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POST UTME FUTO 2021 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 7 View Details

A circle with center (C\) passes through points $A\\((C) passes through points$ and (B\). If $AB = 6\\((B). If$ 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 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of the function ( f(x) = $\frac{1}${\sqrt{1 - $x^2}}$\) ) using 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 View Details

Evaluate the definite integral $\int_0^1 x^2 $1x \$ 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 View Details

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 View Details

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 View Details

A binary operation (*\) on the set $\\((*) on the set \{0, 1}$ is defined as follows: $0*0 = 0, 0*1 = 1, 1*0 = 1, 1*1 = 0\\(}) is defined as follows:$. 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

A histogram shows that the heights of a group of people are normally distributed with a mean of 170 cm and a standard 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 View Details

Find the derivative of the function ( f(x) = $\frac{1}${$\sqrt{x}$}\) ) using 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 View Details

A histogram of exam scores has a mean of 75 and a standard 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 View Details

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 View Details

Solve the system of equations using 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 View Details

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