| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2023 |
| Session | October |
| Marks | 4 |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Moderate -0.8 This is a routine surds rationalisation question requiring multiplication by the conjugate and simplification. While it involves multiple steps (recognising √20 = 2√5, multiplying by conjugate 3-√5, expanding, and simplifying), it's a standard technique tested at AS-level with no problem-solving insight required. The 4 marks reflect working steps rather than conceptual difficulty. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
This question requires detailed reasoning.
Express $\frac{3 + \sqrt{20}}{3 + \sqrt{5}}$ in the form $a + b\sqrt{5}$.
[4]
\hfill \mbox{\textit{SPS SPS FM 2023 Q1 [4]}}