| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Easy -1.2 This is a straightforward C1 question testing basic surd manipulation: simplifying √48 to 4√3 (standard technique) and rationalizing denominators with conjugates. Both parts are routine textbook exercises requiring only direct application of well-practiced methods with no problem-solving or insight needed. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(5\sqrt{3}\) | Marks: 2 | Guidance: M1 for \(\sqrt{48} = 4\sqrt{3}\) |
| (ii) common denominator \(= (5 - \sqrt{2})(5 + \sqrt{2}) = 23\); numerator \(= 10\) | Marks: M1, A1, B1 | Guidance: allow M1A1 for \(\frac{5 - \sqrt{2}}{23} + \frac{5 + \sqrt{2}}{23}\); allow 3 only for 10/23 |
**(i)** $5\sqrt{3}$ | **Marks:** 2 | **Guidance:** M1 for $\sqrt{48} = 4\sqrt{3}$ | **Total:** 2
**(ii)** common denominator $= (5 - \sqrt{2})(5 + \sqrt{2}) = 23$; numerator $= 10$ | **Marks:** M1, A1, B1 | **Guidance:** allow M1A1 for $\frac{5 - \sqrt{2}}{23} + \frac{5 + \sqrt{2}}{23}$; allow 3 only for 10/23 | **Total:** 3
**Total for Question 8:** 58 (i) Write $\sqrt { 48 } + \sqrt { 3 }$ in the form $a \sqrt { b }$, where $a$ and $b$ are integers and $b$ is as small as possible.\\
(ii) Simplify $\frac { 1 } { 5 + \sqrt { 2 } } + \frac { 1 } { 5 - \sqrt { 2 } }$.
\hfill \mbox{\textit{OCR MEI C1 2008 Q8 [5]}}