Quiz about AP Calculus Review - Limits, Derivatives, and Integrals

Question 1

Evaluate the limit

Accepted Answer

d

Answer

a

Answer

b

Answer

c

Question 2

Evaluate the limit

Accepted Answer

a

Answer

b

Answer

c

Answer

d

Question 3

Find the equation of the line tangent to the function at the given point

Accepted Answer

a

Answer

b

Answer

c

Answer

d

Question 4

What is the derivative of csc(x)?

Accepted Answer

-csc(x)cot(x)

Answer

csc(x)cot(x)

Answer

-csc2(x)

Answer

-cot2(x)

Question 5

Find h'(3)

Accepted Answer

1

Answer

-2

Answer

0

Answer

3

Question 6

When we "take the derivative" of a function what are we finding?

Accepted Answer

The slope of the tangent line

Answer

What's a derivative?

Answer

The rate at which our struggles in Calculus are increasing.

Answer

The slope of the secant line

Question 7

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

Accepted Answer

2

Answer

0

Answer

1

Answer

1.5

Answer

No such value exists

Question 8

Find the average rate of change of Pete's height from 3 years old to 5 years old.

Accepted Answer

4 inches per year

Answer

2 inches per year

Answer

8 inches per year

Answer

2 years

Question 9

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

Accepted Answer

The function is decreasing

Answer

The function is increasing

Answer

The concavity of the function is up

Answer

The concavity of the function is down

Question 10

Use L'Hospital to evaluate the limit.

Accepted Answer

1/2

Answer

-1/2

Answer

0

Answer

1

Answer

nonexistent

Question 11

Where is the graph continuous yet NOT differentiable?

Accepted Answer

x = b, d

Answer

x = a, b, c, d

Answer

x = b, c, d

Answer

x = a, b,

Question 12

True or False: Continuity implies differentiability

Accepted Answer

False

Answer

True

Question 13

True or False: Differentiability implies continuity

Accepted Answer

True

Answer

False

Question 14

When applying calculus, the second derivative of position helps find...

Accepted Answer

acceleration of an object at any given time

Answer

the distance traveled by an object.

Answer

The velocity of a particle at any given point

Question 15

What is the derivative of xⁿ?

Accepted Answer

nxn-1

Answer

(n-1)xn

Answer

nxn+1

Answer

(n+1)xn-1

Question 16

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?

Accepted Answer

100ft x 200ft

Answer

102ft x 196 ft

Answer

50 ft x 300 ft

Answer

50 ft x 175 ft

Question 17

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

Accepted Answer

x = 0

Answer

None

Answer

x = 0, 2

Answer

x = -2, 0, 2

Question 18

Find the derivative f(x) = xe^x

Accepted Answer

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

Answer

f'(x) = e^x

Answer

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

Answer

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

Question 19

Given the attached graph of the object's POSITION, identify intervals where the object is moving right.

Accepted Answer

(7,9), (13,18)

Answer

(0,1), (17,18)

Answer

(6,8), (11,18)

Answer

(4,7), (9,13)

Question 20

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?

Accepted Answer

-7.2 ft/sec

Answer

3 ft/sec

Answer

7.2 ft/sec

Answer

12

Question 21

May is Asian American Pacific Islander Heritage Month!

This person was the first woman to serve as the district attorney of the state of California. Her mother is from India.

Accepted Answer

Senator Kamala Harris

Answer

Representative Alexandria Ocasio-Cortez

Answer

Senator Tammy Duckworth

Answer

Secretary Elaine Chow

Question 22

Why was May selected to celebrate Asian American Pacific Islander Heritage Month? Pick 2 only.

Accepted Answer

The transcontinental railroad (which was mostly built by Chinese Americans) was completed on May 10, 1869.

Accepted Answer

The immigration of the first Japanese to the United States was on May 7, 1843.

Answer

Japanese Americans were forced to leave their homes and live in internment camps in May 1942.

Answer

The Vietnam - American war ended in May 1975.

Question 23

May is Asian American Pacific Islander Heritage Month!

Eric Yuan is the founder of which video conferencing app?

Accepted Answer

Zoom

Answer

Instagram Live

Answer

WebEx

Answer

Google Meet / Hangouts

Question 24

Question 24.

