| 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 | Moderate -0.8 This is a straightforward two-part question testing basic surd manipulation: (i) expanding a binomial with surds using standard algebraic techniques, and (ii) simplifying a surd fraction by rationalizing/simplifying radicals. Both are routine C1-level exercises requiring only direct application of standard methods with no problem-solving or insight needed, making it easier than average but not trivial. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
# Question 2
## (i)
**Answer:** $61 + 28\sqrt{3}$ [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 $49 + 14\sqrt{3} + 14\sqrt{3} + 12$
If the correct answer obtained then spoilt earns SC2 only
## (ii)
**Answer:** $4\sqrt{3}$ [2]
M1 for $50 - 5 \times 2$ or $300 - 10\sqrt{3}$ or $20\sqrt{300} - 200\sqrt{3}$ or $48\sqrt{2} - 12$ seen2 (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 Q2 [5]}}