Surds: WJEC GCSE Higher June 2022 Unit 1 Q15

Higher June 2022 Unit 1 Q15

WJECHigherCurrent spec5 marksSurds

15. Simplify the following.

\[\frac{\sqrt{800}}{\left(\sqrt{2}\right)^3} + \left(3 - \sqrt{7}\right)^2\]

State whether the answer is rational or irrational. [5]

The answer is rational ☐ The answer is irrational ☐

Mark scheme

Scheme	Marks	Comments
10	B2	B1 for (numerator of) \(20\sqrt{2}\) or \(10\times 2\times \sqrt{2}\) or (denominator of) \(2\sqrt{2}\) or \(\sqrt{8}\) or appropriate factorisation of both numerator and denominator e.g. \(\dfrac{\sqrt{2} \times \sqrt{2} \times \sqrt{2} \times \sqrt{100}}{\sqrt{2} \times \sqrt{2} \times \sqrt{2}}\) (or \(\sqrt{100}\))
\(16 - 6\sqrt{7}\)	B2	B1 for 3 or 4 correct terms within \(9 - 3\sqrt{7} - 3\sqrt{7} + 7\) (e.g. B0 for ‘2’, from 2 sign errors) \(+\sqrt{49}\) might be seen instead of +7. \(-6\sqrt{7}\) is equivalent to ‘two correct terms’.
\(26 - 6\sqrt{7}\) AND irrational indicated.	B1	Mark final answer. FT for equivalent difficulty (requiring collection of terms) provided either of B2s is awarded AND final answer is irrational AND requires no further simplification.