| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2024 |
| Session | October |
| Marks | 4 |
| Topic | Indices and Surds |
| Type | Simplify algebraic expressions with indices |
| Difficulty | Moderate -0.8 This is a straightforward algebraic manipulation requiring factorization of powers and simplification of indices. While it requires careful handling of fractional powers and recognizing common factors, it's a routine exercise testing index law fluency with no conceptual depth or problem-solving insight needed—easier than the typical A-level question. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
Express $\frac{a^{\frac{1}{2}} - a^{\frac{2}{3}}}{a^{\frac{1}{3}} - a}$ in the form $a^m + \sqrt{a^n}$, where $m$ and $n$ are integers and $a \neq 0$ or 1. [4]
\hfill \mbox{\textit{SPS SPS SM 2024 Q7 [4]}}