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Algebraic Methods

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Question 158

The difference in signal attenuation, A(k)A(k)A(k), between two experimental microwave waveguides depends on a positive integer parameter kkk according to the formula:

A(k)=83+7k−87k−3 A(k) = \frac{8}{3+7\sqrt{k}} - \frac{8}{7\sqrt{k}-3} A(k)=3+7k​8​−7k​−38​
a.

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

[4]
b.

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

[2]
Markscheme

Algebraic Methods Questions

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

368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.

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