| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2007 |
| Session | June |
| 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 surds by factoring out perfect squares, and rationalizing a denominator by multiplying by the conjugate. Both parts are standard textbook exercises requiring only routine application of well-practiced techniques with no problem-solving or insight needed. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \(\sqrt{98} = 7\sqrt{2}\), \(\sqrt{50} = 5\sqrt{2}\) | M1 | Either surd simplified |
| \(\sqrt{98} - \sqrt{50} = 2\sqrt{2}\) | A1 | Correct answer |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{6\sqrt{5}}{2+\sqrt{5}} \times \frac{2-\sqrt{5}}{2-\sqrt{5}}\) | M1 | Multiply by conjugate |
| \(= \frac{12\sqrt{5} - 6\times5}{4-5}\) | M1 | Expand numerator and denominator |
| \(= \frac{12\sqrt{5}-30}{-1}\) | A1 | Correct numerator/denominator |
| \(= 30 - 12\sqrt{5}\) | A1 | \(a=30\), \(b=-12\) |
## Question 8:
**(i)**
$\sqrt{98} = 7\sqrt{2}$, $\sqrt{50} = 5\sqrt{2}$ | M1 | Either surd simplified
$\sqrt{98} - \sqrt{50} = 2\sqrt{2}$ | A1 | Correct answer
**(ii)**
$\frac{6\sqrt{5}}{2+\sqrt{5}} \times \frac{2-\sqrt{5}}{2-\sqrt{5}}$ | M1 | Multiply by conjugate
$= \frac{12\sqrt{5} - 6\times5}{4-5}$ | M1 | Expand numerator and denominator
$= \frac{12\sqrt{5}-30}{-1}$ | A1 | Correct numerator/denominator
$= 30 - 12\sqrt{5}$ | A1 | $a=30$, $b=-12$
---8 (i) Simplify $\sqrt { 98 } - \sqrt { 50 }$.\\
(ii) Express $\frac { 6 \sqrt { 5 } } { 2 + \sqrt { 5 } }$ in the form $a + b \sqrt { 5 }$, where $a$ and $b$ are integers.
\hfill \mbox{\textit{OCR MEI C1 2007 Q8 [5]}}