Free Printable REDEMPTION ROM 2

1.

Find the area of a shaded region

a)

80/3

b)

40/3

c)

26/3

d)

80/6

2.

Find the area under the curve

a)

^17/5

b)

6/5

c)

13/3

d)

1/3

3.

Find the area under the curve

a)

1/3

b)

3

c)

2/3

d)

4/3

4.

Which definite integral models the area highlighted above?

a)

b)

c)

d)

5.

$\int_0^1f\left(x\right)dx\$ is

a)

Positive

b)

Negative

c)

0

d)

Cannot be determined

6.

Using the areas of each region given
$\int_a^df\left(x\right)=$

a)

6

b)

20

c)

2

d)

24

7.

Which integral has the largest value?

a)

$\int_a^bf\left(x\right)dx$

b)

$\int_b^cf\left(x\right)dx$

c)

$\int_a^cf\left(x\right)dx$

d)

$\int_a^df\left(x\right)dx$

8.

Calculate the area for the shaded region on the parabola y = 8 - 2x - x²

a)

63.64 units²

b)

18.34 units²

c)

4.56 units²

d)

30.67 units²

e)

39.33 units²

9.

Calculate the area for the shaded region on the function y = x³ - 3x² +2x

a)

1.4 units²

b)

0.5 units²

c)

0.56 units²

d)

2.67 units²

e)

0.33 units²

10.

Which integral best represents the shaded area?

a)

$2\int_0^a\left(x^2-3\right)dx$

b)

$2\int_{-a}^0\left(x^2-3\right)dx$

c)

$\int_{-a}^a\left(x^2-3\right)dx$

d)

$\int_{-a}^a\left(3-x^2\right)dx$

11.

Which integral best represents the shaded region?

a)

$\int_3^5x\ dx$

b)

$\int_3^5\sqrt{x-3}\ dx$

c)

$\int_0^{\sqrt{2}}\left(x-3\right)dy$

d)

$\int_0^{\sqrt{2}}\left(y^2+3\right)dy$

12.

Which integral best represents the shaded region?

a)

$\int_1^{e^3}\left(\frac{1}{3}\ln y\right)dy$

b)

$\int_0^1e^{3x}dx$

c)

$\int_1^{e^3}\left(\ln\frac{1}{3}y\right)dy$

d)

$e^3-\int_0^1e^{3x}dx$

13.

Find the area of the region bounded by the graphs of y = x² and y = 4x.

a)

32/3

b)

64/3

c)

32

d)

64

e)

32/5

14.

The area of the shaded region is:

a)

b)

c)

15.

a)

A

b)

B

c)

C

d)

D

16.

a)

A

b)

B

c)

C

d)

D

17.

a)

A

b)

B

c)

C

d)

D

18.

a)

A

b)

B

c)

C

d)

D

19.

a)

General solution

b)

Particular solution

20.

a)

Highest derivative

b)

Highest power

c)

Lowest derivative

d)

Lowest power

21.

a)

power of highest derivative

b)

power of lowest derivative

c)

derivative of highest power

d)

derivative of lowest power

22.

23.

a)

Integrating factor

b)

Separable Variable

24.

a)

Particular solution

b)

General solution

25.

a)

General solution

b)

Particular solution

26.

a)

Highest derivative

b)

Highest power

c)

Lowest derivative

d)

Lowest power

27.

a)

power of highest derivative

b)

power of lowest derivative

c)

derivative of highest power

d)

derivative of lowest power

28.

29.

a)

Integrating factor

b)

Separable Variable

30.

a)

Particular solution

b)

General solution

31.

32.

*can replace modulus with bracket

33.

34.

35.

36.

37.

38.

39.

40.

41.

give your answer in terms of x

42.

give your answer in terms of x

43.

Find the area under the curve y =3x²-2x from x= 1 to x =5.

a)

100

b)

99

c)

150

d)

152

44.

Find the area of a shaded region

a)

80/3

b)

40/3

c)

26/3

d)

80/6

45.

Find the area under the curve

a)

^17/5

b)

6/5

c)

13/3

d)

1/3

46.

Find the area under the curve

a)

-1/3

b)

3

c)

-2/3

d)

-4/3

47.

Calculate the area for the shaded region on the parabola y = 8 - 2x - x²

a)

63.64 units²

b)

18.34 units²

c)

30.67 units²

d)

39.33 units²

48.

Calculate the area for the shaded region on the function y = x³ - 3x² +2x

a)

1.4 units²

b)

0.5 units²

c)

2.67 units²

d)

0.33 units²

49.

Find the area of the highlighted section

a)

$\frac{11}{4}$

b)

$\frac{7}{4}$

c)

$\frac{3}{4}$

d)

$\frac{15}{4}$

50.

Calculate the area for the shaded region on the function y = x⁴ - 5x² + 4

a)

12 units²

b)

8 units²

c)

11 units²

d)

10 units²

51.

