Practice Page
Directions: Read carefully. Choose the best answers.

1.
When driving a car, an unsuspected hazard appears in the roadway. The table at the right shows the "total" stopping distance which is the sum of the "thinking" distance and the actual "braking" distance.
What is the average rate of change in the total stopping distance (feet/mph) between one car traveling 40 mph and one traveling 60 mph?
Choose:
 
6 ft/mph
10 ft/mph
 
60 ft/mph
120 ft/mph

Speed (mph)
Total Stop Distance (ft.)
10
15
20
40
30
74
40
119
50
174
60
239
Total stopping distances calculated with "Car Stopping Distance Calculator" with "thinking" time as stated in
The Higheway Code.

 

 

2.

f (x) = | 2x + 1| - 3

x
g(x)
-3
-4
-2
3
-1
-6
0
2
1
-8

m(x)
comparegraph3a
Which of the three functions shown above has the largest and smallest average rate of change on the interval [-3,0]?
Choose:
 
largest f (x); smallest m (x)
 
largest m (x); smallest g (x)
 
largest g (x); smallest m (x)
 
largest g (x); smallest f (x)

 

 

3.
The table below shows the snowfall in a north-eastern city in inches for the first week in January.
Date
1/6
1/7
1/8
1/9
1/10
1/11
1/12
Snowfall (in.)
8"
4"
10"
18"
9"
12"
24"
Find the average rate of change in the number of inches of snowfall from January 8 to January 11.
   

Choose:
 
2/3 in.
2 in.
3 in.
6 in.

 

 

4.
For which of the following two functions is the average rate of change constant?
x
2
4
6
r (x)
20
36
52
x
1
3
6
m (x)
8
10
13
   

Choose:
 
r (x)
m (x)
Both
Neither

 

 

5.
When training for an event, a cross country runner used a FitBit to track his total distances traveled at half hour intervals.
a) What was the runner's average speed (mi/hr), during the first time interval?
Choose:
 
1.1
1.7
2.2
4.4
Reading
Time (hrs)
Distance
(mi)
1
0.5
2.2
2
1
4.7
3
1.5
6.5
4
2
7.5
5
2.5
8.7

b) State between which two consecutive readings that the runner's average speed was the highest.
Choose:
 
1 and 2
2 and 3
3 and 4
4 and 5

c) State between which two consecutive readings that the runner's average speed was the lowest.
Choose:
 
1 and 2
2 and 3
3 and 4
4 and 5

 

 

 

 

 

6.
Given: f (x) = e x
When examining equal consecutive intervals, which of the following statements is true regarding the average rate of change as x moves to the right?
Choose:
 
The average rate of change is continually decreasing.
 
The average rate of change is constant.
 
The average rate of change is continually increasing.
 
More information is needed to determine the average rate of change.
 

 

 

7.
The graph of a straight line is shown below.
Which of the statements are true in relation to the statement:
"The average rate of change is ...."
(Check all that apply, and hit SUBMIT!)

positive.

negative.

constant.

1 on interval [1,4]

-1 on interval [-2,0]

      

avline

 

 

8.
An object is thrown upward from a height of 60 feet with an initial velocity of 48 feet per second. The height of the object t seconds after it is thrown is given by h (t) = -16t2 + 48t + 60.

a) What is the average velocity in the first two seconds after the object is thrown?
Choose:
 
8 feet per second
16 feet per second
 
24 feet per second
32 feet per second

b) What is the average velocity from t = 1 to t = 3?
Choose:
 
8 feet per second
16 feet per second
 
-8 feet per second
-16 feet per second

 

 

9.
A rocket is 1.5 miles above the Earth in 20 seconds and is 8 miles above the Earth in 2 minutes. What is the rocket's rate of change in miles per second?

Choose:
 
0.065 mps
0.361 mps
 
3.892 mps
4.145 mps
 

 

 

10.
Let f (x) = mx + b.
Find the average rate of change of f (x) between the points x = a and x = a + h.

Choose:
 
mh
m / h
m
mh + b
 

 

divider

NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation
 and is not considered "fair use" for educators. Please read the "Terms of Use".