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Jodie measures the same map - OCR - GCSE Maths - Question 5 - 2018 - Paper 6
Question 5
Jodie measures the same map. She says I think Packer Street is longer than Neil's measurement of 3.5cm. Therefore, High Street must be longer than 576m in real lif... show full transcript
Worked Solution & Example Answer:Jodie measures the same map - OCR - GCSE Maths - Question 5 - 2018 - Paper 6
Step 1
Is Jodie's reasoning correct?
Answer
To determine whether Jodie's reasoning is correct, we need to analyze the relationship between the measurements on the map and the actual distances.
The scale provided is that 180 degrees on the map corresponds to 576 meters in real life. Therefore, we can calculate the real-life distance represented by Jodie’s measurement of Packer Street compared to Neil’s measurement of 3.5cm:
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Comparing Packer Street Measurement to Neil's:
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As per Jodie's statement, if Packer Street is longer than Neil's 3.5cm, it implies:
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Using the scale: ext{Real Length} = rac{576 ext{ m}}{11.2 ext{ cm}} imes ext{ Length on Map (cm)}
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Finding Real Length for 3.5 cm:
- Now we calculate the real length for Neil's measurement: L_{real} = rac{576 ext{ m}}{11.2 ext{ cm}} imes 3.5 ext{ cm} = 180 ext{ m}
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Conclusion:
- If Jodie thinks Packer Street is longer than 3.5 cm, then its real length is greater than 180 m. Consequently, for Jodie’s reasoning that High Street must be longer than 576m to be correct, a further comparison of measurements is necessary.
Step 2
Express the scale of the map in the form 1 : n.
Answer
To express the scale of the map where Packer Street is 2.4 cm long, we first find how many centimeters correspond to 1 meter:
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Using the previous scale of 1 : 11.2 cm for 576 m:
- This is equivalent to a simplified scale of: rac{11.2 ext{ cm}}{576 ext{ m}} = rac{1 ext{ cm}}{51.43 ext{ m}}
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Converting to scale 1 : n:
- Now we calculate the scale based on Packer Street’s length on the new map:
- Since it is 2.4 cm long, we find out what 1 cm represents:
- From this we can then also calculate:
- Therefore:
Thus, the final scale of the map can be represented as approximately 1 : 7500.