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Unit 4 – Lesson 1 Worksheet – Day 1
Independent versus Dependent Variable Worksheet.
An independent variable is the one thing you intend to vary in an experiment.
A dependent variable is the thing that will change that you intend to measure as a quantitative
assessment of the effect.
Sample Hypotheses
1. If skin cancer is related to ultraviolet light, then people with a high exposure to UV light will have a
higher frequency of skin cancer. What will you do to test this proposal? What will you vary or
change? What will you measure?
Independent variable –
Dependent variable 2. If leaf color change is related to temperature, then exposing plants to low temperatures will result
in changes in leaf color.
Independent variable –
Dependent variable 3. If the speed of plant germination is related to the hardness of the hull of its seed, then softening
the seed with water or a weakly acidic solution prior to planting will hasten germination. Blah, Blah,
Blah…
Independent variable –
Dependent variable 4. If photosynthesis is related to light energy, then the portions of a leaf shaded from light will test
negative for starch, since starch is a product of photosynthesis.
Independent variable –
Dependent variable 5. If animal metabolism is related to temperature, then increasing resting room temperature will
increase animal metabolism (as measured by carbon dioxide gas production which is one of the
waste products of animal metabolism).
Independent variable –
Dependent variable 6. If root growth is related to gravity, then roots will always turn toward the earth regardless of a
seed's orientation.
Independent variable –
Dependent variable 7. If hatching of brine shrimp is related to salinity (or temperature), then the greater the salt
concentration, the higher the hatching rate.
Independent variable –
Dependent variable 9. If the thickness of annual growth rings in trees is related to annual rainfall, then examining wood
samples will reveal correlations in the growth rings to the historical records for rainfall in its
environment.
Independent variable –
Dependent variable -
Unit 4 – Lesson 1 Worksheet Day 2
Scatter Plots and Lines of Best Fit
For the following graphs, determine whether a linear, non-linear or no relationship exists.
Justify you decision for each. Sketch a line/curve of best fit when appropriate.
Chapters in a Book vs. Total Pages
45
40
35
30
25
20
15
10
5
0
Number of Chapters
Shoe Size
Shoe Size vs. Hand Width
0
2
4
6
8
10
12
14
16
9
8
7
6
5
4
3
2
1
0
0
50
100
Hand Width (cm)
160
350
140
300
Tree height (cm)
Rebound Height (cm)
200
250
80
100
8
10
Sunlight vs. Tree Height
Number of Bounces vs. Rebound Height
120
100
80
60
40
250
200
150
100
50
20
0
0
0
2
4
6
8
0
10
20
40
60
Sunlight (% each day)
Bounce Number
Time vs. Number of Bacteria
Student Height vs. Level
140
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Number of Bacteria
Level
150
Total Pages
120
100
80
60
40
20
0
0
50
100
150
Student Height (cm)
200
250
0
2
4
6
Time (h)
Applying Scatter Plots
1. Two students recorded the measurements for the length of a spring when a given
mass is hung on it. The table of values represents the scientific data they collected.
Mass (g)
5
10
20
25
30
Length (cm)
1
2
4
5
6
A. Identify which variable is independent and dependent. Justify your answer.
B. Graph the data. Extend the x-axis to 50.
C. Draw a line/curve of best fit.
D. Using your line/curve of best fit, interpolate the following:
i. What is the mass when the spring is stretched 8 cm?
ii. What is the length of the spring if 40 g is hung?
E. What are the restrictions on the variables?
F. Develop an equation for you line/curve of best fit.
G. If 100 g was hung on the spring, how long would it stretch?
H. What would happen if the spring was less stiff (stretches more)? Explain and
justify what changes you would see with your graph and equation.
2. The following table shows the relation for the amount of gasoline needed by a
motorcycle traveling at a steady speed.
Time (h)
0
1
2
3
4
Gas Consumed (L)
0
0.5
1.0
1.5
2.0
A. Identify which variable is independent and dependent. Justify your answer.
B. Graph the data. Extend the x-axis to 10.
C. Draw a line/curve of best fit.
D. Using your line/curve of best fit, interpolate the following:
i. What is the time when the gas consumed is 9 L?
ii. What is the gas consumed when the time is 10 h?
E. What are the restrictions on the variables?
F. Develop an equation for you line/curve of best fit.
G. If the motorcycle gas tank holds 20 L, how long can it travel for?
H. What would happen if the motorcycle was twice as efficient (used half as much
gas)? Explain and justify what changes you would see with your graph and
equation.
3. Radioactive material, which has a mass of 100 g is used in a physics experiment. As
the material emits radioactive waves a record of its mass is kept.
Time (h)
1
2
3
4
5
6
7
Mass (g)
55
27
11
5
3
1
0.5
A. Identify which variable is independent and dependent. Justify your answer.
B. Graph the data. Extend the x-axis to 10.
C. Draw a line/curve of best fit.
D. Using your line/curve of best fit, interpolate the following:
i. What is the time when the mass is 40 g?
ii. What is the mass when the time is 0.5 h?
iii. What is the mass when the time is 10 h?
E. What are the restrictions on the variables?
F. Develop an equation for you line/curve of best fit.
G. When will the mass be 0 g? Justify your answer.
Unit 4 – Lesson 1 Worksheet Day 3
Lines of Best Fit
Name: ____________________
1. Which of the following have a linear relationship? Explain your answer.
2. The table shows the world record times for women’s 500-m speed skating from 1983 to
2001. Answer the following.
Year
Time
(s)
1983
1986
1987
1987
1988
1994
1995
1997
1997
1997
2001
2001
2001
39.69
39.52
39.43
39.39
39.10
38.99
38.69
37.90
37.71
37.55
37.40
37.29
37.22
A.
