The task is to make up an exam style question of your choice worth 7 marks on algebra in context. And to create your own mark scheme on it.
You can also highlight potential mistakes people answering the question may make therefore add tips and hints and it must be for top/high level stundents.
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Amanda plants a sunflower seed. After 10 days, a small sprout appears and begins to grow steadily. On day 18, the plant has reached a height of 16 cm.
a) Predict the height of the plant on day 24 using any method. Show work.
b) Graph the data, then write an equation in the form y = mx + b to represent the height of the plant on day x after the seed was planted.
c) Use your equation to predict the height of the plant on day 60.
d) What factors might affect the accuracy of your prediction?
a) Students should notice that the plant grows 16cm in 8 days. They could use several methods to predict the height on day 24, but should come up with 28cm. I would award 2 points here, one for developing a reasonable technique and one for finding 28cm. (+2)
b) Accurate graph should be worth a point (consider providing axes for the students, depending on what you're trying to assess). Students should see that the y-intercept is -20, and the slope is 2 (2 more points for the answer: y = 2x-20) (+3)
c) 100cm. But if the equation was incorrect, it will affect this answer. If the result is consistent with the equation, I award the point. (+1)
d) Plant might not grow at a steady rate (eventually the sunflower will slow down and reach a constant height, so the linear approximation will fail after awhile). (+1)
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