| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2014 |
| 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 expanding a binomial with surds using standard algebraic techniques, and part (ii) involves simplifying a surd fraction by rationalizing and reducing—both are routine textbook exercises with no problem-solving or insight required, making it easier than average. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(61 - 28\sqrt{3}\) | B2 for 61 or B1 for \(49 + 12\) found in expansion (may be in a grid) | |
| B1 for \(-28\sqrt{3}\) | ||
| If B0, allow M1 for at least three terms correct in \(49 - 14\sqrt{3} - 14\sqrt{3} + 12\) | ||
| The correct answer obtained then spoilt earns SC2 only | ||
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(4\sqrt{3}\) | M1 for \(\sqrt{50} = 5\sqrt{2}\) or \(\sqrt{300} = 10\sqrt{3}\) or \(20\sqrt{300} = 200\sqrt{3}\) or \(\sqrt{48} = 2\sqrt{12}\) seen | |
| [2] |
## Question 4(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $61 - 28\sqrt{3}$ | B2 for 61 or B1 for $49 + 12$ found in expansion (may be in a grid) | |
| | B1 for $-28\sqrt{3}$ | |
| | If B0, allow M1 for at least three terms correct in $49 - 14\sqrt{3} - 14\sqrt{3} + 12$ | |
| | The correct answer obtained then spoilt earns SC2 only | |
| | **[3]** | |
---
## Question 4(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $4\sqrt{3}$ | M1 for $\sqrt{50} = 5\sqrt{2}$ or $\sqrt{300} = 10\sqrt{3}$ or $20\sqrt{300} = 200\sqrt{3}$ or $\sqrt{48} = 2\sqrt{12}$ seen | |
| | **[2]** | |
---4 (i) Expand and simplify $( 7 - 2 \sqrt { 3 } ) ^ { 2 }$.\\
(ii) Express $\frac { 20 \sqrt { 6 } } { \sqrt { 50 } }$ 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 2014 Q4 [5]}}