B.
C.
D.
E.
F.
G.
H.
Draw a scatter plot.
Identify any outliers.
Describe the relationship between the x and y variables.
Draw a line of best fit.
Find an equation for the line of best fit.
Using your graph, interpolate what the record was in 1999.
Using your equation, extrapolate the record time for the 2010 Olympics.
State any restrictions on your equation.
3. A ball is dropped from different heights. The drop height and the rebound height were
recorded. Answer the following.
Drop Height (m)
Rebound Height (m)
A.
B.
C.
D.
E.
F.
G.
H.
1.0
0.7
2.0
1.3
3.0
2.3
4.0
3.0
5.0
3.8
Draw a scatter plot.
Identify any outliers.
Describe the relationship between the x and y variables.
Draw a line of best fit.
Find an equation for the line of best fit.
What does the slope of your equation represent?
Using your equation, extrapolate the rebound height if the drop height is 25 m.
Using your equation, extrapolate the rebound height if the drop height is 0 m.
Does your answer make sense?
I. State any restrictions on your equation.
4. A skateboarder starts from various points along a steep ramp and practices coasting to
the bottom. The table is a record of his practice runs. Answer the following.
Initial Height (m)
Speed (m/s)
A.
B.
C.
D.
E.
F.
G.
2.0
4.4
2.7
5.2
3.4
5.8
3.8
6.1
4.0
4.5
4.5
6.5
4.7
6.6
5.0
6.9
Draw a scatter plot.
Identify any outliers.
Describe the relationship between x and y variables.
Draw a line of best fit.
Find an equation for the line of best fit.
Using your equation, extrapolate the speed if the initial height is 10 m.
Using your equation, extrapolate the initial height if the speed was 8 m/s.
5. A chair company has a contract to build all 1790 seats in a concert hall. The progress
over the first week of work is shown. Answer the following.
# of days
Total chairs
1
97
A.
B.
C.
D.
E.
F.
G.
2
204
3
327
4
443
5
539
6
661
7
795
Draw a scatter plot.
Identify any outliers.
Describe the relationship between x and y variables.
Draw a line of best fit.
Find the equation for the line of best fit.
Using your equation, extrapolate when the company will finish.
Using your equation, extrapolate when the company will have 1500 ready.
6. A family doctor has the following records of Ian’s height and mass. Answer the
following.
Height (cm)
58
60
64
68
73
74
Mass (kg)
5.0
6.3
7.3
8.1
8.8
8.2
A.
B.
C.
D.
E.
F.
G.
H.
I.
Draw a scatter plot.
Identify and outliers.
Describe the relationship between x and y variables.
Draw a line of best fit.
Find the equation for the line of best fit.
Using your graph, interpolate Ian’s mass when his height was70 cm.
Using your graph, interpolate Ian’s height when his mass was 5.7 kg.
Using your equation, extrapolate Ian’s current mass if he is now 186 cm tall.
State any restrictions on your equation.
Unit 4 – Lesson 4 Worksheet
Relationship Questions
1.
Alexis works part-time at a clothing store. She is paid an hourly rate of $10.25/h
and also earns a commission of 3.5% of her total weekly sales. Alexis works at the store
12 hours a week. If Alexis’s goal is to earn $150 every week, what do her total weekly
sales need to be? Show your work.
2.
The charges on a monthly water bill are $0.86 per m3 of water used plus a
service charge of $4.49. Let C=total charge, in dollars, and w=total amount of water
used, in m3.
a) Is this a direct or partial variation? b) Write an equation that models this
situation.
3.
The following scatter plot
shows the relationship between N,
the number of pages in Annie’s
textbook that she has left to read,
and t, the time in minutes she
spends reading the book.
Write an equation that represents
this relationship.
4.
Temira needs to rent a car. She considers the following price equations, where C
is the total cost, in dollars, and n is the number of days. Which company should she
choose if she is planning to rent the car for at least 10 days?
5.
Two Internet service providers are competing.
The equation C = 0.04t +10 represents the
relationship between the total cost, C, charged by
Internet Connections and the time, t.
Surf Away wants always to be cheaper than Internet
Connections. Which of the following equations
represents this situation?
A C = 15
B C = 0.02t +11
C C = 0.03t + 9
D C = 0.05t + 8
6.
Alvin is researching the population of Canada. He finds data for the year 2001
and predictions for every 5 years after that, as shown below. Determine an algebraic
model for Alvin’s data, and use it to make a reasonable prediction for the population of
Canada in 2036. Justify your answer.
7.
A computer decreases in value over time. The
relationship between the value of the computer, v, in dollars
after t years is written as the equation v = -300t + 2100. A line
representing the relationship is graphed. What does the vintercept of the line represent?
F The decrease in value per year
G The initial value of the computer
H The number of years until the value is $0
J The number of years the computer will work
8.
The graph below shows the cost to print a document at the Graphics Shop. Line
A represents the cost of printing the document in colour. Line B represents the cost to
print it with black ink only. Determine the difference in cost to print 8 pages in colour
versus black ink only.
Answers:
1.
2.
3.
4.
5.
6.
7.
8.
$771.43
A. Partial variation
B. C = 0.86w + 4.49
N = 0.5t + 100
Drive Away
C
Approximately 38.6 million
G
$2