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POST UTME FUTA 2019 Mathematics | Objective

Are you preparing for POST UTME FUTA exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the mean of the following dataset: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. If the mean is 12, what is the value of the unknown variable x in the dataset?

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 2

Solve for x in the equation: \( \sin^2\( x \ \) + \cos^2(x) = 1 ). If \( \sin\( x \ \) = \frac{3}{5} ), find the value of \( \cos\( x \ \) ).

Correct A. \( \frac{4}{5} \)

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

C. \( \frac{2}{5} \)

D. \( \frac{1}{5} \)

Correct Answer: A

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Question 3

A histogram is constructed from the following data: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. If the mean is 12, what is the value of the unknown variable x in the dataset?

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 4

A right-angled triangle has a hypotenuse of length 10 and one leg of length 6. Find the length of the other leg.

A. \( \sqrt{64} \)

B. \( \sqrt{36} \)

C. \( \sqrt{100} \)

Correct D. \( \sqrt{144} \)

Correct Answer: D

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Question 5

A probability experiment consists of rolling a fair six-sided die. If the outcome is an even number, the player wins. What is the probability that the player wins?

Correct A. \( \frac{1}{2} \)

B. \( \frac{1}{3} \)

C. \( \frac{2}{3} \)

D. \( \frac{3}{4} \)

Correct Answer: A

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Question 6

Find the derivative of ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

Correct A. \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

B. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

C. \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

D. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

Correct Answer: A

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Question 7

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

Correct A. \frac{-5 + \sqrt{49}}{4}

B. \frac{-5 - \sqrt{49}}{4}

C. \frac{-5 + \sqrt{49}}{4}

D. \frac{-5 - \sqrt{49}}{4}

Correct Answer: A

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Question 8

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 9

Solve the system of equations \( x + y = 3 \) and \( x - y = 1 \).

Correct A. \left\{\left( 2, \ 1\right)\right\}

B. \left\{\left( 1, \ 2\right)\right\}

C. \left\{\left( 2, \ -1\right)\right\}

D. \left\{\left( 1, \ -2\right)\right\}

Correct Answer: A

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Question 10

Find the value of ( x ) in the equation \( x^2 + 2x - 6 = 0 \).

Correct A. \frac{-2 + \sqrt{4 + 24}}{2}

B. \frac{-2 - \sqrt{4 + 24}}{2}

C. \frac{-2 + \sqrt{4 + 24}}{2}

D. \frac{-2 - \sqrt{4 + 24}}{2}

Correct Answer: A

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Question 11

Solve the inequality \( \frac{x^2 - 4}{x + 2} geq 0 \) for ( x in mathbb{R} ).

Correct A. \( -infty, -2 \ \) cup [0, infty) )

B. \( -infty, -2 \ \) cup \( -2, 0 \) cup (0, infty) )

C. \( -infty, 0 \ \) cup (0, infty) )

D. \( -infty, -2 \ \) cup [2, infty) )

Correct Answer: A

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Question 12

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.

Correct A. ( f'(x) = -\frac{1}{2}x^{-\frac{3}{2}} )

B. ( f'(x) = \frac{1}{2}x^{-\frac{3}{2}} )

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

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

Correct Answer: A

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Question 13

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.

Correct A. \( x = -2 \) or \( x = -3 \)

B. \( x = 2 \) or \( x = 3 \)

C. \( x = -1 \) or \( x = -6 \)

D. \( x = 1 \) or \( x = 6 \)

Correct Answer: A

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Question 14

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. \( -1 \)

D. ( 2 )

Correct Answer: A

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Question 15

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

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

B. \( x = 2, y = 0 \)

C. \( x = 0, y = 2 \)

D. \( x = 1, y = 2 \)

Correct Answer: A

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Question 16

A random variable X follows a binomial distribution with parameters n = 10 and p = 0.4. Find the probability that X is greater than 6.

A. 0.011

B. 0.032

Correct C. 0.063

D. 0.094

Correct Answer: C

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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.

Correct A. 512\pi

B. 256\pi

C. 128\pi

D. 64\pi

Correct Answer: A

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Question 18

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).

Correct A. -2

B. 2

C. -1

D. 1

Correct Answer: A

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Question 19

A vector \( \vec{a} \) has a magnitude of 5 units and makes an angle of 60\circ with the positive x-axis. Find the x and y components of \( \vec{a} \).

Correct A. 2.5, 4.33

B. 4.33, 2.5

C. 3.54, 3.54

D. 2.5, 2.5

Correct Answer: A

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Question 20

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

Correct A. 8

B. 6

C. 4

D. 2

Correct Answer: A

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Question 21

In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?

A. 0.1587

B. 0.3413

C. 0.4772

Correct D. 0.6827

Correct Answer: D

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Question 22

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

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

Correct Answer: A

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Question 23

In a circle with center ( O ) and radius 6 cm, a chord ( AB ) is drawn such that \( AB = 8 cm \). Find the dis\tance from ( O ) to the midpoint of ( AB ).

A. 3 cm

B. 4 cm

Correct C. 5 cm

D. 6 cm

Correct Answer: C

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Question 24

Simplify the expression \( \sqrt[3]{64x^3y^3} \).

A. \( 4x^3y^3 \)

B. \( 4xy^3 \)

C. \( 4x^3y \)

Correct D. \( 4x^3y^3 \)

Correct Answer: D

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Question 25

Find the value of ( x ) in the equation \( 2^x = 32 \).

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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