| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Simplify numerical surds |
| Difficulty | Easy -1.3 This is a straightforward C1 question testing basic manipulation of surds and fractional indices. All three parts are routine textbook exercises requiring only direct application of standard techniques (rationalizing denominators, simplifying surds, and converting fractional powers). No problem-solving or insight needed, making it easier than average. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| i) \(2\sqrt{3}\) | B1 [1] | cao. Do not accept \(\frac{6\sqrt{3}}{3}\) |
| ii) \(10\sqrt{3} - 18\sqrt{3} = -8\sqrt{3}\) | B1, B1 [2] | \(\sqrt{27} = 3\sqrt{3}\) soi, not just \(\sqrt{9}\sqrt{3}\) |
| iii) \(3^2 \times 3^2 \times 3^{\frac{1}{2}} = 9\sqrt{3}\) | B1, B1 [2] | Separate \(\sqrt{3}\) from \(3^2\). Allow only \(3 \times 3 \times 3^{\frac{1}{2}}, 3^2 \times \sqrt{3}, 3 \times 3 \times \sqrt{3}\), or \(\sqrt{81/3}, 3\sqrt{9/3}\) for first mark |
**i)** $2\sqrt{3}$ | B1 [1] | cao. Do not accept $\frac{6\sqrt{3}}{3}$
**ii)** $10\sqrt{3} - 18\sqrt{3} = -8\sqrt{3}$ | B1, B1 [2] | $\sqrt{27} = 3\sqrt{3}$ soi, not just $\sqrt{9}\sqrt{3}$
**iii)** $3^2 \times 3^2 \times 3^{\frac{1}{2}} = 9\sqrt{3}$ | B1, B1 [2] | Separate $\sqrt{3}$ from $3^2$. Allow only $3 \times 3 \times 3^{\frac{1}{2}}, 3^2 \times \sqrt{3}, 3 \times 3 \times \sqrt{3}$, or $\sqrt{81/3}, 3\sqrt{9/3}$ for first markExpress each of the following in the form $k\sqrt{3}$, where $k$ is an integer.
\begin{enumerate}[label=(\roman*)]
\item $\frac{6}{\sqrt{3}}$ [1]
\item $10\sqrt{3} - 6\sqrt{27}$ [2]
\item $3^{\frac{3}{2}}$ [2]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 2014 Q2 [5]}}