Find the area enclosed by

y=x^3-4x\

and the x-axis.

a)

8

b)

6

c)

10

d)

12

52.

Given $f\left(x\right)=x^3+1\ and\ g\left(x\right)=x+1$

Choose the CORRECT statement

a)

The shaded area is bounded between f(x) and y axis

b)

$Area=\int_{-1}^1f\left(x\right)-g\left(x\right)\ dx$

c)

$Area=\int_{-1}^0g\left(x\right)-f\left(x\right)\ dx+\int_0^1f\left(x\right)-g\left(x\right)\ dx$

d)

$Area=\int_{-1}^0f\left(x\right)-g\left(x\right)\ dx+\int_0^1g\left(x\right)-f\left(x\right)\ dx$

53.

Which of the following is the correct formula of integration to find the volume of the solid of the shaded area when revolved about the y-axis?

a)

A

b)

B

c)

C

d)

D

54.

Which integral best represents the volume of revolution when the shaded area is rotated $2\pi$ radians about the y-axis.

a)

$\pi\int_0^3\left(x-3\right)dx$

b)

$\pi\int_0^3y^2dy$

c)

$\pi\int_0^{\sqrt{2}}y^2+3\ dy$

d)

$\pi\int_0^{\sqrt{2}}\left(y^2+3\right)^2\ dy$

55.

Which integral best represents the volume of revolution when the shaded area is rotated 2π radians about the x-axis.

a)

$\pi\int_{-\sqrt[]{3}}^{\sqrt[]{3}}-\left(x^2-3\right)^2\ dx$

b)

$\pi\int_{-\sqrt[]{3}}^{\sqrt[]{3}}\left(x^2-3\right)^2\ dx$

c)

$2\pi\int_{-\sqrt[]{3}}^{\sqrt[]{3}}-\left(x^2-3\right)^2\ \ dx$

d)

$2\pi\int_{-\sqrt[]{3}}^{\sqrt[]{3}}\left(x^2-3\right)^2\ dx$

56.

Which integral best represents the volume of revolution when the shaded area is rotated 2π radians about the x-axis.

a)

$\pi\int_1^{e^3}\left(\frac{1}{3}\ln y\right)^2dy$

b)

$\pi\int_0^1\left(e^5-e^{5x}\right)dx$

c)

$\pi\int_0^1\left(e^3-e^{3x}\right)^2dx$

d)

$\pi\int_0^1e^6-e^{6x}\ dx$

57.

Which integral best represents the volume of revolution when the shaded area is rotated $360\degree$ about the x-axis.

a)

$\pi\int_{-1}^1\left(x^2-9+e^{-x}\right)dx$

b)

$\pi\int_{-1}^1\ e^{-2x}-\left(x^2-9\right)^2\ dx$

c)

$\pi\int_{-1}^1\left(x^2-9\right)^2-e^{-2x}dx$

d)

$\pi\int_{-1}^1\left(x^2-9-e^{-x}\right)^2dx$

58.

Write the integral that would be used to find the volume of the region bounded by x = -1, x = 2, y = 0 and $y=\frac{1}{2}x^2+2$ .

a)

b)

c)

d)

59.

a)

b)

c)

d)

60.

Which integral would be used to find the volume of the solid that results when the region enclosed by the curves is revolved about the indicated axis?

a)

A

b)

B

c)

C

d)

D

61.

Which integral would be used to find the volume of the solid that results when the region enclosed by the curves is revolved about the x-axis?

a)

A

b)

B

c)

C

d)

D

62.

Find the volume of the solid obtained by rotating the region bounded by $y=x^2-6x+11$ and $y=6$ 360 degree about the x-axis .

a)

286.613

b)

294.891

c)

312.431

d)

320.108

63.

Find the volume of the solid obtained by rotating the region bounded by $y=x^2-6x+11$ and $y=7$ $2\pi$ about the x axis in terms of $\pi$

a)

$\frac{582}{5}\pi$

b)

$-\frac{582}{5}\pi$

c)

$\frac{528}{5}\pi$

d)

$-\frac{528}{5}\pi$

64.

Find the volume of the solid obtained by rotating the region bounded by $y=x^2-6x+11$ , $x=3$ and both axes $2\pi$ about the y axis.

a)

460.2 $unit^3$

b)

6.283 $unit^3$

c)

466.5 $unit^3$

d)

777.5 $unit^3$

65.

Which integral would be used to find the volume of the solid that results when the region enclosed by the curves is revolved about the x axis?

a)

A

b)

B

c)

C

d)

D

66.

2. Solve the differential equation

𝑑𝑦/𝑑𝑡 =3𝑡²/𝑦 with initial condition

𝑦(2) = 0.

a)

$y=\ln\left|15t\right|$

b)

$y=16t^3$

c)

$y\ =\ \sqrt{2t^3-16}$

d)

$y=2t^3-16$

67.

