| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2025 |
| Session | October |
| Marks | 3 |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Moderate -0.3 This is a straightforward surds question requiring rationalizing the denominator by multiplying by the conjugate (1+2√5), then collecting like terms. It's slightly easier than average as it follows a standard procedure with no conceptual difficulty, though the arithmetic requires care. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
In this question you must show detailed reasoning.
Simplify $10 + 7\sqrt{5} + \frac{38}{1 - 2\sqrt{5}}$, giving your answer in the form $a + b\sqrt{5}$. [3]
\hfill \mbox{\textit{SPS SPS SM 2025 Q2 [3]}}