Question 2 - A-Level Maths

Exam Board	Edexcel
Module	C1 (Core Mathematics 1)
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Indices and Surds
Type	Rationalize denominator simple
Difficulty	Moderate -0.8 This is a standard rationalizing the denominator question requiring multiplication by the conjugate surd. It's a routine C1 technique with straightforward algebraic manipulation, making it easier than average but not trivial since students must recognize the method and execute it correctly.
Spec	1.02b Surds: manipulation and rationalising denominators

Express $$\frac{2}{3\sqrt{5} + 7}$$ in the form $a + b\sqrt{5}$ where $a$ and $b$ are rational. [3]

Answer	Marks	Guidance
$= \frac{2}{3\sqrt{5}+7} \times \frac{3\sqrt{5}-7}{3\sqrt{5}-7} = \frac{6\sqrt{5}-14}{45-49} = \frac{7}{2} - \frac{3}{2}\sqrt{5}$	M2 A1	(3)

$= \frac{2}{3\sqrt{5}+7} \times \frac{3\sqrt{5}-7}{3\sqrt{5}-7} = \frac{6\sqrt{5}-14}{45-49} = \frac{7}{2} - \frac{3}{2}\sqrt{5}$ | M2 A1 | (3)

Express
$$\frac{2}{3\sqrt{5} + 7}$$
in the form $a + b\sqrt{5}$ where $a$ and $b$ are rational. [3]

\hfill \mbox{\textit{Edexcel C1  Q2 [3]}}