Exam Body

Year

Subject

Paper Type

POST UTME FUTA 2022 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 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard 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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 3

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 4

Find the volume of the solid formed by revolving the region bounded by the parabola \[ y = x^2 \] and the line \[ y = 2x \] 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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 5

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 6

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 7

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 8

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 9

The equation of a circle is given by \(\( x - 2 \)^2 + \( y - 3 \)^2 = 4\). Find the equation of the \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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 10

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 11

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 12

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 13

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 14

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 15

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

A. x = 0

Correct B. x = π/2

C. x = π

D. x = 2π

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 16

Find the equation of the circle pas\sing 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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 17

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 18

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 19

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 20

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 21

Find the equation of the line pas\sing 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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 22

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 23

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 24

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 25

Find the equation of the circle pas\sing 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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows

Help others prepare! Share this practice hub:

Chat with Support