Free Printable AP Calculus Ultimate Quizizz

1.

a)

0

b)

2

c)

3

d)

4

2.

What is the limit?

a)

Infinity

b)

20

c)

DNE

d)

12

3.

a)

Does not exist

b)

6

c)

4

d)

3

4.

a)

0

b)

2

c)

3

d)

4

5.

a)

0

b)

3

c)

4

d)

DNE

6.

a)

0

b)

1

c)

2

d)

DNE

7.

a)

0

b)

1

c)

2

d)

DNE

8.

a)

0/0

b)

DNE

c)

-1/4

d)

1/4

9.

a)

0

b)

∞

c)

- ∞

d)

DNE

10.

a)

0

b)

0/0

c)

1/4

d)

DNE

11.

a)

Infinity

b)

-4

c)

-infinity

d)

3

12.

a)

4

b)

0

c)

1/2500

d)

Does not exist

13.

a)

3

b)

0

c)

1

d)

Does not exist

14.

a)

A

b)

B

c)

C

d)

D

15.

a)

Does Not Exist

b)

9

c)

1

d)

0

16.

a)

A

b)

B

c)

C

d)

D

17.

What is the limit?

a)

5/2

b)

-2/3

c)

Infinity

d)

17/3

18.

lim_x→0 sin(5x) ∕ x

a)

1/5

b)

5

c)

1

d)

DNE

19.

lim_x→0 e^x∕cos(x)

a)

1/2

b)

0

c)

1

d)

DNE

20.

lim_x→0 sin(6x) ∕ sin(2x)

a)

1/3

b)

3

c)

1

d)

w

21.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

22.

a)

-7

b)

0

c)

1

d)

DNE

23.

Which of the following best describes the continuity at x = 1?

a)

Continuous

b)

Removable Point Discontinuity

c)

Non-removable Infinite Discontinuity

d)

Non-removable Jump Discontinuity

24.

a)

0

b)

∞

c)

sec²x

d)

secxtanx

25.

a)

15x²

b)

(5/4)x⁴

c)

indeterminate

d)

∞

26.

a)

2x

b)

3

c)

6

d)

9

27.

a)

1

b)

2

c)

1/2

d)

√2

28.

the first derivative of f(x) = 3x²

a)

f'(x)=3x

b)

f'(x)=3x²

c)

f'(x)=6x

d)

f'(x)=6x²

29.

the second derivative of f(x) = 3x² + 5x

a)

f''(x) = 6x

b)

f''(x) = 3x + 5

c)

f''(x) = 6x + 5

d)

f''(x) = 6

30.

the value of the first derivative of a function tells you the

a)

slope of the tangent line

b)

the equation of the tangent line

c)

the maximum of the function

d)

where the function is undefined

31.

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

a)

7

b)

0

c)

7x

d)

14

32.

Find the derivative of the given equation
f(x) = -4x

a)

4

b)

x

c)

-4

d)

0

33.

Find the derivative of the given equation
f(x) = 1 - x²

a)

1 - 2x

b)

-2x

c)

-2

d)

-1

34.

Find the derivative of the given equation
f(x) = 1/x²

a)

1/2x

b)

-2x

c)

2x

d)

-2x^-3

35.

Find the derivative of the given equation
f(x) = 1 - x²

a)

1 - 2x

b)

-2x

c)

-2

d)

-1

36.

find

a)

y = 2 x^-1

b)

y=2 x^-2

c)

y= −2x^-2

d)

y= −2 x^-1

37.

Differentiate f(x) =(2/ x⁵) - 5.

a)

x⁵-3

b)

-10x⁶

c)

x⁵-5

d)

-10x^-6

38.

Differentiate y= 12x^-2

a)

24x^-1

b)

-24x^-3

c)

-24x^-1

d)

6x^-3

39.

a)

b)

c)

d)

40.

a)

b)

c)

d)

41.

a)

b)

c)

d)

42.

a)

b)

c)

d)

43.

a)

b)

c)

d)

44.

a)

b)

c)

d)

45.

a)

b)

c)

d)

46.

a)

b)

c)

d)

47.

a)

b)

c)

d)

48.

a)

b)

c)

d)

49.

a)

b)

c)

d)

50.

a)

b)

c)

d)

51.

a)

b)

c)

d)

52.

a)

b)

c)

d)

53.

a)

b)

c)

d)

54.

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

a)

m = 0

b)

f'(x) = -6x - 6

c)

f'(x) = 6x

d)

m = -12

55.

The derivative of

a)

y'=2x – x^-2

b)

y'=x^-1+ 8x

c)

y'=x^-2+ 8x

d)

y=8x – x^-2

56.

f(x)= 9/∛x

f'(x) =

a)

9x ^-1/3

b)

-3x ^{- 4/3}

c)

-9x^2/3

d)

-3x^2/3

57.

