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POST UTME FUTO 2021 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 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

Correct A. $ \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ $ )

B. $ \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ $ + 3 )

C. $ \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ $ - 2 )

D. $ \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ $ + 2 )

Correct Answer: A

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Question 2

Solve the system of equations $ egin{cases} x + y = 4 \ 2x - 3y = -3 \end{cases} $.

Correct A. $ x = \frac{7}{5}, y = \frac{17}{5} $

B. $ x = \frac{7}{5}, y = -\frac{17}{5} $

C. $ x = -\frac{7}{5}, y = \frac{17}{5} $

D. $ x = -\frac{7}{5}, y = -\frac{17}{5} $

Correct Answer: A

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Question 3

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 = 32 )

C. $ x - 2 \ $^2 + $ y - 3 $^2 = 64 )

D. $ x - 2 \ $^2 + $ y - 3 $^2 = 128 )

Correct Answer: A

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Question 4

Find the volume of the solid formed by rotating the region bounded by the curves $ y = x^2 $ and $ y = 2x $ about the x-axis.

Correct A. $ \frac{8}{3} pi $

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

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

D. $ \frac{64}{3} pi $

Correct Answer: A

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Question 5

Find the surface area of the solid formed by rotating the region bounded by the curves $ y = x^2 $ and $ y = 2x $ about the x-axis.

Correct A. ( 16 pi )

B. ( 32 pi )

C. ( 64 pi )

D. ( 128 pi )

Correct Answer: A

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Question 6

Determine the value of $n$ in the equation $2^n + 5 cdot 2^{n-1} = 33$.

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 7

A circle with center $C$ passes through points $A$ and $B$. If $AB = 6$ and $CA = 3$, find the area of the circle.

A. 9\pi

B. 12\pi

Correct C. 18\pi

D. 24\pi

Correct Answer: C

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Question 8

Solve the inequality $\frac{x-2}{x+1} > 0$.

Correct A. $$ -\infty, -1 $ \cup $ 2, \infty $$

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

C. $$ -\infty, 2 $ \cup $ 1, \infty $$

D. $$ -\infty, 2 $ \cup $ -1, \infty $$

Correct Answer: A

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Question 9

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

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 10

A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. \frac{1}{6}

B. \frac{1}{3}

C. \frac{1}{2}

Correct D. \frac{2}{3}

Correct Answer: D

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Question 11

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

Correct A. f'(x) = \frac{x}{$ 1 - x^2 $^{3/2}}

B. f'(x) = \frac{-x}{$ 1 - x^2 $^{3/2}}

C. f'(x) = \frac{1}{$ 1 - x^2 $^{3/2}}

D. f'(x) = \frac{-1}{$ 1 - x^2 $^{3/2}}

Correct Answer: A

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Question 12

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

Correct A. 2\sin(1) - 2\cos(1)

B. 2\sin(1) + 2\cos(1)

C. -2\sin(1) + 2\cos(1)

D. -2\sin(1) - 2\cos(1)

Correct Answer: A

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Question 13

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

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

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

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

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

Correct Answer: A

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Question 14

Find the area under the curve $ y = x^3 - 2x^2 + x + 1 $ from $ x = 0 $ to $ x = 2 $.

Correct A. \frac{23}{2}

B. \frac{25}{2}

C. \frac{27}{2}

D. \frac{29}{2}

Correct Answer: A

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Question 15

A binary operation $*$ on the set $ \{0, 1\} $ is defined as follows: $ 0*0 = 0, 0*1 = 1, 1*0 = 1, 1*1 = 0 $. Find the value of $ 1*0 $*$ 1*1 $.

A. 0

Correct B. 1

C. 10

D. 01

Correct Answer: B

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Question 16

Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.

Correct A. 13

B. 15

C. 17

D. 19

Correct Answer: A

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Question 17

A set of 10 numbers has a mean of 20. If 5 is added to each number, what is the new mean?

A. 22

Correct B. 25

C. 28

D. 30

Correct Answer: B

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Question 18

Find the volume of the frustum of a cone with height 10, lower base radius 4, and upper base radius 6.

A. 100π

Correct B. 120π

C. 140π

D. 160π

Correct Answer: B

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Question 19

A sequence is defined by the formula an = 2n + 1. Find the sum of the first 5 terms.

A. 15

B. 17

C. 19

Correct D. 21

Correct Answer: D

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Question 20

A histogram shows that the heights of a group of people are normally distributed with a mean of 170 cm and a s\tandard deviation of 5 cm. What is the probability that a randomly selected person is taller than 180 cm?

A. 0.1587

B. 0.3413

C. 0.4772

Correct D. 0.6827

Correct Answer: D

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Question 21

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

Correct A. x^{-3/2}

B. -x^{-3/2}

C. x^{-1/2}

D. x^{1/2}

Correct Answer: A

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Question 22

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 23

Find the volume of the solid formed by rotating the region bounded by the curves $ y = x^2 $ and $ y = x^3 $ about the x-axis.

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

B. \frac{\pi}{10}

C. \frac{\pi}{5}

D. \frac{\pi}{2}

Correct Answer: A

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Question 24

Solve the system of equations u\sing matrices: \begin{align*} 2x + 3y &= 7 \ 4x - 2y &= -3 \end{align*}

Correct A. \begin{pmatrix} x = 1 \ y = 2 \end{pmatrix}

B. \begin{pmatrix} x = 2 \ y = 1 \end{pmatrix}

C. \begin{pmatrix} x = 3 \ y = 4 \end{pmatrix}

D. \begin{pmatrix} x = 4 \ y = 3 \end{pmatrix}

Correct Answer: A

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Question 25

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

Correct A. \frac{64}{3}

B. \frac{32}{3}

C. \frac{16}{3}

D. \frac{8}{3}

Correct Answer: A

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