| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Easy -1.3 This is a straightforward surds question requiring only basic manipulation: simplifying surds by factoring out perfect squares (part i) and rationalizing a simple denominator (part ii). Both parts are routine textbook exercises with no problem-solving or novel insight required, making this easier than average for A-level. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \(\sqrt{2}\) | 2 marks | M1 for \(\sqrt{8} = 2\sqrt{2}\) or \(\sqrt{50} = 5\sqrt{2}\) soi; B1 for \(6\sqrt{50}\) or other correct \(a\sqrt{b}\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\dfrac{1}{11} + \dfrac{2}{11}\sqrt{3}\) or \(\dfrac{3}{33} + \dfrac{6}{33}\sqrt{3}\) or mixture of these | 3 marks | M1 for multiplying numerator and denominator by \(6 + \sqrt{3}\); and M1 for denominator \(= 11\) or \(33\) |
## Question 17:
**Part (i)**
$\sqrt{2}$ | 2 marks | M1 for $\sqrt{8} = 2\sqrt{2}$ or $\sqrt{50} = 5\sqrt{2}$ soi; B1 for $6\sqrt{50}$ or other correct $a\sqrt{b}$
**Part (ii)**
$\dfrac{1}{11} + \dfrac{2}{11}\sqrt{3}$ or $\dfrac{3}{33} + \dfrac{6}{33}\sqrt{3}$ or mixture of these | 3 marks | M1 for multiplying numerator and denominator by $6 + \sqrt{3}$; and M1 for denominator $= 11$ or $33$
**Total: 5 marks**17 (i) Simplify $5 \sqrt { 8 } + 4 \sqrt { 50 }$. Express your answer in the form $a \sqrt { b }$, where $a$ and $b$ are integers and $b$ is as small as possible.\\
(ii) Express $\frac { \sqrt { 3 } } { 6 \sqrt { 3 } }$ in the form $p + q \sqrt { 3 }$, where $p$ and $q$ are rational.
\hfill \mbox{\textit{OCR MEI C1 Q17 [5]}}