| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Expand and simplify surd expressions |
| Difficulty | Moderate -0.8 This is a straightforward surds manipulation question testing basic algebraic skills. Part (i) requires simple multiplication of surds and simplification of √24, while part (ii) involves expanding brackets with surds—both are routine C1 exercises requiring only direct application of standard techniques with no problem-solving or insight needed. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(28\sqrt{6}\) | 2 marks | 1 for \(30\sqrt{6}\) or \(2\sqrt{6}\) or \(2\sqrt{2}\sqrt{3}\) or \(28\sqrt{2}\sqrt{3}\) |
| (ii) \(49 - 12\sqrt{5}\) isw | 3 marks | 2 for \(49\) and 1 for \(-12\sqrt{5}\) or M1 for \(3\) correct terms from \(4 - 6\sqrt{5} - 6\sqrt{5} + 45\) |
| 5 marks |
(i) $28\sqrt{6}$ | 2 marks | 1 for $30\sqrt{6}$ or $2\sqrt{6}$ or $2\sqrt{2}\sqrt{3}$ or $28\sqrt{2}\sqrt{3}$
(ii) $49 - 12\sqrt{5}$ isw | 3 marks | 2 for $49$ and 1 for $-12\sqrt{5}$ or M1 for $3$ correct terms from $4 - 6\sqrt{5} - 6\sqrt{5} + 45$
| | 5 marks |\begin{enumerate}[label=(\roman*)]
\item Simplify $6\sqrt{2} \times 5\sqrt{3} - \sqrt{24}$. [2]
\item Express $(2 - 3\sqrt{5})^2$ in the form $a + b\sqrt{5}$, where $a$ and $b$ are integers. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2006 Q7 [5]}}