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1.5 B: Algebra and functions

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Question 129

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]
Markscheme

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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