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POST UTME FUTA 2022 Mathematics | Objective

Prepare for your exams with POST UTME FUTA questions? Reviewing past/model questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1 View Details

A random sample of 25 students from a university had a mean height of 175 cm with a standard deviation of 5 cm. Calculate the probability that a randomly selected student from this population has a height greater than 180 cm.

Correct A. 0.1587

B. 0.3085

C. 0.5

D. 0.6915

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

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

Correct A. 0.375

B. 0.5

C. 0.625

D. 0.75

Correct Answer: A

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Question 4 View Details

Find the volume of the solid formed by revolving the region bounded by the parabola (y = \(x^2\)\) and the line \(y = 2x\\((y = x^2) and the line\) about the x-axis.

Correct A. \(V = \frac{16\pi}{3}\)

B. \(V = \frac{32\pi}{3}\)

C. \(V = \frac{64\pi}{3}\)

D. \(V = \frac{128\pi}{3}\)

Correct Answer: A

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Question 5 View Details

A company produces two products, A and B. The profit from the sale of product A is ₦100 per unit, and the profit from the sale of product B is ₦120 per unit. If the company produces 200 units of product A and 300 units of product B, what is the total profit?

A. ₦58,000

Correct B. ₦58,400

C. ₦58,800

D. ₦59,200

Correct Answer: B

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Question 6 View Details

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 7 View Details

A sequence is defined as: \(a_n = \frac{2n + 1}{n^2 + 1}\). Find the sum of the first 5 terms of the sequence.

A. 1.2

Correct B. 1.5

C. 1.8

D. 2.1

Correct Answer: B

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Question 8 View Details

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

A. 0.5

Correct B. 1.0

C. 1.5

D. 2.0

Correct Answer: B

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Question 9 View Details

The equation of a circle is given by \(x - 2\)^2 + \(y - 3\)\\((^(2\) = 4\)\)\). Find the equation of the \\((2 = 4)\tangent line at the point \(3, 5)\\).

Correct A. \(y - 5 = -\)\(\frac{1}{2}\)\)\(x - 3\)

B. \(y - 5 =\)\(\frac{1}{2}\)\)\(x - 3\)

C. \(y - 5 = 2\)\(x - 3\)

D. \(y - 5 = -2\)\(x - 3\)

Correct Answer: A

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Question 10 View Details

A set of 5 numbers has a mean of 10 and a median of 8. If the largest number is 15, find the sum of the remaining 3 numbers.

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 11 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).

A. 40

B. 60

Correct C. 80

D. 100

Correct Answer: C

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Question 12 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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Question 13 View Details

Find the value of \(\log_{10} x^2 \\) ) given that \(\log_{10} x = 2\).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 14 View Details

A vector ( mathbf{a} ) has components \(a_1 = 2\) and \(a_2 = 3\). Find the magnitude of ( mathbf{a} ).

A. 5

B. 10

Correct C. 15

D. 20

Correct Answer: C

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Question 15 View Details

Solve the equation \(\sin^2 x + \cos^2 x = 1\).

A. \(x = 0\)

Correct B. \(x =\)π/2

C. \(x =\)π

D. \(x = 2\)π

Correct Answer: B

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Question 16 View Details

Find the equation of the circle passing through the points (2, 3), (4, 1), and \(-1, 2\).

Correct A. \boxed{\(x^2\) + \\((y^2 - 7x + 5y + 12\)\(= 0\)\)}

B. \(x^2\) + \\((y^2 - 9x + 3y + 16\)\(= 0\)\)

C. \(x^2\) + \\((y^2 - 5x - 3y + 4\)\(= 0\)\)

D. \(x^2\) + \\((y^2 + 3x - 7y + 9\)\(= 0\)\)

Correct Answer: A

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Question 17 View Details

Find the area under the curve \(y = x\^2 + 2x - 3\) from \(x = 0\) to \(x = 2\).

Correct A. \boxed{\(\frac{13}{3}\)\)}

B. \(\frac{7}{3}\)\)

C. \(\frac{11}{3}\)\)

D. \(\frac{15}{3}\)\)

Correct Answer: A

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Question 18 View Details

Solve the equation \(x^3\) - \\((6x^2 + 11x - 6\)\(= 0.\)\)

Correct A. \boxed{\(x = 1\)}

B. \(x = 2\)

C. \(x = 3\)

D. \(x = 4\)

Correct Answer: A

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Question 19 View Details

Find the volume of the solid formed by revolving the region bounded by \(y = x\^2\), \(y = 0\), and \(x = 2\) about the x-axis.

Correct A. \boxed{\(\frac{16\pi}{3}\)\)}

B. \(\frac{8\pi}{3}\)\)

C. \(\frac{12\pi}{3}\)\)

D. \(\frac{20\pi}{3}\)\)

Correct Answer: A

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Question 20 View Details

Solve the trigonometric equation \\(\sin^2\) x + \\(\cos^2\) \(x = 1\).

Correct A. \boxed{\(x =\)\(\frac{\pi}{4}\)\)}

B. \(x =\)\(\frac{\pi}{2}\)\)

C. \(x =\)\\(\frac{3\pi}{4}\)\)

D. \(x =\)\\(\frac{5\pi}{4}\)\)

Correct Answer: A

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Question 21 View Details

Find the equation of the line passing through the points (1, 2) and (3, 4).

Correct A. \boxed{\(y = x + 1\)}

B. \(y = 2x - 1\)

C. \(y = x - 2\)

D. \(y = 2x + 2\)

Correct Answer: A

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Question 22 View Details

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 2).

Correct A. \boxed{3}

B. 4

C. 5

D. 6

Correct Answer: A

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Question 23 View Details

Solve the system of equations \(x + y = 4\) and \(x - y = 2\).

Correct A. \boxed{\(x = 3\), \(y = 1\)}

B. \(x = 1\), \(y = 3\)

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

D. \(x = 4\), \(y = 0\)

Correct Answer: A

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Question 24 View Details

Find the equation of the circle with center (2, 3) and radius 4.

A. \boxed{ x - 2 ^2 + y - \(3 ^2 = 16\)}

B. \(x - 2\)^2 + \(y - 3\)^\(2 = 8\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 12\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 20\)

Correct Answer: VIEW ANSWER

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Question 25 View Details

Find the equation of the circle passing through the points ( (2,3) ), ( (4,5) ), and ( (6,7) ).

Correct A. \(x^2 + y^2 - 10x - 16y + 39 = 0\)

B. \(x^2 + y^2 - 12x - 20y + 36 = 0\)

C. \(x^2 + y^2 - 14x - 24y + 53 = 0\)

D. \(x^2 + y^2 - 16x - 28y + 70 = 0\)

Correct Answer: A

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