| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2009 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Distance between two points |
| Difficulty | Easy -1.2 This is a straightforward C1 question testing basic algebraic manipulation (simplifying surds and rationalizing denominators) and likely the distance formula. Part (i) requires factorizing radicals and combining like terms; part (ii) is standard rationalization. These are routine textbook exercises requiring only recall and direct application of techniques, making them easier than average A-level questions. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(9\sqrt{3}\) | 2 | M1 for \(5\sqrt{3}\) or \(4\sqrt{3}\) seen |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(6 + 2\sqrt{2}\) www | 3 | M1 for attempt to multiply num. and denom. by \(3 + \sqrt{2}\); M1 for denom. 7 or \(9 - 2\) soi from denom. mult by \(3 + \sqrt{2}\) |
| Total: 5 marks |
# Question 10:
## Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $9\sqrt{3}$ | 2 | M1 for $5\sqrt{3}$ or $4\sqrt{3}$ seen |
## Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $6 + 2\sqrt{2}$ www | 3 | M1 for attempt to multiply num. and denom. by $3 + \sqrt{2}$; M1 for denom. 7 or $9 - 2$ soi from denom. mult by $3 + \sqrt{2}$ |
| **Total: 5 marks** | | |
---10 (i) Express $\sqrt { 75 } + \sqrt { 48 }$ in the form $a \sqrt { 3 }$.\\
(ii) Express $\frac { 14 } { 3 - \sqrt { 2 } }$ in the form $b + c \sqrt { d }$.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{c7fbeb8f-d874-4756-aa53-5471b215902f-3_773_961_354_591}
\captionsetup{labelformat=empty}
\caption{Fig. 11}
\end{center}
\end{figure}
Fig. 11 shows the points A and B , which have coordinates $( - 1,0 )$ and $( 11,4 )$ respectively.\\
\hfill \mbox{\textit{OCR MEI C1 2009 Q10 [5]}}