Question 1

$P$ gives the population of a town $t$ years after it was founded. 
What is the best interpretation for the following statement?
The slope of the line tangent to the graph of $P$ at $t=2$ is equal to $-10$.

Accepted Answer

After 2 years, the town's population decreased at a rate of 10 people per year

Answer

After 2 years, the rate of change of the population decreased at a rate of 10 people per year.

Answer

After 2 years, the town's population decreased at a rate of 10 people.

Answer

Over the first two years, the town's population decreased by 10 people per year.

Question 2

The function $D$ gives the day length, in minutes, of the $n^{th}$ day of the year in Juneau, Alaska.
What is the best interpretation for the following statement?  $D'(10)=3$

Accepted Answer

On January 10, the day length is increasing at a rate of 3 minutes per day.

Answer

On January 10, the day is 3 minutes long.

Answer

On January 10, the day length is increasing at a rate of 3 days per minute.

Answer

Until January 10, the day length is increasing at a rate of 3 minutes per day.

Question 3

$P$ give the lion population at a certain game reserve t years after the reserve was established. What is the best interpretation for the following statement?
The value of the derivative of $P$ at $t=6$ is equal to 12.

Accepted Answer

After 6 years, the lion population grows at a rate of 12 lions per year.

Answer

After 6 years, there were 12 lions in the reserve.

Answer

The lion population grows at a rate of 12 lions per 6 years.

Answer

After 6 years, the lion population grows at a rate of 12 lions.

Question 4

Gaia is driving her truck from Paris to Lyon. The function $D$ gives the total distance Gaia has driven (in kilometers) after t hours.
What is the best interpretation for the following statement?
The slope of the line tangent to the graph of $D$ at $t=3$ is equal to $90$.

Accepted Answer

3 hours after leaving, Gaia drove at a rate of 90 kilometers per hour.

Answer

At time 3, Gaia drove at a rate of 90 kilometers.

Answer

During the first 3 hours, Gaia drove 90 kilometers per hour.

Answer

3 hours after leaving, Gaia was 90 kilometers away from Paris.

Question 5

An object moves along a straight line so that at any time  $t$ ,  $0≤t≤9$ , its position is given by  $x(t)=7+6t−t²$ . For what value of  $t$  is the object at rest? (Remember find $t$ when $x'(t)=0$)

Accepted Answer

$t=3$

Answer

$t=7$

Answer

$t=6$

Answer

$t=\frac{13}{2}$

Question 6

An object moves along a straight line so that at any time  $t$ , for  $0≤t≤8$, its position is given by  $x(t)=5+4t−t²$ . For what value of  t  is the object at rest? (Remember find $t$ when $x'(t)=0$)

Accepted Answer

$t=2$

Answer

$t=\frac{9}{2}$

Answer

$t=5$

Answer

$t=4$

Question 7

The function  $t=f(A)$  models the time, in minutes, for a chemical reaction to occur as a function of the amount  $A $ of catalyst used, measured in milliliters. What are the units for  $f''(A)$ ?

Accepted Answer

minutes per milliliter per milliliter

Answer

minutes per milliliter

Answer

milliliters per minute per minute

Answer

milliliters per minute

Question 8

The function  $t=f(S)$  models the time, in hours, for a sample of water to evaporate as a function of the size  $S$  of the sample, measured in milliliters. What are the units for  $f''(S)$

Accepted Answer

hours per milliliter per milliliter

Answer

hours per milliliter

Answer

milliliters per hour

Answer

milliliters per hour per hour

Question 9

Oil is spilled onto a kitchen floor. The area covered by the oil at time $t$ is given by the function  $A$ , where $A(t)$ is measured in square centimeters and $t$  is measured in seconds. Which of the following gives the rate at which the area covered by the oil is changing at time $t=10$?

Accepted Answer

$A'(10)$

Answer

$A(11)−A(9)$

Answer

$\frac{A(10)}{10}$

Answer

$A(10)$

Question 10

The number of times the chain rule is applied to derive the function $g\left(t\right)=\sin^3\left(4\cos\left(6t\right)\right)$ is:

Accepted Answer

3

Answer

1

Answer

4

Answer

2

Question 11

The number of times the chain rule is applied to derive the function $h\left(xight)=\cos^4\left(7	an\left(xight)ight)$ is

Accepted Answer

2

Answer

1

Answer

0

Answer

3

Question 12

An object is moving along a line. The graph gives the object's velocity over time.
When $t = 8$ on the graph, the object is moving:

Accepted Answer

backward

Answer

forward

Answer

perpendicular

Answer

neither

Question 13

An object is moving along a line. The graph gives the object's position, relative to its starting point, over time.
 When $t = 5$ on the graph, the object is moving:

Accepted Answer

forward

Answer

neither

Answer

perpendicular

Answer

backward

Question 14

The principal rule to differentiate the function $f\left(x\right)=\frac{\cos^4\left(7x\right)}{x^2+3x}$ is

Accepted Answer

The quotient rule

Answer

Trigonometric rule

Answer

The Chain rule

Answer

The power rule

Question 15

The principal rule to differentiate the function $g\left(x\right)=\left(x^2+3x\right)\sin^3\left(7+x\right)$ is

Accepted Answer

The product rule

Answer

The power rule

Answer

The addition rule

Answer

The Chain rule

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