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

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