Exam Body

Year

Subject

Paper Type

POST UTME FUTA 2023 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 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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

Question 2

A particle moves in a straight line with an initial velocity of 5 m/s. If it decelerates uniformly at a rate of 2 m/s^2, find its velocity after 4 seconds.

A. 3 m/s

Correct B. 4 m/s

C. 5 m/s

D. 6 m/s

Correct Answer: B

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

Question 3

Find the value of x in the quadratic equation \( x^2 + 4x + 4 = 0 \).

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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

Question 4

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?

A. \frac{1}{3}

Correct B. \frac{1}{4}

C. \frac{1}{5}

D. \frac{1}{6}

Correct Answer: B

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

Question 5

Solve the system of equations \( x + y = 2 \) and \( x - y = 1 \).

Correct A. x = 1, y = 1

B. x = 1, y = 2

C. x = 2, y = 1

D. x = 2, y = 2

Correct Answer: A

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 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 12π cm³

Correct B. 24π cm³

C. 36π cm³

D. 48π cm³

Correct Answer: B

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

Question 7

Solve the inequality \( x^2 + 4x - 5 > 0 \).

A. \( -∞, -5 \) ∪ (1, ∞)

Correct B. \( -∞, -5 \) ∪ (1, ∞)

C. \( -∞, -5 \) ∪ \( -1, ∞ \)

D. \( -∞, -5 \) ∪ (1, ∞)

Correct Answer: B

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

Question 8

Find the derivative of the function ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the quotient rule.

Correct A. \( \frac{2x\( x^2 + 1 \ \) - 2x^3}{\( x^2 + 1 \)^2} )

B. \( \frac{2x\( x^2 + 1 \ \) - 2x^3}{\( x^2 + 1 \)^2} )

C. \( \frac{2x^2 - 2x^3}{\( x^2 + 1 \ \)^2} )

D. \( \frac{2x^2 + 2x^3}{\( x^2 + 1 \ \)^2} )

Correct Answer: A

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

Question 9

Evaluate the definite integral \( int_0^1 x^2 \sin x dx \).

A. \( left[ -x^2 \cos x + 2 int x \cos x dx \right]_0^1 \)

B. \( left[ -x^2 \cos x + 2 int x \cos x dx \right]_0^1 \)

C. \( left[ -x^2 \cos x + 2x \sin x + 2 \cos x \right]_0^1 \)

Correct D. \( left[ -x^2 \cos x + 2x \sin x + 2 \cos x \right]_0^1 \)

Correct Answer: D

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

Question 10

Solve the equation \( \sin 2x = \frac{1}{2} \).

A. \( x = \frac{pi}{12} + \frac{k pi}{2} \)

B. \( x = \frac{pi}{12} + \frac{k pi}{2} \)

C. \( x = \frac{pi}{6} + \frac{k pi}{2} \)

Correct D. \( x = \frac{pi}{6} + \frac{k pi}{2} \)

Correct Answer: D

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

Question 11

Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).

Correct A. x = \frac{\pi}{4}

B. x = \\frac{3\\pi}{4}

C. x = \\frac{5\\pi}{4}

D. x = \\frac{7\\pi}{4}

Correct Answer: A

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

Question 12

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing integration.

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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

Question 13

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.

A. x = -2

Correct B. x = -3

C. x = -1

D. x = 1

Correct Answer: B

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

Question 14

Find the value of ( x ) in the equation \( 2^x = 16 \) u\sing \logarithms.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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

Question 15

Solve the inequality \( x^2 - 4x + 4 > 0 \) u\sing algebraic manipulation.

A. x < 0

B. x > 0

Correct C. x < 2

D. x > 2

Correct Answer: C

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

Question 16

Find the value of ( x ) in the equation \( \sin x = \frac{1}{2} \) u\sing trigonometric identities.

Correct A. x = \frac{\pi}{6}

B. x = \frac{\pi}{4}

C. x = \frac{\pi}{3}

D. x = \frac{\pi}{2}

Correct Answer: A

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

Question 17

Solve the system of equations \( x + y = 2 \) and \( x - y = 1 \) u\sing algebraic manipulation.

Correct A. x = 1, y = 1

B. x = 1, y = -1

C. x = -1, y = 1

D. x = -1, y = -1

Correct Answer: A

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

Question 18

Find the area under the curve \( y = x^3 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.

A. 8

B. 16

Correct C. 32

D. 64

Correct Answer: C

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

Question 19

Solve the inequality \( x^2 + 2x - 3 > 0 \) u\sing algebraic manipulation.

A. x < -3

B. x > -3

Correct C. x < 1

D. x > 1

Correct Answer: C

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

Question 20

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

Correct A. \left\( x - 1 \right \)^2 + \left\( y - 2 \right \)^2 = 13

B. \left\( x + 1 \right \)^2 + \left\( y - 2 \right \)^2 = 13

C. \left\( x - 1 \right \)^2 + \left\( y + 2 \right \)^2 = 13

D. \left\( x + 1 \right \)^2 + \left\( y + 2 \right \)^2 = 13

Correct Answer: A

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

Question 21

A rec\tangular box has dimensions 3 cm, 4 cm, and 5 cm. Find the volume of the box.

A. 60 cm^3

B. 80 cm^3

Correct C. 100 cm^3

D. 120 cm^3

Correct Answer: C

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

Question 22

Solve the equation \tan x = \sqrt{3} \sin x.

A. \frac{\pi}{4}

Correct B. \frac{\pi}{3}

C. \frac{\pi}{2}

D. \frac{\pi}{6}

Correct Answer: B

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

Question 23

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

Correct A. y = -\frac{1}{2}x + 5

B. y = \frac{1}{2}x + 3

C. y = -2x + 7

D. y = 2x - 1

Correct Answer: A

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

Question 24

A polynomial function f(x) has zeros at x = -2, x = 1, and x = 3. Write the function in factored form.

Correct A. f(x) = \( x + 2 \)\( x - 1 \)\( x - 3 \)

B. f(x) = \( x - 2 \)\( x + 1 \)\( x - 3 \)

C. f(x) = \( x + 2 \)\( x + 1 \)\( x - 3 \)

D. f(x) = \( x - 2 \)\( x - 1 \)\( x + 3 \)

Correct Answer: A

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

Question 25

Find the determinant of the matrix \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix}.

A. 10

Correct B. 12

C. 15

D. 20

Correct Answer: B

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