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POST UTME FUTO 2019 Mathematics | Objective

Prepare for your exams with POST UTME FUTO questions? Reviewing past/model 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 View Details

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

Correct A. 0.1587

B. 0.3413

C. 0.4772

D. 0.6827

Correct Answer: A

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Question 2 View Details

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

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 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 + \(y - 3\)^\(2 = 4\) )

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 View Details

A set of 5 numbers has a mean of 10 and a standard 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 View Details

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 View Details

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 View Details

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 View Details

Find the volume of the rectangular 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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

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

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

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

Correct Answer: A

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Question 15 View Details

Solve the equation \(x^2 - 6x + 8 = 0\) using 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

A random sample of 25 students from a university had a mean height of 175.6 cm with a standard deviation of 5.8 cm. If the population standard 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 View Details

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 View Details

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 View Details

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 View Details

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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