Free Printable Differential Equation Exam Easy

1.

A geometry student wants to draw a rectangle inscribed in a semicircle of radius 7. If one side must be on the semicircle's diameter, what is the area of the largest rectangle that the

student can draw?

a)

49

b)

42

c)

14

d)

7√7

2.

A farmer wants to construct a rectangular pigpen using 400 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area?

a)

100ft x 200ft

b)

102ft x 196 ft

c)

50 ft x 300 ft

d)

50 ft x 175 ft

3.

If y=2x-8, what is the minimum value of the product xy?

a)

-16

b)

-8

c)

-4

d)

2

4.

The volume of a cylindrical tin can with a top and a bottom is to be 16π cubic inches. If a minimum amount of tin is to be used to construct the can, what must be the height, in inches, of the can?

a)

2 ³√2

b)

2√2

c)

4

d)

2 ³√4

5.

A rectangular page is to contain 144 sq. inches of print. the margins on each side are 1 inch. Find the dimensions of the page that would use the least paper

a)

16, 16

b)

15,15

c)

14,14

d)

13,13

6.

We want to construct a box whose base length is 3 times the base width. If the box must have a volume of 50 ft³, determine the dimensions that will minimize the amount of material used.

a)

w=2.027ft, h=4.055ft, l=6.082ft

b)

w=1.488ft, h=3.347ft, l=6.694ft

c)

w=2.231ft, h=3.347ft, l=6.694ft

d)

w=0.485ft, h=2.111ft, l=4.222ft

7.

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?

a)

3 ft/sec

b)

-7.2 ft/sec

c)

7.2 ft/sec

d)

12

8.

(3 min) The area of a circular region is increasing at a rate of 96 π square meters per second. When the area of the region is 64 π square meters, how fast, in meters per second, is the radius of the region increasing?

a)

6

b)

8

c)

16

d)

4√3

9.

What are the intervals of the graph increasing for f(x) = 2x⁴- 4x² + 1

a)

(-1,0)

b)

(0,1)

c)

(-∞,-1) and (1,∞)

d)

(0,1) and (-1,0)

10.

Find the point(s) of inflection for f(x) = 2(x)^1/5 + 3

a)

None

b)

x = 0

c)

x = 0, 2

d)

x = -2, 0, 2

11.

a)

b)

c)

d)

12.

a)

b)

c)

d)

13.

a)

b)

c)

d)

14.

a)

b)

c)

d)

15.

a)

b)

c)

d)

16.

a)

b)

c)

d)

17.

a)

b)

c)

d)

18.

a)

b)

c)

19.

a)

b)

c)

20.

a)

b)

c)

21.

a)

b)

c)

d)

22.

a)

b)

c)

d)

23.

a)

b)

c)

d)

24.

a)

b)

c)

d)

25.

a)

b)

c)

d)

26.

a)

b)

c)

d)

27.

FInd the derivative:

f(x) = (-2/3)x³ - (1/2)x² + 9x

a)

-2x² - x + 9

b)

-2x² + x + 9

c)

2x² - x + 9

d)

2x² - x - 9

28.

Find the second derivative of the function:
f (x) = 2x - 5x⁶

a)

f ''(x)= 2 - 30x

b)

f ''(x) = 2-30x⁵

c)

f ''(x) = -30x⁵

d)

f ''(x) = -150x⁴

29.

Set up the derivative of y=(3x⁴- 7)*(5x²+ 1)

a)

(12x³)*(10x)

b)

(3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)

c)

(3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)

d)

(3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

30.

Find the derivative of y = 2x² (3x - 4)

a)

6x³ - 8x²

b)

18x² - 16x

c)

15x²- 6x

d)

6x - 4

31.

Differentiate f(x) =(2/ x⁵) - 5.

a)

x⁵-3

b)

-10x⁶

c)

x⁵-5

d)

-10x^-6

32.

Find the derivative of the given equation
f(x) = x⁴ + 4x³- 2x²

a)

x³ + x²- x

b)

4x³ + 12x²+ 4x

c)

4x + 12x - 4x

d)

4x³ + 12x²- 4x

33.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

34.

Find the derivative f(x) = xe^x

a)

f'(x) = e^x

b)

f'(x) = xe^x + xe^x

c)

f'(x) = e^x - xe^x

d)

f'(x) = e^x + xe^x

35.

.

a)

(3x²-2)cos(x³-2x)

b)

-(3x²-2)cos(x³-2x)

c)

cos(2x²-2)

d)

sin(2x²-2)

36.

Find the derivative of g(x)=(3x-2)/(x²+2)

a)

9x²+2

b)

3(x²+2)/(x²+2)²

c)

(-3x²+4x +6)/(x²+2)²

d)

(-3x²+10)/(x²+2)²

37.

The position of an object is given as a function of time by x = 3t² + 5t³- 2t
What is the acceleration of the object at time t = 2 s?

a)

64 m/s/s

b)

60 m/s/s

c)

66 m/s/s

d)

70 m/s/s

38.

