| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Simplify numerical surds |
| Difficulty | Easy -1.3 This is a routine surd simplification exercise requiring only standard techniques: factoring out perfect squares and rationalizing denominators. Both parts are straightforward applications of basic surd rules with no problem-solving or insight required, making it easier than the average A-level question. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(10\sqrt{3} - 4\sqrt{3} = 6\sqrt{3}\) | M1, B1, A1, 3 | Attempt to express both surds in terms of \(\sqrt{3}\) |
| (ii) \(\sqrt{5(15 + \sqrt{40})} / 5 = \frac{15\sqrt{5} + 10\sqrt{2}}{5} = 3\sqrt{5} + 2\sqrt{2}\) | M1, B1, A1, 3, 6 | Multiply numerator and denominator by \(\sqrt{5}\) or - \(\sqrt{5}\) or attempt to express both terms of numerator in terms of \(\sqrt{5}\) (e.g. dividing both terms by \(\sqrt{5}\)) |
**(i)** $10\sqrt{3} - 4\sqrt{3} = 6\sqrt{3}$ | M1, B1, A1, 3 | Attempt to express both surds in terms of $\sqrt{3}$ | One term correct | Fully correct (not $\pm 6\sqrt{3}$) | e.g. $\sqrt{3×100} - \sqrt{3×16}$
**(ii)** $\sqrt{5(15 + \sqrt{40})} / 5 = \frac{15\sqrt{5} + 10\sqrt{2}}{5} = 3\sqrt{5} + 2\sqrt{2}$ | M1, B1, A1, 3, 6 | Multiply numerator and denominator by $\sqrt{5}$ or - $\sqrt{5}$ or attempt to express both terms of numerator in terms of $\sqrt{5}$ (e.g. dividing both terms by $\sqrt{5}$) | One of a, b correctly obtained | Both a = 3 and b=2 correctly obtained | Check both numerator and denominator have been multiplied5 (i) Express $\sqrt { 300 } - \sqrt { 48 }$ in the form $k \sqrt { 3 }$, where $k$ is an integer.\\
(ii) Express $\frac { 15 + \sqrt { 40 } } { \sqrt { 5 } }$ in the form $a \sqrt { 5 } + b \sqrt { 2 }$, where $a$ and $b$ are integers.
\hfill \mbox{\textit{OCR C1 2011 Q5 [6]}}