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1.5.6 Polynomials and rational expressions

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Question 38

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

\frac{12}{7 + 4\sqrt{k}} - \frac{12}{4\sqrt{k} - 7}

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

[3]

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

[2]

Markscheme

1.5.6 Polynomials and rational expressions Questions

A Level
Maths
1.5.6 Polynomials and rational expressions

113 exam-style questions on AQA A Level Maths 1.5.6 Polynomials and rational expressions. Each one has a worked solution and a mark scheme showing where the marks go.

1.5.6 Polynomials and rational expressions

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1.5.6 Polynomials and rational expressions

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Question 38

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

\frac{12}{7 + 4\sqrt{k}} - \frac{12}{4\sqrt{k} - 7}

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

[3]

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

[2]

Markscheme

1.5.6 Polynomials and rational expressions Questions

A Level
Maths
1.5.6 Polynomials and rational expressions

113 exam-style questions on AQA A Level Maths 1.5.6 Polynomials and rational expressions. Each one has a worked solution and a mark scheme showing where the marks go.