| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Simplify numerical surds |
| Difficulty | Easy -1.8 This is a routine surd simplification requiring only basic factorization (75 = 25×3, 27 = 9×3) and collecting like terms to get 2√3. It's a standard textbook exercise with no problem-solving element, making it significantly easier than average A-level questions. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance Notes |
| \((\sqrt{75} - \sqrt{27}) = 5\sqrt{3} - 3\sqrt{3}\) | M1 | For \(5\sqrt{3}\) from \(\sqrt{75}\) or \(3\sqrt{3}\) from \(\sqrt{27}\) seen anywhere |
| \(= 2\sqrt{3}\) | A1 | For \(2\sqrt{3}\); allow \(\sqrt{12}\) or \(k=2, x=3\); allow \(k=1, x=12\) |
| Common errors: \(\sqrt{75}-\sqrt{27}=\sqrt{48}\) leading to \(4\sqrt{3}\) is M0A0; \(25\sqrt{3}-9\sqrt{3}=16\sqrt{3}\) is M0A0 | ||
| Total | 2 |
## Question 1:
| Answer/Working | Marks | Guidance Notes |
|---|---|---|
| $(\sqrt{75} - \sqrt{27}) = 5\sqrt{3} - 3\sqrt{3}$ | M1 | For $5\sqrt{3}$ from $\sqrt{75}$ or $3\sqrt{3}$ from $\sqrt{27}$ seen anywhere |
| $= 2\sqrt{3}$ | A1 | For $2\sqrt{3}$; allow $\sqrt{12}$ or $k=2, x=3$; allow $k=1, x=12$ |
| | | Common errors: $\sqrt{75}-\sqrt{27}=\sqrt{48}$ leading to $4\sqrt{3}$ is M0A0; $25\sqrt{3}-9\sqrt{3}=16\sqrt{3}$ is M0A0 |
| **Total** | **2** | |
---\begin{enumerate}
\item Write
\end{enumerate}
$$\sqrt { } ( 75 ) - \sqrt { } ( 27 )$$
in the form $k \sqrt { } x$, where $k$ and $x$ are integers.\\
\hfill \mbox{\textit{Edexcel C1 2010 Q1 [2]}}