The velocity of an object is given as v = 2t + 3t³. what is the acceleration of the object at t = 2 s?

a)

38 m/s/s

b)

27 m/s/s

c)

16 m/s/s

d)

49 m/s/s

39.

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle?

a)

v(t) = -2

b)

v(t) = -2t - 1

c)

v(t) = t³

d)

v(t) = -t

40.

If the position of a particle is represented by x(t) = -t² + 1, what is its instantaneous velocity at t = 1?

a)

v = 0

b)

v = 1

c)

v = -1

d)

v = -2

41.

Find the derivative.
f(x) = -8x^-3 + 5x - e^x

a)

f'(x) = -24x^-4 + 5 - e^x

b)

f'(x) = 24x^-4 + 5 - e^x

c)

f'(x) = 24x^-2 + 5 - e^x

d)

f'(x) = 24x^-4 + 5 - e^x-1

42.

Find the derivative
f(t) = (t² + 2t)⁵

a)

f'(t) = 5(2t+2)⁴

b)

f'(t) = 5(t² + 2t)⁴

c)

f'(t) = 5(t² + 2t)⁴(2t)

d)

f'(t) = 5(t² + 2t)⁴(2t + 2)

43.

Find the second derivative of
f(x) = x²+ e^x - cosx

a)

f"(x) = 2 + e^x + cosx

b)

f"(x) = 2x + e^x + cosx

c)

f"(x) = 2x + xe^x - cosx

d)

f"(x) = 2x + e^x + sinx

44.

f(x)= 9/∛x
f'(x) =

a)

9x^-1/3

b)

-3x^-4/3

c)

-9x^2/3

d)

-3x^2/3

45.

a)

330

b)

165

c)

190

d)

255

46.

a)

9

b)

2

c)

3

d)

6

47.

a)

2

b)

3

c)

1

d)

4

48.

a)

{1/3,-1}

b)

{1/3,1}

c)

{-1/3,-1}

d)

{-1/3,1}

49.

a)

[0,1/2]u[1,infinity]

b)

[-1,1/2]u[1,infinity]

c)

[0,infinity]

d)

[-1/2,0]u[1,infinity]

50.

A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50cm^3/min. When the thickness of the ice is 5cm, then the rate at which the thickness (in cm/min) of the ice decreases, is

a)

$\frac{1}{9\pi}$

b)

$\frac{1}{18\pi}$

c)

$\frac{1}{36\pi}$

d)

$\frac{5}{6\pi}$

51.

a)

6

b)

4

c)

2

d)

0

52.

a)

four rational numbers

b)

two irrational and two rational numbers

c)

four irrational numbers

d)

two irrational and one rational number

53.

a)

-1

b)

1

c)

5/2

d)

-5/2

54.

a)

(-1/5,1)

b)

(1/5,0)

c)

(1/5,-1)

d)

(-1/5,-1)

55.

a)

$-\pi$

b)

$-2\pi$

c)

$\pi$

d)

$2\pi$

56.

a)

( $\sqrt[]{-2}$ ,0 )

b)

( $\sqrt[]{2}$ ,0 )

c)

( $\sqrt[]{-2}$ ,0 )

d)

( $\sqrt[]{-2}$ , $\sqrt[]{2}$ )

57.

a)

3

b)

6

c)

9

d)

15

58.

a)

5

b)

4

c)

3

d)

2

59.

a)

1/4

b)

1/2

c)

1

d)

1/16

60.

a)

b)

c)

d)

61.

a)

b)

c)

d)

62.

The function f is continuous on the closed interval [0,6] and has values given in the table above. The trapezoidal approximation found with 3 subintervals is 52. What is the value of k?

a)

2

b)

6

c)

7

d)

10

63.

A particle moves along an axis so that at any time t>0, its velocity is given by v(t)=4-6t². If the particle is at position p=7 at t=1, what is the position of the particle at t=2?

a)

-10

b)

-5

c)

-3

d)

3

64.

a)

6

b)

ln 25

c)

2

d)

5+ 2/e

65.

a)

b)

c)

d)

66.

What is the area of the region enclosed by the graphs of f(x)=x-2x² and g(x)=-5x?

a)

7/3

b)

16/3

c)

20/3

d)

9

67.

The velocity of a particle moving along an axis is given by v(t)=2-t² for t>0, what is the average velocity of the particle from t=1 to t=3?

a)

-4

b)

-3

c)

8/3

d)

- 7/3

68.

a)

10

b)

20

c)

23

d)

35

69.

a)

b)

c)

d)

70.

Find the limits

\lim_{x\rightarrow2}2x

a)

4

b)

-4

c)

0

71.

$\lim_{x\rightarrow5}x^3$

a)

15

b)

125

c)

20

72.

find the limits

\lim_{x\rightarrow2}\left(x^5-2x^3+x^2-8\right)

a)

11

b)

15

c)

12

73.

