Free Printable Calculus: 5th 6-Weeks Bonus Quiz

1.

Find the limit

a)

0

b)

8

c)

16

d)

Does Not Exist (DNE)

2.

Find the Limit

a)

0

b)

-1/4

c)

-5/4

d)

1

e)

DNE

3.

Find the limit as x approaches 1⁺

a)

1

b)

-1

c)

-3

d)

Infinity

e)

DNE

4.

Find the limit as x approaches 1

a)

1

b)

-1

c)

-3

d)

DNE

5.

Select all statements that are TRUE.

a)

b)

c)

d)

e)

6.

Determine the Limit at Infinity

a)

0

b)

-1

c)

-5/2

d)

DNE

e)

infinity

7.

Find the limit at infinity

a)

0

b)

1

c)

infinity

d)

DNE

8.

Which of the following statement(s) are false?

a)

f is continuous at a

b)

the limit as x approaches a exists

c)

f is differentiable at a

d)

f(a) exists

e)

None, all statements are true

9.

Find the value for that makes f(x) continuous.

a)

0

b)

1

c)

1.5

d)

2

e)

No such value exists

10.

a)

-12

b)

-4

c)

3

d)

7

e)

No such value exists

11.

If f(x)=a^x, what does f'(x) equal to?

a)

ln(x)

b)

ln(a)

c)

a^x

d)

ln(a)a^x

12.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

13.

Differentiate f(x) =(2/x⁵) - 5.

a)

x⁵-3

b)

-10x⁶

c)

x⁵-5

d)

-10x^-6

14.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

15.

If a function has a derivative that is negative, what does that tell you?

a)

The function is increasing

b)

The function is decreasing

c)

The concavity of the function is up

d)

The concavity of the function is down

16.

Velocity is the anti derivative of...

a)

jerk

b)

position function

c)

a vector

d)

acceleration

17.

Find the derivative of the given equation
f(x) = 7

a)

7

b)

0

c)

7x

d)

14

18.

When applying calculus. The second derivative helps find...

a)

the distance traveled by an object.

b)

The velocity of a particle at any given point

c)

acceleration of an object at any given time

19.

a)

b)

c)

d)

20.

a)

b)

c)

d)

21.

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

22.

a)

b)

c)

d)

23.

What is the derivative of sin(x)?

a)

sin(x)

b)

cos(x)

c)

-sin(x)

d)

-cos(x)

24.

What is the derivative?

a)

A

b)

B

c)

C

d)

D

25.

What is the derivative of cos(x)?

a)

sin(x)

b)

cos(x)

c)

-sin(x)

d)

-cos(x)

26.

Find the derivative of the given equation
f(x) = x³ + x² + 3

a)

3x² + 2x

b)

3x + 2x

c)

3x + 2x + 3

d)

x³ + x²

27.

f(x)=5x
find f'(x)

a)

5

b)

1

c)

0

d)

5x

28.

y=9
y'=

a)

9

b)

0

c)

1

d)

undefinded

29.

f(x)= 5/x^{2
f'(x) =}

a)

5x

b)

5/2x

c)

5x^-2

d)

-10/x³

30.

When do you use the chain rule?

a)

anytime you want

b)

when there is a function in a function

c)

where there are multiple layers to a lasagna (yum)

d)

when there is division

31.

d/dx (sin²x) = ?

a)

2sin x

b)

2(sin x)(cos x)

c)

2cos x

d)

2x(cos x)

32.

Find dy/dx for
y = (x² + 1)³

a)

dy/dx = 3(x² + 1)²

b)

dy/dx = 3(2x)²

c)

dy/dx = 3(x² + 1)²(2x)

d)

dy/dx = 2x(x² + 1)²

33.

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

34.

Find the derivative: h(x)=(3x+2)(5x³+2x)

a)

60x³+30x +12x-4

b)

60x³-30x²+12x-4

c)

45x³+30x²+12x+4

d)

60x³+30x²+12x+4

35.

How many derivatives can you take of a function?

a)

only 3

b)

only 2

c)

only 1

d)

until you can no longer derive it

36.

The derivative of

a)

y'=2x-x^-2

b)

y'=x^-1+8x

c)

y'=x^-2+8x

d)

y=8x-x^-2

37.