Determine the value of "c" that satisfies the differential equation $\frac{dy}{dx}=\frac{x+1}{y+2}$ if the curve goes through the point (0, -1).

a)

5/2

b)

-3/2

c)

-1/2

d)

1

68.

Which of the following is the solution to the differential equation $\frac{dy}{dx}=\frac{x^2}{y}$ with the initial condition y(3) = -2?

a)

$y=-2e^{\left(-9+\frac{x^3}{3}\right)}$

b)

$y=\sqrt{\frac{2x^3}{3}}$

c)

$y=\sqrt{\frac{2x^3}{3}-14}$

d)

$y=-\sqrt{\frac{2x^3}{3}-14}$

69.

Given the differential equation dP/Dt=5P

A) Find the general solution for P to the differential equation

B)Find the particular solution for P to the differential equation given P(0)= 418

a)

A) P=Ce^5t

B) P= 5e^418t

b)

A) P=Ce^5t

B) P= 418e^5t

c)

A) P=Ce^t

B) P= 418e^t

d)

A) P=Ce^10t

B) P= 418e^10t

70.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=\frac{1}{\cos y}$

a)

$\sin y=1+C$

b)

$\sin y=x+C$

c)

$-\sin y=\frac{x^2}{2}+C$

d)

$\sin y=0+C$

71.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=e^x$

a)

$1=e^x+C$

b)

$y=\frac{e^x}{2}+C$

c)

$y=e^x+C$

d)

$0=e^x+C$

72.

Let $\frac{dy}{dx}=-0.4y$ and $y=5\$ when $x=0$ .

What is the solution for $y$ ?

a)

$y=5e^{-0.4x}$

b)

$y=-0.4e^{5x}$

c)

$y=5e^{-\frac{x}{0.4}}$

d)

$y=0.4e^{\frac{x}{5}}$

73.

Solve the differential equation $\frac{dy}{dt}=\frac{3t^2}{y}$ with initial condition 𝑦(2) = 0.

a)

𝑦 = ln(15t)

b)

𝑦 = 16t³

c)

𝑦 = (2𝑡³− 16)^1/2

d)

𝑦 = (2𝑡³−16)

74.

The population of the little town of Scorpion Gulch is now 1000 people. The population is presently growing at about 5% per year.

Find the general solution.

a)

P=0.05e^1000t

b)

P=1000e^5t

c)

P=1000e^0.05t

d)

p=lne^1000t

75.

The number of mosquitoes at the beginning of the summer was 4000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 month?

a)

9765

b)

9766

c)

9006

d)

5433

76.

Which cooling equation correctly represents the following scenario? Boiling soup is $100\degree F$ when it is taken off of the stove in a $69\degree F$ . After 15 minutes the temperature of the soup is $95\degree F$

a)

$T\left(t\right)=100e^{-0.011726t}+69$

b)

$T\left(t\right)=31e^{-0.011726t}+69$

c)

$T\left(t\right)=31e^{-0.05435t}+100$

d)

$T\left(t\right)=31e^{-0.05435t}+69$

77.

Given the cooling equation $T\left(t\right)=90e^{-0.008377t}+75$ is the temperature of a turkey after t minutes, what would the temperature be after 50 minutes?

a)

about $200\degree F$

b)

about $164\degree F$

c)

about $134\degree F$

d)

about $100\degree F$

78.

Find the particular solution W = W(t) to the differential equation $\frac{dW}{dt}=\frac{1}{25}\left(W-300\right)$ knowing that W(0) = 1400

a)

$W\left(t\right)=300+1100e^{\frac{1}{25}t}$

b)

$W\left(t\right)=300+\frac{1}{25}e^{1100t}$

c)

$W\left(t\right)=1100+300e^{\frac{1}{25}t}$

d)

$W\left(t\right)=300t+1100e^{\frac{1}{25}}$

79.

A rumor spreads among a population of N people at a rate proportional to the product of the number of people who have heard the rumor and the number of people who have not heard the rumor. If p denotes the number of people who have heard the rumor, which of the following differential equations could be used to model this situation with respect to time t, where k is a positive constant.

a)

$\frac{dp}{dt}=kp\left(N-p\right)$

b)

$\frac{dp}{dt}=kp$

c)

$\frac{dp}{dt}=kp\left(N-t\right)$

d)

$\frac{dp}{dt}=kp\left(p-N\right)$

80.

Population y grows according to the equation dy/dt = ky, where k is a constant and t is measured in years. If the population doubles every 10 years then the value of k is

a)

0.200

b)

0.069

c)

0.301

d)

3.322

81.

A puppy weighs 2.0 pounds at birth and 3.5 pounds two months later. If the weight of the puppy during its first 6 months is increasing at a rate proportional to its weight, then how much will the puppy 3weigh when it is 3 months old?

a)

4.6 pounds

b)

6.5 pounds

c)

4.8 pounds

d)

5 pounds

REDEMPTION ROM 2

Total questions: 81

Worksheet time: 7hrs 45mins

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