| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| 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 two basic surd techniques: rationalizing a denominator by multiplying by the conjugate, and expanding a binomial with a surd. Both are standard textbook exercises requiring only direct application of learned procedures with no problem-solving or insight needed. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{5-\sqrt{3}}{22}\) or \(\frac{5+(-1)\sqrt{3}}{22}\) or \(\frac{5-1\sqrt{3}}{22}\) | 2 | or \(a=5\), \(b=-1\), \(c=22\); M1 for attempt to multiply numerator and denominator by \(5-\sqrt{3}\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(37 - 12\sqrt{7}\) | 3 | 2 for 37 and 1 for \(-12\sqrt{7}\) or M1 for 3 correct terms from \(9 - 6\sqrt{7} - 6\sqrt{7} + 28\) or \(9 - 3\sqrt{28} - 3\sqrt{28} + 28\) or \(9 - \sqrt{252} - \sqrt{252} + 28\); 3 for \(37 - \sqrt{1008}\) but not other equivs |
# Question 7:
## Part (i)
| $\frac{5-\sqrt{3}}{22}$ or $\frac{5+(-1)\sqrt{3}}{22}$ or $\frac{5-1\sqrt{3}}{22}$ | 2 | or $a=5$, $b=-1$, $c=22$; M1 for attempt to multiply numerator and denominator by $5-\sqrt{3}$ |
## Part (ii)
| $37 - 12\sqrt{7}$ | 3 | 2 for 37 and 1 for $-12\sqrt{7}$ or M1 for 3 correct terms from $9 - 6\sqrt{7} - 6\sqrt{7} + 28$ or $9 - 3\sqrt{28} - 3\sqrt{28} + 28$ or $9 - \sqrt{252} - \sqrt{252} + 28$; 3 for $37 - \sqrt{1008}$ but not other equivs |
---7 (i) Express $\frac { 1 } { 5 + \sqrt { 3 } }$ in the form $\frac { a + b \sqrt { 3 } } { c }$, where $a , b$ and $c$ are integers.\\
(ii) Expand and simplify $( 3 - 2 \sqrt { 7 } ) ^ { 2 }$.
\hfill \mbox{\textit{OCR MEI C1 2008 Q7 [5]}}