| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 4 |
| 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 direct application of standard rules (√a × √b = √(ab), rationalizing denominators, and a^(3/2) = a√a) with no problem-solving or insight needed. The multi-part structure and low mark allocation (4 marks total) confirm this is easier than average. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks |
|---|---|
| Marks: M1 | A1 [2] |
| Guidance: For method mark, makes a correct start to manipulate the expression i.e. at least combines two parts correctly or splits one part correctly. | Correctly simplified answer |
## (i)
**Answer:** $4\sqrt{45} = 12\sqrt{5}$
**Marks:** M1 | A1 [2]
**Guidance:** For method mark, makes a correct start to manipulate the expression i.e. at least combines two parts correctly or splits one part correctly. | Correctly simplified answer
## (ii)
**Answer:** $\frac{20\sqrt{5}}{5} = 4\sqrt{5}$
**Marks:** B1 [1]
**Guidance:** cao, do not allow unsimplified, do not allow if clearly from wrong working
## (iii)
**Answer:** $5\sqrt{5}$
**Marks:** B1 [1]
**Guidance:** cao www, do not allow unsimplified, do not allow if clearly from wrong working
---Express each of the following in the form $a\sqrt{5}$, where $a$ is an integer.
\begin{enumerate}[label=(\roman*)]
\item $4\sqrt{15} \times \sqrt{3}$ [2]
\item $\frac{20}{\sqrt{5}}$ [1]
\item $5^{\frac{3}{2}}$ [1]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 2013 Q1 [4]}}