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POST UTME FUTA 2019 Mathematics | Objective

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Question 1 View Details

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 View Details

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

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 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of ( f(x) = \(\frac{x^2 + 2x - 3}{x^2 - 4}\)\)\) ) using 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 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\) using 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\(\sqrt{x}\)}\) ) using 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 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using 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 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. \(-1\)

D. ( 2 )

Correct Answer: A

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Question 15 View Details

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 View Details

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 View Details

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 View Details

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 View Details

A vector (\(\vec{a}\)\) has a magnitude of 5 units and makes an angle of 60\\((vec{a}\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 View Details

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 View Details

In a random sample of 100 students, the mean height is 175 cm with a standard 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 View Details

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

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

Correct Answer: A

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Question 23 View Details

In a circle with center ( O ) and radius 6 cm, a chord ( AB ) is drawn such that \(AB = 8 cm\). Find the distance 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 View Details

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 View Details

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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