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1.2 Algebra

1.2 Algebra

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Question 136

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

1.2 Algebra Questions

  1. A Level
  2. /Maths
  3. /1.2 Algebra

303 exam-style questions on OCR (MEI) A Level Maths 1.2 Algebra, covering 1.2.1 Algebraic vocabulary and notation, 1.2.2 Solve linear equations, 1.2.3 Change the subject of a formula, 1.2.4 Solve quadratic equations, 1.2.5 Discriminant of a quadratic, 1.2.6 Linear simultaneous equations, 1.2.7 One linear one quadratic simultaneous equations, 1.2.8 Points of intersection and solutions, 1.2.9 Linear inequalities, 1.2.10 Quadratic inequalities, 1.2.11 Expressing solutions of inequalities, 1.2.12 Use and manipulate surds, 1.2.13 Rationalise the denominator, 1.2.14 Laws of indices, 1.2.15 Negative, fractional and zero indices, 1.2.16 Proportional relationships, 1.2.17 Partial fractions (A-level only), and 1.2.18 Simplify rational expressions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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