Practice Post UTME FUTA mathematics 2021 Past Questions

Question 1 View Details

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

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

Correct Answer: A

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Question 2 View Details

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 View Details

Let ( P(x) = \(2x^3 - 5x^2 + x - 1\) ). Find the derivative of ( P(x) ) using 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 View Details

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 View Details

Let ( f(x) = \\(\sin^2\) x ). Find the derivative of ( f(x) ) using 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 View Details

In a circle of radius 8 cm, a chord of length 12 cm subtends 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

A circle with center ( C(2,3) ) and radius (r = 4\) has equation \(x - h \\((r = 4) has equation \\)^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 View Details

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

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 14 View Details

A histogram shows the distribution of exam scores with a mean of 60 and a standard 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 View Details

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 View Details

A circle with center ( C(2,3) ) and radius (r = 4\) has equation \(x - h \\((r = 4) has equation \\)^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 View Details

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

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 18 View Details

A histogram shows the distribution of exam scores with a mean of 60 and a standard 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 View Details

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 View Details

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 View Details

A rectangular 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 View Details

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 View Details

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 View Details

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 View Details

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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