OCR MEI C1 — Question 8 5 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Marks5
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TopicIndices and Surds
TypeRationalize denominator simple
DifficultyEasy -1.2 This is a straightforward rationalizing the denominator question requiring multiplication by the conjugate and simple algebraic manipulation. It's a standard C1 exercise with a clear method and minimal steps, making it easier than average but not trivial since students must recognize the technique and execute it correctly.
Spec1.02b Surds: manipulation and rationalising denominators
8 Find the values of \(a\) and \(b\) for which \(\frac { 4 } { ( 2 \sqrt { 3 } - 1 ) } = a + b \sqrt { 3 }\).
\[\frac{4}{2\sqrt{3}-1} = \frac{4(2\sqrt{3}+1)}{(2\sqrt{3}-1)(2\sqrt{3}+1)}\]
\[= \frac{4(2\sqrt{3}+1)}{11} = \frac{4}{11} + \frac{8\sqrt{3}}{11}\]
AnswerMarks
\(\Rightarrow a = \frac{4}{11}, b = \frac{8}{11}\)M1, A1, M1, A1, A1 
$$\frac{4}{2\sqrt{3}-1} = \frac{4(2\sqrt{3}+1)}{(2\sqrt{3}-1)(2\sqrt{3}+1)}$$

$$= \frac{4(2\sqrt{3}+1)}{11} = \frac{4}{11} + \frac{8\sqrt{3}}{11}$$

$\Rightarrow a = \frac{4}{11}, b = \frac{8}{11}$ | M1, A1, M1, A1, A1 |
8 Find the values of $a$ and $b$ for which $\frac { 4 } { ( 2 \sqrt { 3 } - 1 ) } = a + b \sqrt { 3 }$.

\hfill \mbox{\textit{OCR MEI C1  Q8 [5]}}
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