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POST UTME FUTO 2019 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 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

In a survey of 100 students, the mean height was 170 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?

Correct A. 0.1587

B. 0.3413

C. 0.4772

D. 0.6827

Correct Answer: A

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Question 2

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

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

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

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

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

Correct Answer: A

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Question 3

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

Correct A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)

B. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)

C. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)

D. \( x > -\frac{5}{4} \) or \( x > \frac{3}{2} \)

Correct Answer: A

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Question 4

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 = 4 )

C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )

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

Correct Answer: A

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Question 5

A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. If the numbers are 8, 12, 15, 18, and x, find the value of x.

Correct A. 22

B. 24

C. 26

D. 28

Correct Answer: A

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Question 6

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 2 & 3 \ 1 & 2 & 4 \end{pmatrix} ].

Correct A. 0

B. 10

C. 15

D. 20

Correct Answer: A

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Question 7

A circle has a radius of 5 cm. Find the area of the circle.

A. 50\pi

Correct B. 100\pi

C. 150\pi

D. 200\pi

Correct Answer: B

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Question 8

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

Correct A. x = -2

B. x = 2

C. x = -1

D. x = 1

Correct Answer: A

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Question 9

Find the volume of the rec\tangular prism with dimensions 5 cm, 3 cm, and 2 cm.

Correct A. 30

B. 60

C. 90

D. 120

Correct Answer: A

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Question 10

A right-angled triangle has a hypotenuse of 10 cm and one leg of 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 11

Solve the inequality \( \frac{x}{x+1} > \frac{2x}{x-1} \) for ( x in mathbb{R} setminus {1} ).

A. \( x < -1 \)

B. \( x > 1 \)

Correct C. \( x in \( -1, 1 \ \) cup (1, infty) )

D. \( x in \( -infty, -1 \ \) cup (1, infty) )

Correct Answer: C

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Question 12

Find the equation of the circle with center \( C\( -2, 3 \ \) ) and radius \( r = \sqrt{10} \).

Correct A. \( x+2 \ \)^2 + \( y-3 \)^2 = 10 )

B. \( x-2 \ \)^2 + \( y+3 \)^2 = 10 )

C. \( x+2 \ \)^2 + \( y+3 \)^2 = 10 )

D. \( x-2 \ \)^2 + \( y-3 \)^2 = 10 )

Correct Answer: A

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Question 13

A cylindrical \tank with radius \( r = 3 \) m and height \( h = 5 \) m is filled with water. Find the volume of water in the \tank.

A. ( 150pi ) m³

B. ( 300pi ) m³

Correct C. ( 450pi ) m³

D. ( 600pi ) m³

Correct Answer: C

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Question 14

Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{i} = 3 \), \( mathbf{a} cdot mathbf{j} = -2 \), and \( mathbf{a} cdot mathbf{k} = 1 \).

Correct A. \( mathbf{a} = 3mathbf{i} - 2mathbf{j} + mathbf{k} \)

B. \( mathbf{a} = 3mathbf{i} + 2mathbf{j} - mathbf{k} \)

C. \( mathbf{a} = -3mathbf{i} + 2mathbf{j} - mathbf{k} \)

D. \( mathbf{a} = 3mathbf{i} - 2mathbf{j} - mathbf{k} \)

Correct Answer: A

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Question 15

Solve the equation \( x^2 - 6x + 8 = 0 \) u\sing the quadratic formula.

Correct A. \( x = 2 \) or \( x = 4 \)

B. \( x = 1 \) or \( x = 7 \)

C. \( x = 3 \) or \( x = 5 \)

D. \( x = -2 \) or \( x = -4 \)

Correct Answer: A

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Question 16

Find the equation of the circle with centre \( -2, 3 \) 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 17

Solve the inequality \( 2x^2 + 3x - 1 > 0 \).

Correct A. \( x < -\frac{1}{2} \) or \( x > \frac{1}{2} \)

B. \( x < -\frac{1}{2} \) or \( x < \frac{1}{2} \)

C. \( x > -\frac{1}{2} \) or \( x < \frac{1}{2} \)

D. \( x > -\frac{1}{2} \) or \( x > \frac{1}{2} \)

Correct Answer: A

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Question 18

A die is rolled. Find the probability that the number obtained is a multiple of 3 or 5.

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

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

C. \( \frac{1}{2} \)

Correct D. \( \frac{2}{3} \)

Correct Answer: D

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Question 19

Solve the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. \( x = 10^2 \)

Correct B. \( x = 10^4 \)

C. \( x = 10^{-2} \)

D. \( x = 10^{-4} \)

Correct Answer: B

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Question 20

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

Correct A. \( \frac{8}{3} \)

B. \( \frac{16}{3} \)

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

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

Correct Answer: A

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Question 21

A random sample of 25 students from a university had a mean height of 175.6 cm with a s\tandard deviation of 5.8 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of all students in the university.

Correct A. 173.4 cm, 177.8 cm

B. 174.2 cm, 176.9 cm

C. 175.2 cm, 175.9 cm

D. 173.9 cm, 177.3 cm

Correct Answer: A

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Question 22

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

Correct A. 5.77 cm

B. 5.33 cm

C. 5.00 cm

D. 5.66 cm

Correct Answer: A

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Question 23

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

Correct A. 50.24 cm^2

B. 50.27 cm^2

C. 50.00 cm^2

D. 50.32 cm^2

Correct Answer: A

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Question 24

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is blue?

Correct A. \frac{1}{3}

B. \frac{1}{4}

C. \frac{1}{5}

D. \frac{1}{6}

Correct Answer: A

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Question 25

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

A. y = 1x + 1

Correct B. y = 2x - 1

C. y = 3x + 2

D. y = 4x - 3

Correct Answer: B

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