| 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 -1.2 This is a routine C1 question testing standard surd manipulation techniques: simplifying surds by factoring out perfect squares, and rationalizing a denominator by multiplying by the conjugate. Both parts are textbook exercises requiring only procedural recall with no problem-solving or insight needed, making it easier than average. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \(9\sqrt{3}\) (www oe as final answer) | 2 marks | M1 for \(\sqrt{48} = 4\sqrt{3}\) or \(\sqrt{75} = 5\sqrt{3}\) soi |
| Answer | Marks | Guidance |
|---|---|---|
| \(\dfrac{39 + 7\sqrt{5}}{44}\) (www as final answer) | 3 marks | |
| - Attempt to multiply numerator and denominator by \(7 - \sqrt{5}\) | M1 | Condone \(\dfrac{39}{44} + \dfrac{7\sqrt{5}}{44}\) for 3 marks |
| - Each of numerator and denominator correct (must be simplified) | B1+B1 | eg M0B1 if denominator correctly rationalised to 44 but numerator not multiplied |
## Question 5:
**(i)**
$9\sqrt{3}$ (www oe as final answer) | 2 marks | M1 for $\sqrt{48} = 4\sqrt{3}$ or $\sqrt{75} = 5\sqrt{3}$ soi
**(ii)**
$\dfrac{39 + 7\sqrt{5}}{44}$ (www as final answer) | 3 marks |
- Attempt to multiply numerator and denominator by $7 - \sqrt{5}$ | M1 | Condone $\dfrac{39}{44} + \dfrac{7\sqrt{5}}{44}$ for 3 marks
- Each of numerator and denominator correct (must be simplified) | B1+B1 | eg M0B1 if denominator correctly rationalised to 44 but numerator not multiplied
---5 (i) Express $\sqrt { 48 } + \sqrt { 75 }$ in the form $a \sqrt { b }$, where $a$ and $b$ are integers.\\
(ii) Simplify $\frac { 7 + 2 \sqrt { 5 } } { 7 + \sqrt { 5 } }$, expressing your answer in the form $\frac { a + b \sqrt { 5 } } { c }$, where $a , b$ and $c$ are integers.
\hfill \mbox{\textit{OCR MEI C1 Q5 [5]}}