Find f '(2) if
f(x) = x² + 2x

a)

2x + 2

b)

6

c)

12

d)

2x

58.

When you plug a given point into the derivative of a function, you get this.

a)

tangent line

b)

normal line

c)

slope

d)

average rate of change

59.

Write the slope of the line tangent to the graph of y=x² – 2 at the point x = -8.

a)

2

b)

-4

c)

-8

d)

-16

60.

This is the equation of the line tangent to the graph of y=x²+3 at the point x = -1.

a)

y = -2x + 2

b)

y = 2x + 2

c)

-(1/2)x + (7/2)

d)

y = (1/2)x + (7/2)

61.

Which represents the same function?

a)

b)

c)

d)

62.

Which shows the quotient rule correctly?

a)

b)

c)

d)

63.

What's the derivative?

a)

b)

c)

d)

64.

Which shows the product rule correctly?

a)

b)

c)

d)

65.

a)

8x⁴ -60x²

b)

16x⁴

c)

(8x⁴ -60x²)/(2x²-5)²

d)

3x

66.

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

67.

Find dy/dx by Implicit Differentiation
x³ +y³ = 36

a)

6 -x

b)

3x² +3y²

c)

−x²/y²

d)

0

68.

Find dy/dx by Implicit Differentiation
xy = 6

a)

-x/ y

b)

-y/ x

c)

-6y/ x

d)

y/x

69.

Find dy/dx
xy+y²=2

a)

-y/(x+2y)

b)

y/(x+2y)

c)

-3y/x

d)

-3x/y

70.

Find dy/dx
xy+y²=2

a)

-y/(x+2y)

b)

y/(x+2y)

c)

-3y/x

d)

-3x/y

71.

What is x-value at which the function below has the same slope as the average rate of change over the indicated interval?
f(x) = x² - 3x - 28, [-4,7]

a)

1.5

b)

-1.5

c)

0.5

d)

-0.5

72.

What is x-value at which the function below has the same slope as the average rate of change over the indicated interval?
f(x) = x² +5x +5, [-2,6]

a)

2

b)

-2

c)

7

d)

-7

73.

What is the derivative of
f(x) = ^(x-4)/_(x+1) ?

a)

f'(x) =⁵/ _(x+1)^₂

b)

f'(x) =^-3/ _(x+1)^₂

c)

f'(x) =^(2x-3)/ _(x+1)^₂

d)

f'(x) =^(2x+5)/ _(x+1)^₂

74.

Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The radius of the spill increases at a rate of 5 m/min. How fast is the area of the spill increasing when the radius is 5 m?

a)

50π m²/min

b)

47π m²/min

c)

52π m²/min

d)

40π m²/min

75.

A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 4 in?

a)

-262π in³/sec

b)

-247π in³/sec

c)

-256π in³/sec

d)

-263π in³/sec

76.

A 5 ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 2 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 3 ft from the wall?

a)

4/3 ft/sec

b)

8/7 ft/sec

c)

1 ft/sec

d)

8/3 ft/sec

77.

An observer stands 2400 ft away from a launch pad to observe a rocket launch. The rocket blasts off and maintains a velocity of 200 ft/sec. Assume the scenario can be modeled as a right triangle. How fast is the observer to rocket distance changing when the rocket is 700 ft from the ground?

a)

56 ft/sec

b)

57 ft/sec

c)

52 ft/sec

d)

61 ft/sec

78.

(3 min) The volume of a cone of radius r and height h is given by v = (1/3) π r²h. If the radius and the height both increase at a constant rate of 1/2 centimeter per second, at what rate, in cubic centimeters per second, is the volume increasing when the height is 9 centimeters and the radius is 6 centimeters?

a)

10π

b)

24π

c)

54π

d)

108π

79.

Find the antiderivative of
x²

a)

(1/3)x³+C

b)

x³

c)

(1/3)x³

d)

2x

80.

Find the antiderivative of
(1/3)x³-5x

a)

(1/12)x⁴-(5/2)x²+C

b)

(1/4)x⁴-(1/2)x²+C

c)

(1/12)x³-(5)x²+C

d)

(12)x⁴-(5)x²+C

81.

∫(4 - 18x)dx

a)

F(x) = -18

b)

F(x) = 4x - 9x²

c)

F(x) = 4x - 9x²+ C

d)

F(x) = (4 - 18x)² /2 + C

82.

∫ 1/x dx

a)

ln x

b)

ln x + C

c)

-1/x²

d)

-1/x² + C

83.

INTEGRATE

a)

A

b)

B

c)

C

d)

D

84.