Find h'(3)

a)

-2

b)

0

c)

1

d)

3

38.

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

39.

The acceleration function is the first derivative of...

a)

position

b)

velocity

c)

calculus

d)

particle motion

40.

A railroad track and a road cross at right angles. An observer stands on the road 70 meters south of the crossing and watches an eastbound train traveling at 60 meters per second. At how many meters per second is the train moving away from the observer 4 seconds after it passes through the intersection?

a)

57.60

b)

57.88

c)

59.20

d)

67.40

41.

The radius of a sphere is decreasing at a rate of 2 cm/sec. At the instant when the radius of the sphere is 3 cm, what is the rate of change, in cm²/sec, of the surface area of the sphere? (The surface area of a sphere is A = 4πr².)

a)

-108π

b)

-72π

c)

-48π

d)

-24π

42.

Which of the following best describes the continuity at x = 0?

a)

Continuous

b)

Removable Point Discontinuity

c)

Non-removable Infinite Discontinuity

d)

Non-removable Jump Discontinuity

43.

Which of the following best describes the continuity at x = -3?

a)

Continuous

b)

Removable Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

44.

What is the limit?

a)

Infinity

b)

20

c)

DNE

d)

12

45.

Answer the following:

a)

B

b)

C

c)

D

d)

E

46.

At time t ≥ 0, the acceleration of a particle moving on the x-axis is a(t)=t+sint. At t=0, the velocity of the particle is -2. For what value of t will the velocity be zero?

a)

1.02

b)

1.48

c)

1.85

d)

2.81

47.

F(3)=8 and F’(3)=-4 the F(3.02) is approximately

a)

7.92

b)

7.98

c)

8.02

d)

8.08

48.

a)

A

b)

B

c)

C

d)

D

49.

Consider the differential equation dy/dx = x + 2y for which g(x) is the solution. Which of the following statements is true if the particular solution contains (0,-1)

a)

g(x) is increasing and concave up

b)

g(x) is increasing and concave down

c)

g(x) is decreasing and concave up

d)

g(x) is decreasing and concave down

50.

Find the limit of the function as x approaches 2.

a)

1

b)

-1

c)

5

d)

DNE

51.

The acceleration function is the first derivative of...

a)

position

b)

velocity

c)

calculus

d)

particle motion

52.

Differentiate y= 12x^-2

a)

24x^-1

b)

-24x^-3

c)

-24x^-1

d)

6x^-3

53.

If f'(x) = 0 what does that imply about the x value?

a)

It is a critical point, it is a possible max, min, or point of inflection.

b)

That the limit does not exist.

54.

Integration is the inverse of differentiation but it applications it can be used to....

a)

find the area under a curve

b)

calculate the force of an object

c)

Find the altitude of an objects perimeter

55.

Is differentiating the same as taking the derivative?

a)

yes

b)

no

c)

banana on my rice

56.

What is the limit?

a)

Infinity

b)

20

c)

DNE

d)

12

57.

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

58.

a)

Intermediate Value Theorem

b)

Rolle's Theorem

c)

Average Rate of Change

d)

Average Value of f

59.

a)

Average Rate of Change

b)

Average Value of f

c)

Intermediate Value Theorem

d)

Rolle's Theorem

60.

a)

f(a) - f(b)

b)

f(b) - f(a)

c)

f '(b) - f '(a)

d)

f '(a) - f '(b)

61.

a)

Mean value theorem

b)

Rolle's theorem

c)

Intermediate Value Theorem

d)

Fundamental Theorem of Calculus

62.

a)

speed

b)

acceleration

c)

displacement

d)

total distance

63.

a)

A

b)

B

c)

C

d)

E

64.

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

a)

Position = 0

b)

Position = 1

c)

Position = 2

d)

Position = -1

65.

a)

position

b)

velocity

c)

acceleration

d)

total distance

66.

a)

position

b)

velocity

c)

acceleration

d)

total distance

67.

a)

Does Not Exist

b)

9

c)

1

d)

0

68.

a)

6

b)

3

c)

1/6

d)

-1/6

69.

Find the value that will make the following continuous

a)

-3

b)

-2

c)

-1

d)

c=0

70.

