| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2015 |
| Session | June |
| 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 simple expansion of brackets (FOIL method) with surds, and part (ii) involves simplifying surds using standard techniques (extracting square factors and rationalizing denominators). Both are routine textbook exercises requiring only procedural recall with no problem-solving or insight needed. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(-31 + 6\sqrt{5}\) | B2 | B2 for \(-31\) or B1 for \(9-40\) or SC1 for 49 and B1 for \(6\sqrt{5}\); if 0, allow M1 for three terms correct in \(9 - 6\sqrt{5} + 12\sqrt{5} - 40\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(22\sqrt{2}\) | M1, A1 | M1 for \(\sqrt{72} = 6\sqrt{2}\) soi or for \(\frac{32}{\sqrt{2}} = 16\sqrt{2}\); soi or for \(\frac{12+32}{\sqrt{2}}\) oe |
## Question 6(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $-31 + 6\sqrt{5}$ | B2 | B2 for $-31$ or B1 for $9-40$ or SC1 for 49 and B1 for $6\sqrt{5}$; if 0, allow M1 for three terms correct in $9 - 6\sqrt{5} + 12\sqrt{5} - 40$ |
## Question 6(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $22\sqrt{2}$ | M1, A1 | M1 for $\sqrt{72} = 6\sqrt{2}$ soi or for $\frac{32}{\sqrt{2}} = 16\sqrt{2}$; soi or for $\frac{12+32}{\sqrt{2}}$ oe |6 (i) Expand and simplify $( 3 + 4 \sqrt { 5 } ) ( 3 - 2 \sqrt { 5 } )$.\\
(ii) Express $\sqrt { 72 } + \frac { 32 } { \sqrt { 2 } }$ in the form $a \sqrt { b }$, where $a$ and $b$ are integers and $b$ is as small as possible.
\hfill \mbox{\textit{OCR MEI C1 2015 Q6 [5]}}