∫₁³ 5x² dx

a)

a. 43

b)

b. 130/3

c)

c. 40

d)

d. 19/3

85.

∫₁² (3x² + 4x³)dx

a)

a. 24

b)

b. -8

c)

c. -10

d)

d. 22

86.

a)

12/3

b)

6.5

c)

5.5

d)

11/3

87.

∫ 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

88.

∫ sin (2x) dx

a)

cos(2x)+C

b)

-(1/2)cos(2x)+C

c)

-cos(2x)+C

d)

(1/2)cos(2x)+C

89.

∫ (2 - x)⁵ dx

a)

-5 (2 - x )⁴ + C

b)

( 2 - x )⁶+ C

c)

(1/6) ( 2 - x )⁶+ C

d)

-(1/6) ( 2 - x )⁶+ C

90.

∫ 9 / x⁴ dx

a)

9x^-4 +c

b)

-3x^-3 + c

c)

9x^-3 + c

d)

-9x^-5/ 5 + c

91.

∫ x² + 5x + 3 dx

a)

x³ / 3 + 5x²/ 2 + 3x + c

b)

2x + 5 + c

c)

x³ + 5x²+ 3x + c

d)

x³ / 3 + 5x² /2 + 3

92.

∫ 4sec²(2x) dx

a)

2tan(x) + c

b)

4tan(2x) + c

c)

4tan(2x)

d)

2tan(2x) + c

93.

∫ 1/x dx

a)

ln x

b)

ln x + C

c)

-1/x²

d)

-1/x² + C

94.

∫ - sinx dx

a)

-cos x + C

b)

cos x + C

c)

tan x + C

d)

1/√1- x²

95.

∫-csc²x dx

a)

cscx + C

b)

cotx + C

c)

secx + C

d)

tanx + C

96.

∫ (2x - 5)⁴dx

a)

(2x - 5)⁵ / 5 +c

b)

(2x - 5)⁵ / 5

c)

(2x - 5)⁵/ 10 + c

d)

(2x - 5)³ / 3 + c

97.

∫ √x dx

a)

2x^3/2 / 3 + c

b)

3x^3/2 / 2 + c

c)

2x^1/2 + c

d)

x^3/2 + c

98.

∫ e^{3x + 3} dx

a)

e^x / 3 + c

b)

e^{3x + 3} / 6 + c

c)

e^{3x + 3} + c

d)

e^{3x + 3} / 3 + c

99.

Find

a)

b)

c)

d)

100.

Evaluate

a)

cscx cotx

b)

secx tanx

c)

sec²x

d)

-cscx cotx

101.

a)

-1

b)

-2

c)

1/2

d)

-1/2

102.

a)

2

b)

4

c)

5

d)

6

103.

Using 5 subintervals, calculate the distance traveled using a left sum.

a)

360

b)

420

c)

396

d)

390

104.

Based on the table, use a left Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.)

a)

5(3) + 1(4) + 2(5) + 1(7)

b)

5(4) + 1(5) + 2(7) + 1(6)

c)

5(3) + 6(4) + 8(5) + 9(7)

d)

0(3) + 5(4) + 6(5) + 8(7)

105.

Based on the table, use a left Riemann sum with sub-intervals given by the table to estimate the area under the curve. (Choose the correct set-up.)

a)

5(3) + 1(4) + 2(5) + 1(7)

b)

5(4) + 1(5) + 2(7) + 1(6)

c)

5(3) + 6(4) + 8(5) + 9(7)

d)

0(3) + 5(4) + 6(5) + 8(7)

106.

Use a trapezoidal sum with four intervals from the table to estimate the integral of 0 to 9 of V(t).

a)

155/2

b)

134/2

c)

186/2

d)

151/2

107.

Find the right-hand Riemann Sum, with three sub-intervals indicated by the table.

a)

23

b)

15

c)

34

d)

21

108.

For a function that is strictly decreasing, a right hand Riemann Sum is which of the following:

a)

Overestimate

b)

Underestimate

c)

Exact Solution

d)

Unable to Determine

109.

a)

(A)

b)

(B)

c)

(C)

d)

(D)

110.

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

a)

100

b)

99

c)

150

d)

152

111.

a)

0

b)

∞

c)

sec²x

d)

secxtanx

112.

a)

15x²

b)

(5/4)x⁴

c)

indeterminate

d)

∞

113.

a)

1/(3a)

b)

ln(3a)

c)

(1/3)e^3a

d)

3e^3a

114.

a)

2x

b)

3

c)

6

d)

9

115.

a)

1

b)

2

c)

1/2

d)

√2

AP Calculus Ultimate Quizizz

Total questions: 115

Worksheet time: 7hrs 1mins

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