What is the limit?

a)

∞

b)

20

c)

DNE

d)

12

71.

What is the limit?

a)

DNE

b)

2/3

c)

1/4

d)

∞

72.

What is the limit?

a)

∞

b)

-∞

c)

3

d)

-3

73.

Find the vertical asymptote(s) (if any) of the graph of the function.
3x / (x² + 9)

a)

x=3

b)

x=0

c)

None

d)

X=3, x=-3

74.

What is the limit of the function as x approaches -4 from the left?

a)

2

b)

-4

c)

DNE

d)

-2

75.

Find the limit of the function as x approaches 2⁺.

a)

1

b)

-1

c)

5

d)

DNE

76.

lim_x→0 sin(6x) ∕ sin(2x)

a)

1/3

b)

3

c)

1

d)

DNE

77.

tan (x) is negative in

a)

quadrants 1 and 2

b)

quadrants 1 and 3

c)

quadrants 2 and 4

d)

quadrants 3 and 4

78.

The radius r of a circle is increasing at a rate of 5 ft per hour. Find the rate of change of the area (in square feet per hour) of the circle when the radius is 10 ft.

a)

$100\pi$

b)

$50\pi$

c)

$200\pi$

d)

$500\pi$

79.

A ladder 20 feet long is leaning against a wall of a house. The base of the ladder is pulled away from the wall at a rate of 1 feet per second. How fast is the top of the ladder moving down the wall when its base is 12 feet from the wall?

a)

1.33 ft/sec

b)

0.75 ft/sec

c)

-1.33 ft/sec

d)

-0.75 ft/sec

80.

The position of the particle is given by the equation $x\left(t\right)=4t^3-3t^2+5t-1$ . What is the acceleration of the particle when $t=5$ ?

a)

449

b)

114

c)

125

d)

281

81.

What is the derivative of $f\left(x\right)=x^2\left(2x-2\right)$ ?

a)

$f'\left(x\right)=6x^2-4x$

b)

$f'\left(x\right)=6x^2+4x$

c)

$f'\left(x\right)=12x-4$

d)

$f'\left(x\right)=12x+4$

82.

If $f'\left(x\right)=g'\left(x\right)$ , then $f\left(x\right)=g\left(x\right)$ .

a)

True

b)

False

83.

If $f'\left(x\right)=x^5$ , find $f'''\left(x\right)$ .

a)

$5x^4$

b)

$20x^3$

c)

$0$

d)

$60x^2$

84.

The maximum of a function that is continuous on a closed interval can occur at two different values in the interval.

a)

True

b)

False

85.

Find the absolute extrema of the function $f\left(x\right)=2x^2-8x$ on the interval $\left[0,6\right]$ .

a)

min: $\left(2,-8\right)$ , max: $\left(6,24\right)$

b)

min: $\left(6,-8\right)$ , max: $\left(2,24\right)$

c)

min: $\left(2,2\right)$ , max: $\left(6,18\right)$

d)

min: $\left(0,0\right)$ , max: $\left(6,24\right)$

86.

If $f\left(x\right)=g\left(x\right)$ , then $f'\left(x\right)=g'\left(x\right)$ .

a)

True

b)

False

87.

Find $\frac{dy}{dx}$ by implicit differentiation.
$x^3-xy+y^2=7$

a)

$\frac{-\sqrt{x}}{\sqrt{y}}$

b)

$\frac{3x^2-y}{2y-x}$

c)

$\frac{-3x^2+y}{-x+2y}$

88.

Use the Mean Value Theorem to find all values of c in the open interval (a,b) such that $f'\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$ .
$f\left(x\right)=x^4-8x\ ,\ \left[0,2\right]$

a)

$\left\{-2,2\right\}$

b)

$\left\{\sqrt{2}\right\}$

c)

$\left\{2^{\frac{1}{3}}\right\}$

d)

$\left\{-2^{\frac{1}{3}}\right\}$

89.

What is the derivative of the position function?

a)

velocity function

b)

acceleration function

c)

jerk function

90.

What is the slope of the tangent line to the graph of $\left(4-x\right)y^2=x^3$ at $\left(2,2\right)$ ?

a)

$\frac{1}{2}$

b)

$2$

c)

$0$

d)

$-\frac{1}{2}$

91.

