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POST UTME FUTO 2022 Mathematics | Objective

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Question 1 View Details

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

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

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

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

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

Correct Answer: A

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Question 2 View Details

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 View Details

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 View Details

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 View Details

Two events ( A ) and ( B ) are independent. 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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

A. 31

B. 32

C. 33

Correct D. 34

Correct Answer: D

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Question 11 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = x\^2\), the x-axis, and the line \$(y = x^2\(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 View Details

Solve the system of equations using 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 View Details

A histogram of exam scores has a mean of 60 and a standard 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 View Details

Find the equation of the line passing 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 View Details

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 View Details

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 View Details

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

Correct A. 2

B. -2

C. 1

D. 0

Correct Answer: A

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Question 18 View Details

A rectangular 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 View Details

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 View Details

A company produces two products, A and B. The profit from product A is 10 per unit, and the profit from product B is15 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 View Details

Find the volume of the solid formed by revolving the region bounded by the parabola (y = $x^2$\), the x-axis, and the line $x = 2\\((y = x^2), the x-axis, and the line$ 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 View Details

Solve the system of linear equations using 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 View Details

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 View Details

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 View Details

Find the equation of the line passing 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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