Easy -1.2 This is a routine AS-level question testing rationalisation of surds by multiplying by the conjugate. It requires only one standard technique (multiply by conjugate, expand, simplify) with straightforward arithmetic. The 3-mark allocation and 'show that' format make it a guided exercise rather than a problem-solving task, placing it below average difficulty.
Question 4:
4 | Multiplies numerator and
denominator by the conjugate surd of
the denominator | AO1.1a | M1 | (5 2+2)(3 24)
(3 2+4)(3 24)
3020 26 28
2
2214 2
2
117 2
Obtains either numerator or
denominator correctly, in expanded
or simplified form | AO1.1b | A1
Constructs rigorous mathematical
argument to show the required result
Only award if they have a completely
correct solution, which is clear, easy
to follow and contains no slips
NMS = 0 | AO2.1 | R1
Total | 3
Q | Marking Instructions | AO | Marks | Typical Solution
Show that $\frac{5\sqrt{2} + 2}{3\sqrt{2} + 4}$ can be expressed in the form $m + n\sqrt{2}$, where $m$ and $n$ are integers.
[3 marks]
\hfill \mbox{\textit{AQA AS Paper 1 Q4 [3]}}