What is the derivative of $y=\sin\ \left(xy\right)$ ?

a)

$\frac{dy}{dx}=\frac{y\ \cos\ \left(xy\right)}{1-x\ \cos\ \left(xy\right)}$

b)

$\frac{dy}{dx}=\frac{x\ \cos\ \left(xy\right)}{1-y\ \cos\ \left(xy\right)}$

c)

$\frac{dy}{dx}=\frac{1-x\ \cos\ \left(xy\right)}{y\ \cos\ \left(xy\right)}$

d)

$\frac{dy}{dx}=\frac{1-y\ \cos\ \left(xy\right)}{x\ \cos\ \left(xy\right)}$

92.

∫cos(4x+5)dx

a)

-¼sin(4x + 5) + C

b)

4sin(4x + 5) + C

c)

¼sin(4x + 5) + C

d)

4cos(4x + 5) + C

93.

^∫2x+4dx

a)

x² + 4x + c

b)

2

c)

x² + 4x

d)

2x² + 4x + c

94.

a)

62

b)

64/11

c)

56/3

d)

50/3

95.

Evaluate the indefinite integral.

a)

A

b)

B

c)

C

d)

D

96.

a)

(x¹¹⁄ 11) - 1

b)

(x¹⁰) - 1

c)

x¹⁰

d)

t¹¹ ∕ 11

97.

How do you get from the first derivative the the original function?

a)

Differentiate

b)

Integrate

98.

How do you integrate uⁿ du ?

a)

Increase the exponent and multiply by n

b)

Increase the exponent and divide by n

c)

decrease the exponent and divide by n+1

d)

Increase the exponent and divide by n+1

99.

∫ 2 x (x²- 3)^(1/2) dx

a)

(x²- 3)^(3/2⁾+C

b)

(3/2)(x²- 3)^(3/2)+C

c)

(2/3)(x²- 3)^(3/2)+C

d)

(2/3)(x²- 3)^(-1/2)+C

100.

∫ e^2x dx

a)

e^2x +C

b)

2e^2x + C

c)

(1/2)e^{x + C}

d)

(1/2)e^2x +C

101.

Find the derivative of f(x) = 6x³⁰-2x¹⁵ + 4x³ - 2x + 1

a)

f'(x) = 18x²⁹+ 30x¹⁵ + 12x³

b)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x²

c)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² - 2

d)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² +1

102.

Find the slope of the tangent line to f(x) = -3x²-6x at x = 1.

a)

m = 0

b)

m = 12

c)

m = -9

d)

m = -12

103.

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

a)

v(t) = -2

b)

v(t) -2t - 1

c)

v(t) = t³

d)

v(t) = -t

104.

Find the derivative f(x) = (x² + 2x)⁵

a)

f'(x) = 5(2x+2)⁴

b)

f'(x) = 5(x² + 2x)⁴

c)

f'(x) = 5(x² + 2x)⁴(2x)

d)

f'(x) = 5(x² + 2x)⁴(2x + 2)

105.

Find the derivative f(x) = tanxcosx

a)

f'(x) = sec²xcosx - tanxsinx

b)

f'(x) = sec²xcosx + tanxsinx

c)

f'(x) = sec²xsinx

d)

f'(x) = sec²xcosx - tanxcosx

106.

Find the limit of the function as x approaches 4 from the right.

a)

-1

b)

2

c)

-2

d)

DNE

107.

At which x-value is f continuous but not differentiable?

a)

a

b)

b

c)

c

d)

d

108.

Where is the graph neither continuous nor differentiable?

a)

x = -1, 0, 1, 2

b)

x = -1, 1

c)

x = -1, 0, 1

d)

x = -1, 0, 2

109.

f(x)=(sin²x), f'(x)= ?

a)

2sin x

b)

2(sin x)(cos x)

c)

2cos x

d)

2x(cos x)

110.

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

111.

Where does the function, f(x) = 2x³ - 9x²+ 12x -3 have relative max/min values?

a)

Rel max x = -1, Rel min x = 2

b)

Rel min x = 1, Rel min x = 2

c)

Rel max x = 1, Rel min x = 2

d)

Rel max x = 2, Rel min x = 1

112.

