| 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 surds question testing basic manipulation skills: 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 standard techniques with no problem-solving or insight needed. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \(7\sqrt{3}\) | 2 marks | M1 for \(\sqrt{48} = 4\sqrt{3}\) or \(\sqrt{27} = 3\sqrt{3}\) |
| Answer | Marks |
|---|---|
| \(\dfrac{10 + 15\sqrt{2}}{7}\) (www isw) | 3 marks |
| - B1 for 7 [B0 for 7 wrongly obtained] | B1 |
| - B2 for \(10 + 15\sqrt{2}\) or B1 for one term of numerator correct | B1/B2 |
| - If B0, then M1 for attempt to multiply numerator and denominator by \(3 + \sqrt{2}\) | M1 |
## Question 9:
**(i)**
$7\sqrt{3}$ | 2 marks | M1 for $\sqrt{48} = 4\sqrt{3}$ or $\sqrt{27} = 3\sqrt{3}$
**(ii)**
$\dfrac{10 + 15\sqrt{2}}{7}$ (www isw) | 3 marks |
- B1 for 7 [B0 for 7 wrongly obtained] | B1 |
- B2 for $10 + 15\sqrt{2}$ or B1 for one term of numerator correct | B1/B2 |
- If B0, then M1 for attempt to multiply numerator and denominator by $3 + \sqrt{2}$ | M1 |
---9 (i) Express $\sqrt { 48 } + \sqrt { 27 }$ in the form $a \sqrt { 3 }$.\\
(ii) Simplify $\frac { 5 \sqrt { 2 } } { 3 - \sqrt { 2 } }$. Give your answer in the form $\frac { b + c \sqrt { 2 } } { d }$.
\hfill \mbox{\textit{OCR MEI C1 Q9 [5]}}