Speed | 1. a) Plot the following points on the graph: Time, x | 10 | 20 | 30 | 40 | 50 | 60 | Speed, y | 5 | 12 | 16 | 20 | 25 | 32 |
(2 marks)b) Using your calculator, find the equation of the line of best fit(3 marks) |
The Wedding Singer | 2. The graph (figure 1) shows the cost of hiring a singer at a wedding where x is the number of songs that will be sung and y is the cost in pounds.Figure 1 a. Calculate the gradient of the graph (3 marks) b. Write an equation of the from y = mx + C to calculate the cost of hiring the singer. (2 marks) c. What does the value of C tell you? Explain your answer in context (1 mark) d. What does the value m tell you? Explain your answer in context (1 mark) e. Another singer charges according to the following equation y = 60 + 10xComplete the table for this singer (1 mark) x | 0 | 2 | 4 | 6 | 8 | 10 | 12 | y | | | | | | | | f. Draw a line on your graph to represent this singer. (2 marks) g. Find the number of songs for which both singers would charge the same amount. (2 marks) h. What is the most amount of songs that a singer could have sung at your wedding if your budget is £150? Which singer would this have been? (1 mark) | The Ozone Hole | 3. The graph (fig 1) shows the the minimum ozone level (Dobson units) plotted against the year.Figure 2It is thought that the function y = 190 – 5.3t is a suitable model for this data, where t is the number of years since 1980 {so t = 4 represents 1984, t = 6 represents 1986} and y is the minimum ozone level (Dobson units) a. What does this model predict for the minimum ozone level in 1980?(1 mark) b. What does this model predict for the minimum ozone level in 1990?(1 mark) c. What does this model predict for the minimum ozone level in 2000?(1 mark) d. Use these points to plot the line y = 190 – 5.3t on the graph.(3 marks) e. In 1996 the equation predicts that the ozone level should have been 105.2. The measured level was 111. What is the percentage difference between these two results?(2 marks) f. Why do you think this linear model would be unsuitable for predicting the ozone level in 2020? (2 marks) |
The Ozone Hole 2 | 4.Figure 3The graph (figure 2) shows the average size of the ozone hole for the years 1980 – 2000. A straight line has been added to the graph to model the data. a. For this model, the area of the ozone in 1983 is 7.5 million km2 and the area of the ozone hole in 1998 is 26 million km2. Use these answers to calculate the gradient of the straight line model. (1 mark) b. What information does the value of the gradient of the straight line model give you?(1 mark) c. Write down an equation of the form y = at + b for the straight line model, where t is the number of years since 1980 and y is the average area of the ozone hole (million km2) (2 marks) d. What information does the intercept of the straight line give you?(1 mark) e. Use your model to predict the size of the ozone hole in 2020.(2 marks) f. Why is this answer likely to be unreliable?(2 marks) |
