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Algebraic Methods

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Question 115

A researcher is measuring the difference in signal attenuation, AAA, at two distinct observation points. For a positive integer parameter k≥1k \ge 1k≥1, the attenuation is modelled by

A(k)=127+4k−124k−7 A(k) = \frac{12}{7 + 4\sqrt{k}} - \frac{12}{4\sqrt{k} - 7} A(k)=7+4k​12​−4k​−712​
a.

Express A(k)A(k)A(k) as a single fraction that does not involve surds.

[3]
b.

Hence, deduce that A(k)A(k)A(k) is a rational number for all positive integer values of kkk.

[2]

Algebraic Methods Questions

  1. A Level
  2. /Maths
  3. /Algebraic Methods

Practise Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 226 questions covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank