Easy -1.2 This is a straightforward application of the standard technique for rationalising denominators with surds—multiply by the conjugate. It's a single-step procedure requiring only recall of the method and basic algebraic manipulation, making it easier than average but not trivial since students must remember to use (3-√n) and expand correctly.
Attempt to multiply numerator and denominator by \((3-\sqrt{n})\). May be implied by fully correct answer
\(\frac{6+\sqrt{n}-n}{9-n}\)
A1
Correct expansion for either numerator or denominator
Final answer fully correct
A1
Final answer fully correct
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{(2+\sqrt{n})(3-\sqrt{n})}{(3+\sqrt{n})(3-\sqrt{n})}$ | M1 | Attempt to multiply numerator and denominator by $(3-\sqrt{n})$. May be implied by fully correct answer |
| $\frac{6+\sqrt{n}-n}{9-n}$ | A1 | Correct expansion for either numerator or denominator |
| Final answer fully correct | A1 | Final answer fully correct |
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1 Rationalise the denominator of the fraction $\frac { 2 + \sqrt { n } } { 3 + \sqrt { n } }$, where $n$ is a positive integer.
\hfill \mbox{\textit{OCR MEI AS Paper 1 2022 Q1 [3]}}