| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2015 |
| Session | June |
| Marks | 3 |
| Topic | Indices and Surds |
| Type | Show surd expression equals value |
| Difficulty | Easy -1.8 This is a straightforward rationalising the denominator exercise requiring only multiplication by the conjugate surd and simplification. It's a single-step standard technique with no problem-solving element, making it significantly easier than average A-level questions which typically require multiple techniques or conceptual understanding. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
**Question 1:** Show that $\frac{31}{6-\sqrt{5}} = 6+\sqrt{5}$
$$\frac{31}{6-\sqrt{5}} \times \frac{6+\sqrt{5}}{6+\sqrt{5}} = \frac{186+31\sqrt{5}}{31} = 6+\sqrt{5}$$
- **M1**: Show intention to multiply top and bottom by $6+\sqrt{5}$
- **B1**: Correct denominator; at least as far as $36-5$
- **A1**: Show given answer correctly, including 31 seen as denominator before cancelling
If showing that $(6+\sqrt{5})(6-\sqrt{5})=31$ then:
- M1 – attempt to expand
- A1 – at least $36-5$ seen
- A1 – obtain 31
**Total: [3]**1 Show that $\frac { 31 } { 6 - \sqrt { 5 } } = 6 + \sqrt { 5 }$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2015 Q1 [3]}}