| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Moderate -0.8 This is a straightforward surds question testing standard techniques: simplifying surds by factoring out perfect squares, and rationalizing a denominator by multiplying by the conjugate. Both parts are routine textbook exercises requiring only direct application of well-practiced methods with no problem-solving or insight needed. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(9\sqrt{3}\) www oe as final answer | M1 | For \(\sqrt{48} = 4\sqrt{3}\) or \(\sqrt{75} = 5\sqrt{3}\) soi |
| A1 | ||
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\frac{39 + 7\sqrt{5}}{44}\) www as final answer | M1 | For attempt to multiply numerator and denominator by \(7 - \sqrt{5}\) |
| B1 for each of numerator and denominator correct (must be simplified) | e.g. M0B1 if denominator correctly rationalised to 44 but numerator not multiplied. Condone \(\frac{39}{44} + \frac{7\sqrt{5}}{44}\) for 3 marks | |
| [3] |
## Question 7(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $9\sqrt{3}$ www oe as final answer | M1 | For $\sqrt{48} = 4\sqrt{3}$ or $\sqrt{75} = 5\sqrt{3}$ soi |
| | A1 | |
| **[2]** | | |
---
## Question 7(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{39 + 7\sqrt{5}}{44}$ www as final answer | M1 | For attempt to multiply numerator and denominator by $7 - \sqrt{5}$ |
| | B1 for each of numerator and denominator correct (must be simplified) | e.g. M0B1 if denominator correctly rationalised to 44 but numerator not multiplied. Condone $\frac{39}{44} + \frac{7\sqrt{5}}{44}$ for 3 marks |
| **[3]** | | |
---7 (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 2013 Q7 [5]}}