www.ck12.org
Rates of Change Worksheet
Rates of Change
Multiple Choice Questions.
For each question, four alternative choices are given, of which only one is correct. You have to select the correct
alternative and mark it in the appropriate option.
1. Find the slope of line shown in the graph
.
(a)
−1
6
(b)
1
6
(c)
(d)
6
−6
2. If a line passes through a point (2, 3) and (4, 6), then slope is equal to _____.
(a)
2
3
(b)
3
2
(c)
1
2
(d)
None o f the above
3. Find the slope of the set of points (x1 , y1 ) (x2 , y2 ).
(a) y_2 − y_1
x_2 − x1
(b) x_2 − x_1
y_2 − y1
(c) x_2 + x_1
y_2 + y1
(d) y_2 + y_1
x_2 + x1
1
www.ck12.org
4. If the dependent variable increases as the independent variable remains constant, then the rate of change
is_____.
(a)
(b)
(c)
(d)
Positive
Negative
Zero
Undefined
5. The slope of the line in the graph
tells us that _____ liter of petrol is consumed for every mile.
(a)
(b)
(c)
(d)
5liter
1 liter
0.16 liter
can’t be predicted
6. From the graph
, determine the rate of change.
(a)
(b)
(c)
(d)
10 m/s
20 m/s
30 m/s
5 m/s
7.
For which interval of the graph is the slope of the graph negative?
(a)
(b)
(c)
(d)
1 s to 20 s
1 s to 15 s
20 s to 30 s
1 s to 30 s
8. The slope of a line measures the ___ of the line.
(a)
(b)
(c)
(d)
Length
Steepness
Both
None of the above
9. A trader earns a profit of $60,000 in 1998 and a profit of $75,000 in 2003. Find the average rate of change of
the profit.
(a) $3000
2
www.ck12.org
(b) $1000
(c) $5000
(d) None of the above
True or False Questions.
Indicate True or False for the following Statements
10. The balance in Sam’s savings account changed from $ 1200 in June to $ 1600 in Aug, then average rate of
change per month is 100 $. ( True/False )
11. The negative slope of the line DE in the graph
means the rate of change is decreasing. ( True/False )
12. If the dependent variable increases with a decrease in the independent variable, then the rate of change is zero.
( True/False )
13. If Pamela travels 160 miles after 3 hours from the beginning of her journey and 4 hours later she had travelled
400 miles, then her rate of change is 80 miles/hour. ( True/False )
14. For the graph
, the rate of change for the line segment BC is 3 miles/hr. ( True/False )
15. The price of a house increases from $120,000 in 1995 to $250,000 in 2007. Therefore the average annual rate
of change in dollars is $10833 . ( True/False )
16. The average rate of change for the line segment AB in the graph
, is 4 miles/hr. ( True/False )
17. For a uniform motion, displacement varies directly as time, so the slope of a displacement-time graph gives
the velocity. ( True/False )
18. Change in any variable with time is called rate of change. ( True/False )
3