Accepted Answer

Average Rate of Change

Answer

Instantaneous Rate of Change

Answer

Intermediate Value Theorem

Answer

Average Value of f

Question 25

If (a,b) is a local minimum, then what will be true about f''(a)?

Accepted Answer

It's postive

Answer

It's negative

Answer

It's zero

Answer

Cannot be determined

Question 26

Question 26.

Accepted Answer

total distance

Answer

<gs>speed</gs>

Answer

acceleration

Answer

displacement

Question 27

Question 27.

Accepted Answer

Mean value theorem

Answer

Rolle's theorem

Answer

Intermediate Value Theorem

Answer

Fundamental Theorem of Calculus

Question 28

Question 28.

Accepted Answer

f(b) - f(a)

Answer

f(a) - f(b)

Answer

f '(b) - f '(a)

Answer

f '(a) - f '(b)

Question 29

Question 29.

Accepted Answer

acceleration

Answer

position

Answer

velocity

Answer

total distance

Question 30

What does this picture represent?

Accepted Answer

Left Riemann Sum

Answer

Right Riemann Sum

Answer

Middle Riemann Sum

Answer

Trapezoidal Sum

Question 31

What does picture represent?

Accepted Answer

Middle Riemann Sum

Answer

Left Riemann Sum

Answer

Right Riemann Sum

Answer

Trapezoidal Sum

Question 32

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

Accepted Answer

Underestimate

Answer

Overestimate

Answer

Exact Solution

Answer

Unable to Determine

Question 33

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 34

Question 34.

Accepted Answer

Average Value

Answer

Net Area

Answer

Total Area

Answer

Average Rate of Change

Question 35

Find the integral:

Accepted Answer

1/32(4x² + 3)⁴ + c

Answer

1/8(4x² + 3)⁴ + c

Answer

1/2(4x² + 3)⁴ + c

Answer

1/4(4x² + 3)⁴ + c

Question 36

Evaluate the definite integral. I encourage you to practice using the CALCULATOR trick to evaluate.

Accepted Answer

8 pi

Answer

16 pi

Answer

128 pi

Answer

Not possible

Question 37

Which of the following cases would lead to an object slowing down?

Accepted Answer

positive acceleration, negative velocity

Accepted Answer

negative acceleration, positive velocity

Answer

positive acceleration, positive velocity

Answer

negative acceleration, negative velocity

Question 38

The slope of the position-time graph tells us the

Accepted Answer

velocity

Answer

acceleration

Answer

displacement

Answer

direction of travel

Question 39

If f '(x) changes from positive to negative, f(x) has __________ at x.

Accepted Answer

a maximum

Answer

a minimum

Answer

no extrema

Question 40

Given the sign chart for f '(x), f(x) has ...

Accepted Answer

no extrema.

Answer

a local maximum at x = -2.

Answer

a local maximum at x = 4.

Answer

local maxima at x = -2 and x = 4.

Question 41

Given the sign chart for f '(x), f(x) has ...

Accepted Answer

a local maximum at x = -2 and

a local minimum at x = 4.

Answer

a local maximum at x = -2.

Answer

a local minimum at x = -2 and

a local maximum at x = 4.

Answer

no extrema.

Question 42

Given the graph of f '(x), f(x) has ...

Accepted Answer

a local min at x = 2 and

a local max at x = -6

Answer

a local min at x = -6

Answer

a local min at x = 2

Answer

local mins at x = -2, 5 and

a local max at x = 3

Question 43

Given the sign chart for f '(x) and table of f(x), f(x) has ...

Accepted Answer

all of the above

Answer

a local maximum at (-10,5).

Answer

an absolute minimum at (-2,0).

Answer

a local minimum at (20,7).

Question 44

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

Accepted Answer

increasing

Answer

decreasing

Answer

concave up

Answer

concave down

Question 45

Find the critical value(s) of

f(x) = x² + 2x + 1.

Accepted Answer

x = -1

Answer

x = 2

Answer

x = -1, 0

Answer

x = 0

Question 46

The concavity of a function is described by its _______________.

Accepted Answer

second derivative

Answer

first derivative

Answer

third derivative

Answer

the zeros

AP Calculus Review - Limits, Derivatives, and Integrals

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