What is the limit?

a)

Infinity

b)

20

c)

DNE

d)

12

74.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

75.

It is the foundation of knowledge in Calculus?

a)

Basic Operations

b)

Integers

c)

Function

d)

Limit

76.

What is the answer in the given expression?

\lim_{x\rightarrow50}25

a)

50

b)

25

c)

2

d)

125

77.

What is the answer in the given expression?

\lim_{x\rightarrow121}3\pi

a)

121

b)

11

c)

3 $\pi$

d)

3.14

78.

What is the answer in the given expression?

\lim_{x\rightarrow2}-4x

a)

-4

b)

2

c)

-8

d)

-6

79.

$\lim_{x\rightarrow4}6x$

a)

24

b)

32

c)

28

80.

An equation that contains only ordinary derivatives of one or more dependent variables with respect to a single independent variable

a)

Dependent Differential Equation

b)

First Order Differential Equation

c)

Partial Differential Equation

d)

Ordinary Differential Equation

81.

An equation containing derivatives of one or more dependent variables with one or more independent variables?

a)

Partial Equation

b)

Different Equation

c)

Differential Equation

d)

Ordinary Equation

82.

An equation containing partial derivatives of one or more dependent variables of two or more independent variables

a)

Ordinary Partial Differential Equation

b)

Partial Differential Equation

c)

Ordinary Differential Equation

d)

Partially Ordinary Differential Equation

83.

\frac{\text{d}x}{\text{d}y}=\cos\ x

is an ordinary differential equation

a)

True

b)

False

84.

a)

is a differential equation

b)

is not a differential equation

c)

either ordinary or partial differential equation

d)

neither ordinary of partial differential equation

85.

it is number of the highest degree in a differential equation

a)

variable

b)

degree

c)

order

d)

derivative

86.

The power of the differential equation's highest derivative, after the equation has been made rational and integral in all of its derivatives

a)

order

b)

degree

c)

exponent

d)

variable

87.

which is true?

a)

it is a partial differential equation

b)

it is an ordinary differential equation

c)

it is not a differential equation

d)

it is an equation that cannot be differentiated

88.

when the dependent variable and all of its derivatives are of the first degree, the equation is

a)

non linear

b)

linear

c)

both linear and non linear

d)

none of the options

89.

an equation is non-linear if the coefficients depend at most on the "independent" variables

a)

True

b)

False

90.

in $\frac{\text{d}x}{\text{d}y}$ , which is the dependent variable?

a)

x

b)

y

c)

d

d)

secret

91.

in $\frac{\text{d}y}{\text{d}x}$ , the independent variable is

a)

x

b)

y

c)

d

d)

none of the options syempre!

92.

$\frac{\partial x}{\partial y}$ is a partial derivative

a)

Yes

b)

No

c)

neither

d)

Either

93.

Check all ordinary differential equation

a)

$\frac{\text{d}x}{\text{d}t}=5x-3$

b)

$\frac{\partial x}{\partial y}-2=3xy$

c)

$\left(x^2+y^2\right)dx-2xydy=0$

d)

$\left(\frac{\partial^3W}{\partial x^2}\right)^3=xy\frac{\partial^2W}{\partial y^2}+\frac{\partial^2W}{\partial z^2}=0$

94.

Check all partial differential equation

a)

$\frac{\text{d}x}{\text{d}t}=5x-3$

b)

$\frac{\partial x}{\partial y}-2=3xy$

c)

$\left(x^2+y^2\right)dx-2xydy=0$

d)

$\left(\frac{\partial^3W}{\partial x^2}\right)^3=xy\frac{\partial^2W}{\partial y^2}+\frac{\partial^2W}{\partial z^2}=0$

95.

Find the general solution of the differential equation.

a)

A

b)

B

c)

C

d)

D

96.

Find the general solution of the differential equation.

a)

A

b)

B

c)

C

d)

D

97.

Find the general solution of the differential equation.

a)

A

b)

B

c)

C

d)

D

98.

Find the general solution of the differential equation.

a)

A

b)

B

c)

C

d)

D

99.

Find the particular solution of the differential equation that satisfies the initial condition.

a)

A

b)

B

c)

C

d)

D

100.

Find the particular solution of the differential equation that satisfies the initial condition.

a)

A

b)

B

c)

C

d)

D

101.

Find the particular solution of the differential equation that satisfies the initial condition.

a)

A

b)

B

c)

C

d)

D

102.

Find the particular solution of the differential equation that satisfies the initial condition.

a)

A

b)

B

c)

C

d)

D

103.

Find the particular solution of the differential equation that satisfies the initial condition.

a)

A

b)

B

c)

C

d)

D

104.

Find the particular solution of the differential equation that satisfies the initial condition.

a)

A

b)

B

c)

C

d)

D

Differential Equation Exam Easy

Total questions: 104

Worksheet time: 3hrs 55mins

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