A histogram shows the distribution of exam scores with a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is between 50 and 70.

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 19

Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 20

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

Correct A. \( \frac{16}{3} \)

B. \( \frac{32}{3} \)

C. \( \frac{64}{3} \)

D. \( \frac{128}{3} \)

Correct Answer: A

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Question 21

A rec\tangular box has dimensions ( x ), ( 2x ), and ( 3x ). If the surface area of the box is ( 120 ) square units, find the value of ( x ).

A. ( 2 )

Correct B. ( 3 )

C. ( 4 )

D. ( 5 )

Correct Answer: B

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Question 22

Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = -1 \end{cases} \).

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

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

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

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

Correct Answer: C

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Question 23

A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is ( 7 )?

A. \( \frac{1}{6} \)

B. \( \frac{1}{12} \)

C. \( \frac{1}{36} \)

Correct D. \( \frac{5}{36} \)

Correct Answer: D

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Question 24

Find the sum of the first ( 10 ) terms of the geometric series ( 2, 6, 18, ldots ).

Correct A. ( 3097 )

B. ( 3098 )

C. ( 3099 )

D. ( 3100 )

Correct Answer: A

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Question 25

A company produces ( x ) units of a product, where ( x ) is a random variable with a probability density function ( f(x) = \frac{1}{2}x ) for ( 0 leq x leq 2 ). Find the expected value of ( x ).

Correct A. \( \frac{4}{3} \)

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

C. \( \frac{6}{3} \)

D. \( \frac{7}{3} \)

Correct Answer: A

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