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POST UTME FUTO 2017 Mathematics | Objective

Are you preparing for POST UTME FUTO exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the volume of the solid formed by revolving the region bounded by the curve $ y = \frac{1}{2}x^2 $ about the x-axis, from $ x = 0 $ to $ x = 2 $.

Correct A. 4π

B. 8π

C. 16π

D. 32π

Correct Answer: A

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Question 2

If ( f(x) = \frac{x^2 - 4}{x - 2} ), find ( f'(x) ) u\sing the chain rule.

Correct A. ( f'(x) = \frac{$ x - 2 $(2x)}{$ x - 2 $^2} )

B. ( f'(x) = \frac{$ x - 2 $$ 2x - 4 $}{$ x - 2 $^2} )

C. ( f'(x) = \frac{$ x - 2 $$ x + 2 $}{$ x - 2 $^2} )

D. ( f'(x) = \frac{$ x - 2 $$ x - 4 $}{$ x - 2 $^2} )

Correct Answer: A

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Question 3

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. $ x - 3 \ $^2 + $ y - 4 $^2 = 25 )

B. $ x - 4 \ $^2 + $ y - 3 $^2 = 25 )

C. $ x - 5 \ $^2 + $ y - 3 $^2 = 25 )

D. $ x - 3 \ $^2 + $ y - 5 $^2 = 25 )

Correct Answer: A

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Question 4

Solve the inequality $ 2^x > 3^x $ for ( x ).

A. $ x < 0 $

Correct B. $ x > 0 $

C. $ x < 1 $

D. $ x > 1 $

Correct Answer: B

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Question 5

Find the area under the curve $ y = \frac{1}{x} $ from $ x = 1 $ to $ x = 2 $.

Correct A. $ \log 2 - \log 1 $

B. $ \log 2 - \log 2 $

C. $ \log 1 - \log 2 $

D. $ \log 2 - \log 3 $

Correct Answer: A

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Question 6

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the Pythagorean theorem.

A. 8 cm

Correct B. 12 cm

C. 16 cm

D. 20 cm

Correct Answer: B

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Question 7

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

Correct A. 50.24 cm^2

B. 100.48 cm^2

C. 200.96 cm^2

D. 400.96 cm^2

Correct Answer: A

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Question 8

A die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. 1/6

Correct B. 1/12

C. 1/24

D. 1/36

Correct Answer: B

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Question 9

A histogram is shown below. What is the mean of the data?

A. 10

B. 15

Correct C. 20

D. 25

Correct Answer: C

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Question 10

A line passes through the points (2,3) and (4,5). Find the equation of the line in slope-intercept form.

A. y = 2x - 1

Correct B. y = 2x + 1

C. y = -2x + 1

D. y = -2x - 1

Correct Answer: B

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Question 11

Solve for x in the quadratic equation $ x^2 + 5x + 6 = 0 $.

A. x = -2

Correct B. x = -3

C. x = 2

D. x = 3

Correct Answer: B

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Question 12

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. 1/2

B. 1/3

Correct C. 2/5

D. 3/8

Correct Answer: C

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Question 13

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

C. 6x^2 + 4x

D. 6x^2 - 2x

Correct Answer: A

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Question 14

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.

Correct A. 30 cm^3

B. 40 cm^3

C. 50 cm^3

D. 60 cm^3

Correct Answer: A

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Question 15

A company produces two products, A and B. The profit from the sale of product A is $10 per unit, and the profit from the sale of product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. $1500

Correct B. $2000

C. $2500

D. $3000

Correct Answer: B

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Question 16

Let X be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the expected value of X.

Correct A. $ \frac{1}{2} $

B. $ \frac{3}{4} $

C. $ \frac{5}{6} $

D. $ \frac{7}{8} $

Correct Answer: A

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Question 17

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. ( 0.9544 )

Correct B. ( 0.9772 )

C. ( 0.9987 )

D. ( 0.9999 )

Correct Answer: B

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Question 18

Solve the quadratic equation $ x^2 + 4x + 4 = 0 $.

Correct A. $ x = -2 $

B. $ x = -1 $

C. $ x = 0 $

D. $ x = 2 $

Correct Answer: A

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Question 19

Let $ mathbf{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} $ and $ mathbf{b} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} $. Find the cross product $ mathbf{a} \times mathbf{b} $.

Correct A. $ egin{pmatrix} -3 \ 6 \ -3 \end{pmatrix} $

B. $ egin{pmatrix} 3 \ -6 \ 3 \end{pmatrix} $

C. $ egin{pmatrix} 6 \ -3 \ -6 \end{pmatrix} $

D. $ egin{pmatrix} -6 \ 3 \ 6 \end{pmatrix} $

Correct Answer: A

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Question 20

Find the derivative of the function ( f(x) = \sin^2(x) ).

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

B. ( f'(x) = \sin(x) )

C. ( f'(x) = \cos(x) )

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

Correct Answer: A

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Question 21

Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.

Correct A. \frac{16\pi}{3}

B. \frac{32\pi}{3}

C. \frac{64\pi}{3}

D. \frac{128\pi}{3}

Correct Answer: A

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Question 22

Solve the inequality $|x - 2| > 3$.

Correct A. $ -\infty, -1 $ \cup $ 5, \infty $

B. $ -\infty, 1 $ \cup $ 5, \infty $

C. $ -\infty, -1 $ \cup (2, 5)

D. $ -\infty, 1 $ \cup (2, 5)

Correct Answer: A

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Question 23

A binary operation $\ast$ is defined as $a \ast b = a^2 + b^2$. Find the value of $2 \ast 3$.

A. 13

Correct B. 25

C. 37

D. 49

Correct Answer: B

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Question 24

A die is rolled. What is the probability that the number obtained is a multiple of 3?

Correct A. \frac{1}{3}

B. \frac{1}{6}

C. \frac{1}{2}

D. \frac{2}{3}

Correct Answer: A

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Question 25

Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$ with respect to x.

Correct A. -\frac{2x}{$ x^2 + 1 $^2}

B. -\frac{2}{$ x^2 + 1 $^2}

C. \frac{2x}{$ x^2 + 1 $^2}

D. \frac{2}{$ x^2 + 1 $^2}

Correct Answer: A

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