| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Expand and simplify surd expressions |
| Difficulty | Easy -1.2 This is a straightforward C1 question testing basic surd manipulation skills. Part (i) requires routine expansion using FOIL and simplifying √2 terms, while part (ii) involves standard simplification of surds and rationalizing denominators. Both are textbook exercises requiring only direct application of learned techniques with no problem-solving or insight needed. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \(23 + \sqrt{2}\) as final answer | 3 marks | |
| - B2 for 23 and B1 for \(\sqrt{2}\) or \(1\sqrt{2}\); OR M2 for 3 or more terms correct of \(35 - 14\sqrt{2} + 15\sqrt{2} - 12\) | M1 for 2 terms correct | Mark one scheme or other, but not a mixture, to advantage of candidate; eg M2 for \(35 + \sqrt{2} + 24\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(5\sqrt{6}\) isw | 2 marks | |
| - Condone \(\dfrac{30}{\sqrt{6}}\) for 2 marks | eg 2 isw for \(5\sqrt{6} = \sqrt{150}\) | |
| - M1 for \([\sqrt{54} =] 3\sqrt{6}\) or \(\left[\dfrac{12}{\sqrt{6}} =\right] 2\sqrt{6}\) | M1 |
## Question 7:
**(i)**
$23 + \sqrt{2}$ as final answer | 3 marks |
- B2 for 23 and B1 for $\sqrt{2}$ or $1\sqrt{2}$; OR M2 for 3 or more terms correct of $35 - 14\sqrt{2} + 15\sqrt{2} - 12$ | M1 for 2 terms correct | Mark one scheme or other, but not a mixture, to advantage of candidate; eg M2 for $35 + \sqrt{2} + 24$
**(ii)**
$5\sqrt{6}$ isw | 2 marks |
- Condone $\dfrac{30}{\sqrt{6}}$ for 2 marks | | eg 2 isw for $5\sqrt{6} = \sqrt{150}$
- M1 for $[\sqrt{54} =] 3\sqrt{6}$ or $\left[\dfrac{12}{\sqrt{6}} =\right] 2\sqrt{6}$ | M1 |
---7 (i) Expand and simplify $( 7 + 3 \sqrt { 2 } ) ( 5 - 2 \sqrt { 2 } )$.\\
(ii) Simplify $\sqrt { 54 } + \frac { 12 } { \sqrt { 6 } }$.
\hfill \mbox{\textit{OCR MEI C1 Q7 [5]}}