4PM1/01R Jan 2023, Question 1: Surds
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 4 marks
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The question, in short
Rationalise (a − √48)/(√3 + 1), match it to b√3 − 9 with integers a and b, and find a and b, showing working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1√48 = 4√3
- 2a − 4√3 = (b√3 − 9)(√3 + 1) = (3b − 9) + √3(b − 9)
- 3Compare: a = 3b − 9 and −4 = b − 9
- 4b = 5, a = 6
Answera = 6, b = 5
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