Moderate -0.8 This is a straightforward rationalizing denominators question requiring a standard technique applied three times, then simplification. While it involves multiple terms and careful algebra, it's a routine exercise with no conceptual difficulty or novel insight required—easier than average for A-level.
At least one fraction multiplied by \(\frac{\sqrt{2}-1}{\sqrt{2}-1}\) or \(\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}\) or \(\frac{2-\sqrt{3}}{2-\sqrt{3}}\)
M1
Rationalising denominators method
All correct with denominators seen as \(2-1\), \(3-2\), \(4-3\) or \(1,1,1\); answer 1
A1
Must see something correct
Numerator of \((\sqrt{3}+\sqrt{2})(2+\sqrt{3})+(\sqrt{2}+1)(2+\sqrt{3})+(\sqrt{2}+1)(\sqrt{3}+\sqrt{2})\) giving \(3\sqrt{6}+4\sqrt{3}+5\sqrt{2}+7\)
M1
Alternative: combining all three fractions
\(\frac{3\sqrt{6}+4\sqrt{3}+5\sqrt{2}+7}{3\sqrt{6}+4\sqrt{3}+5\sqrt{2}+7}\) before cancelling; answer 1
A1
## Question 4:
| At least one fraction multiplied by $\frac{\sqrt{2}-1}{\sqrt{2}-1}$ or $\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}$ or $\frac{2-\sqrt{3}}{2-\sqrt{3}}$ | M1 | Rationalising denominators method |
| All correct with denominators seen as $2-1$, $3-2$, $4-3$ or $1,1,1$; answer 1 | A1 | Must see something correct |
| Numerator of $(\sqrt{3}+\sqrt{2})(2+\sqrt{3})+(\sqrt{2}+1)(2+\sqrt{3})+(\sqrt{2}+1)(\sqrt{3}+\sqrt{2})$ giving $3\sqrt{6}+4\sqrt{3}+5\sqrt{2}+7$ | M1 | Alternative: combining all three fractions |
| $\frac{3\sqrt{6}+4\sqrt{3}+5\sqrt{2}+7}{3\sqrt{6}+4\sqrt{3}+5\sqrt{2}+7}$ before cancelling; answer 1 | A1 | |