Let f be the function with derivative given by f'(x) = x² - 2/x. On which of the following intervals is f decreasing?

a)

(-∞, 0]

b)

(-1, 0]

c)

(0, ∛2]

d)

(∛2, ∞)

113.

Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.

a)

increasing

b)

decreasing

c)

concave up

d)

concave down

114.

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

a)

0

b)

-1

c)

2

d)

5

115.

What is a point of inflection?

a)

When a function goes from increasing to decreasing

b)

When a function goes from concave up to concave down

116.

If a function has a second derivative that is negative, what does that tell you?

a)

The function is increasing

b)

The function is decreasing

c)

The function is concave up

d)

The function is concave down

117.

If a function has a second derivative that is positive, what does that tell you?

a)

The function is increasing

b)

The function is decreasing

c)

The function is concave up

d)

The function is concave down

118.

Over what interval(s) is f(x) decreasing?

a)

(-3, 1)

b)

(-∞, -5) ∪ (0, 2)

c)

(-∞, -3) ∪ (1, ∞)

d)

(-5, 0) ∪ (2, ∞)

119.

The derivative f'(x) of the function f(x) is shown. On what interval(s) is the FUNCTION f(x) increasing?

a)

(-∞, -1) only

b)

( 3, ∞) only

c)

(-∞, -1) and ( 3, ∞)

d)

(1, ∞)

120.

Find the x-coordinate of the inflection point of f(x)=6x²-x³.

a)

-2

b)

0

c)

2

d)

None

121.

5.9: The graph of a function f is shown. Which of the following could be the graph of f ' , the derivative of f ?

a)

b)

c)

d)

122.

What is the derivative of cot(x)?

a)

sec²(x)

b)

-sec²(x)

c)

csc²(x)

d)

-csc²(x)

123.

What is the derivative of xⁿ?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

124.

What is the derivative of tan(x)?

a)

-sec²(x)

b)

-csc²(x)

c)

sec²(x)

d)

csc²(x)

125.

What is the derivative of sec(x)?

a)

sec(x)tan(x)

b)

csc(x)cot(x)

c)

-sec(x)tan(x)

d)

-csc(x)cot(x)

126.

a)

(3x²-2) cos(x³-2x)

b)

-(3x²-2) cos(x³-2x)

c)

cos(2x²-2)

d)

sin(2x²-2)

127.

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

a)

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

b)

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

c)

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

d)

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

128.

Find f’(x) when f(x) = sin(4x+5)

a)

3cos(3x)

b)

4sin(4x+5)

c)

4cos(4x+5)

d)

4sin(4x)

129.

Find f”(x) when f(x)=x⁵+4x³-5x²+7

a)

9X³+14x-10

b)

5x⁴+12x²-10x

c)

5X³+12x³-10

d)

20x³+24x-10

130.

Find dy/dx for y=-(3x²+5x)⁵

a)

y=-5(x+5)⁴

b)

y=-5(6x+5)(3x²+5x)⁴

c)

y=-6x+5(3x²+5x)⁴

d)

y=-6x(3x²+5x)⁴

131.

Differentiate y = √(x² - 1)

a)

√(x² -1)

b)

(1/2x)(x² - 1)^^(-1/2)

c)

x(x² - 1)^^(-1/2)

d)

x(x² - 1)^^(1/2)

132.

Find the derivative:
y=5x²e^3x

a)

y'=10xe^3x(2x+3)

b)

y'=5xe^3x(3x+2)

c)

y'=10ex^3x(3x+2)

d)

y'=5xe^3x(2x+3)

133.

Find the derivative of f(x) = x²sinx

a)

f'(x) = 2xsinx - x²cosx

b)

f'(x) = 2xsinx + x²sinx

c)

f'(x) = 2xsinx + x²cosx

d)

f'(x) = 2xcosx

134.

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

a)

3/(2x)

b)

(-3x²-4x +6)/(x²+2)²

c)

(-3x²+4x +6)/(x²+2)²

d)

(-3x²+10)/(x²+2)²

Calculus: 5th 6-Weeks Bonus Quiz

Total questions: 134

Worksheet time: 5hrs 17mins

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