| 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 straightforward C1 question testing basic surd manipulation: simplifying surds by extracting square factors and rationalizing a denominator using the conjugate. Both parts are standard textbook exercises requiring only routine application of well-practiced techniques with no problem-solving or insight needed. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \(\sqrt{2}\) or \(\sqrt{8}\) | 2 marks | M1 for \(7\sqrt{2}\) or \(5\sqrt{2}\) seen |
| Answer | Marks | Guidance |
|---|---|---|
| \(-12\sqrt{5}\) | 3 marks | M1 for attempt to multiply numerator and denominator by \(2 - \sqrt{5}\); and M1 (dep) for denominator \(-1\) or \(4 - 5\) soi; or for numerator \(12\sqrt{5} - 30\) |
## Question 15:
**Part (i)**
$\sqrt{2}$ or $\sqrt{8}$ | 2 marks | M1 for $7\sqrt{2}$ or $5\sqrt{2}$ seen
**Part (ii)**
$-12\sqrt{5}$ | 3 marks | M1 for attempt to multiply numerator and denominator by $2 - \sqrt{5}$; and M1 (dep) for denominator $-1$ or $4 - 5$ soi; or for numerator $12\sqrt{5} - 30$
**Total: 5 marks**
---15 (i) Simplify $\sqrt { 98 } \quad \sqrt { 50 }$.\\
(ii) Express $\frac { 6 \sqrt { 5 } } { 2 + \sqrt { 5 } }$ in the form $a + b \sqrt { 5 }$, where $a$ and $b$ are integers.
\hfill \mbox{\textit{OCR MEI C1 Q15 [5]}}