| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| 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 techniques: rationalizing a denominator by multiplying by the conjugate, and expanding a binomial with surds. Both parts 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 |
|---|---|---|
| \(\dfrac{5-\sqrt{3}}{22}\) or \(\dfrac{5+(-1)\sqrt{3}}{22}\) or \(\dfrac{5-1\sqrt{3}}{22}\) | 2 marks | Or \(a=5,\ b=-1,\ c=22\); M1 for attempt to multiply numerator and denominator by \(5 - \sqrt{3}\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(-12\sqrt{7}\) isw www | 3 marks | 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 \(9 - \sqrt{252} - \sqrt{252} + 28\) oe eg using \(2\sqrt{63}\); or M2 for \(9 - 12\sqrt{7} + 28\) or \(9 - 6\sqrt{28} + 28\) or \(9 - 2\sqrt{252} + 28\) or \(9 - \sqrt{1008} + 28\) oe; 3 for \(37 - \sqrt{1008}\) but not other equivs |
## Question 12:
**(i)**
$\dfrac{5-\sqrt{3}}{22}$ or $\dfrac{5+(-1)\sqrt{3}}{22}$ or $\dfrac{5-1\sqrt{3}}{22}$ | 2 marks | Or $a=5,\ b=-1,\ c=22$; M1 for attempt to multiply numerator and denominator by $5 - \sqrt{3}$
**(ii)**
$-12\sqrt{7}$ isw www | 3 marks | 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 $9 - \sqrt{252} - \sqrt{252} + 28$ oe eg using $2\sqrt{63}$; or M2 for $9 - 12\sqrt{7} + 28$ or $9 - 6\sqrt{28} + 28$ or $9 - 2\sqrt{252} + 28$ or $9 - \sqrt{1008} + 28$ oe; 3 for $37 - \sqrt{1008}$ but not other equivs
---12 (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 Q12 [5]}}