Example 1: Using a Diagram
Question 1
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25
9 This question is about waves.
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27
A student uses a microwave source and a receiver to investigate microwaves.
Photograph 1 shows how the student sets up their apparatus.
Photograph 1
The meter shows the strength of the microwaves detected by the receiver.
The strength of the microwaves is measured in arbitrary units.
The student varies the distance between the microwave source and the receiver, and records the meter readings.
The graph shows the results of the student’s investigation.
The student concludes that the meter reading is inversely proportional to the distance between the microwave source and the receiver.
To be inversely proportional
meter reading × distance = constant
Comment on the student’s conclusion.
You should use data from the graph in your answer.
Final answer
The student’s conclusion is incorrect. The relationship is not inversely proportional.
At 10 cm: 100 × 10 = 1000 At 20 cm: 25 × 20 = 500
The products are different, so meter reading × distance is not constant.
Mark scheme points
- M1 State that the relationship is not inversely proportional, or that the student’s conclusion is incorrect.
- M2 Correctly calculate the product for one pair of graph readings, for example 100 × 10 = 1000.
- M3 Correctly calculate the product for a second pair of graph readings, for example 25 × 20 = 500.
- M4 State that meter reading × distance is not constant.
Explanation
For inverse proportionality, multiplying the meter reading by the distance must give the same value for every pair of readings. Read two clear points from the graph and compare their products:
R = 100, d = 10 cm: R × d = 1000 R = 25, d = 20 cm: R × d = 500
Because 1000 and 500 are not equal, the product is not constant. Therefore, the meter reading is not inversely proportional to distance.
Common mistakes
- Do not just state that the graph is curved or decreasing; this does not test inverse proportionality.
- Use the graph values in the calculation rather than claiming that the relationship “looks inverse”.
- Calculate meter reading × distance, not meter reading ÷ distance.
- Give two products and compare them; one calculation alone cannot show whether the product is constant.
- Nearly half of candidates did not use data from the graph, even though the question required it. Always show two products and state whether they are constant.