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

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Question 1

Find the derivative of ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.

Correct A. $ \frac{d}{dx} left\( \frac{1}{\sqrt{x}} \right \ $ = \frac{-1}{2x\sqrt{x}} )

B. $ \frac{d}{dx} left\( \frac{1}{\sqrt{x}} \right \ $ = \frac{1}{2x\sqrt{x}} )

C. $ \frac{d}{dx} left\( \frac{1}{\sqrt{x}} \right \ $ = \frac{1}{x\sqrt{x}} )

D. $ \frac{d}{dx} left\( \frac{1}{\sqrt{x}} \right \ $ = \frac{-1}{x\sqrt{x}} )

Correct Answer: A

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Question 2

Solve for ( x ) in the equation $ 2^x + 5^x = 7^x $.

A. $ x = 2 $

Correct B. $ x = 3 $

C. $ x = 4 $

D. $ x = 5 $

Correct Answer: B

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Question 3

Find the area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 4 $.

Correct A. $ \frac{64}{3} $

B. $ \frac{32}{3} $

C. $ \frac{16}{3} $

D. $ \frac{8}{3} $

Correct Answer: A

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Question 4

A vector ( mathbf{a} ) has magnitude 5 and direction $ 30^circ $ from the positive x-axis. Find the vector ( mathbf{a} ) in component form.

Correct A. $ mathbf{a} = egin{pmatrix} 4 \ 3 \end{pmatrix} $

B. $ mathbf{a} = egin{pmatrix} 3 \ 4 \end{pmatrix} $

C. $ mathbf{a} = egin{pmatrix} 5 \ 0 \end{pmatrix} $

D. $ mathbf{a} = egin{pmatrix} 0 \ 5 \end{pmatrix} $

Correct Answer: A

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Question 5

Two events ( A ) and ( B ) are indep\endent. If ( P(A) = 0.4 ) and ( P(B) = 0.6 ), find ( P(A cap B) ).

Correct A. ( 0.24 )

B. ( 0.36 )

C. ( 0.48 )

D. ( 0.60 )

Correct Answer: A

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Question 6

Determine the value of x in the equation $ \log_{10} \( x^2 \ $ = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 7

Solve for y in the equation $ y = \frac{1}{2} \left\( \frac{1}{3} \right \ $^x ).

Correct A. \frac{1}{6}

B. \frac{1}{12}

C. \frac{1}{18}

D. \frac{1}{24}

Correct Answer: A

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Question 8

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?

A. \frac{1}{2}

Correct B. \frac{2}{7}

C. \frac{3}{8}

D. \frac{5}{8}

Correct Answer: B

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Question 9

Find the determinant of the matrix $ \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} $.

Correct A. 1

B. -1

C. 2

D. -2

Correct Answer: A

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Question 10

A sequence is defined by the recurrence relation $ a_n = 2a_{n-1} + 3 $. If $ a_1 = 2 $, find the value of $ a_5 $.

A. 31

B. 32

C. 33

Correct D. 34

Correct Answer: D

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Question 11

Find the volume of the solid formed by revolving the region bounded by the curve y = x^2, the x-axis, and the line x = 2 about the x-axis.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 12

Solve the system of equations u\sing matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 8 \end{bmatrix}

Correct A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \\ 3 \end{bmatrix}

C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \\ 5 \end{bmatrix}

Correct Answer: A

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Question 13

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 14

Find the equation of the line pas\sing through the points (2, 3) and (4, 5).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x + 2

D. y = x - 2

Correct Answer: A

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Question 15

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

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 16

Find the value of x in the quadratic equation $ x^2 + 5x - 6 = 0 $.

Correct A. 2

B. -3

C. 1

D. -2

Correct Answer: A

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Question 17

A particle moves along the curve $ y = x^2 - 4x + 2 $. Find the rate of change of y with respect to x when x = 2.

Correct A. 2

B. -2

C. 1

D. 0

Correct Answer: A

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Question 18

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.

Correct A. 30

B. 50

C. 60

D. 70

Correct Answer: A

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Question 19

Solve the inequality $ 2x^2 + 5x - 3 > 0 $.

Correct A. $ -\infty, -1 $ \cup $ 3, \infty $

B. $ -\infty, 1 $ \cup $ 3, \infty $

C. $ -\infty, -1 $ \cup $ 1, \infty $

D. $ -\infty, 1 $ \cup $ 1, \infty $

Correct Answer: A

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Question 20

A company produces two products, A and B. The profit from product A is $10 per unit, and the profit from product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. $1500

Correct B. $2000

C. $2500

D. $3000

Correct Answer: B

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Question 21

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

Correct A. $ \frac{32}{15} pi $

B. $ \frac{64}{15} pi $

C. $ \frac{16}{3} pi $

D. $ \frac{32}{3} pi $

Correct Answer: A

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Question 22

Solve the system of linear equations u\sing matrices: $ egin{cases} 2x + 3y = 7 \ x - 2y = -3 \end{cases} $.

Correct A. $ x = 1, y = 2 $

B. $ x = 2, y = 1 $

C. $ x = 3, y = 4 $

D. $ x = 4, y = 3 $

Correct Answer: A

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Question 23

Find the surface area of the sphere with radius $ r = 4 $ cm.

Correct A. ( 32 pi ) cm^2

B. ( 64 pi ) cm^2

C. ( 128 pi ) cm^2

D. ( 256 pi ) cm^2

Correct Answer: A

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Question 24

Solve the inequality $ 2x^2 + 5x - 3 > 0 $.

Correct A. $ x < -1 $ or $ x > \frac{3}{2} $

B. $ x < -1 $ or $ x < \frac{3}{2} $

C. $ x > -1 $ or $ x < \frac{3}{2} $

D. $ x > -1 $ or $ x > \frac{3}{2} $

Correct Answer: A

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Question 25

Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. $ y = 2x + 1 $

B. $ y = 2x - 1 $

C. $ y = -2x + 1 $

D. $ y = -2x - 1 $

Correct Answer: A

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