| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2016 |
| 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 |
|---|---|---|
| \(11\sqrt{2}\) | M1 for \([\sqrt{50}=]5\sqrt{2}\) or \([3\sqrt{8}=]6\sqrt{2}\) | [2] |
| Answer | Marks | Guidance |
|---|---|---|
| attempting to multiply numerator and denominator by \(4+\sqrt{3}\) | M1 | |
| \(2+\sqrt{3}\) or \(2+1\sqrt{3}\) or \(c=2\) and \(d=1\) | A2 | or B1 for denominator \(=13\) soi or numerator \(=26+13\sqrt{3}\) soi |
| or cross-multiplying by \(4-\sqrt{3}\) and forming a pair of simultaneous equations in \(c\) and \(d\), with at most one error | M1 | |
| \(c=2\) and \(d=1\) | A2 (A1 for one correct) | [3] |
# Question 5:
## Part (i)
$11\sqrt{2}$ | M1 for $[\sqrt{50}=]5\sqrt{2}$ or $[3\sqrt{8}=]6\sqrt{2}$ | [2]
## Part (ii)
attempting to multiply numerator and denominator by $4+\sqrt{3}$ | M1 |
$2+\sqrt{3}$ or $2+1\sqrt{3}$ or $c=2$ and $d=1$ | A2 | or **B1** for denominator $=13$ soi or numerator $=26+13\sqrt{3}$ soi
**or** cross-multiplying by $4-\sqrt{3}$ and forming a pair of simultaneous equations in $c$ and $d$, with at most one error | M1 |
$c=2$ and $d=1$ | A2 (**A1** for one correct) | [3]
---5 (i) Express $\sqrt { 50 } + 3 \sqrt { 8 }$ in the form $a \sqrt { b }$, where $a$ and $b$ are integers and $b$ is as small as possible.\\
(ii) Express $\frac { 5 + 2 \sqrt { 3 } } { 4 - \sqrt { 3 } }$ in the form $c + d \sqrt { 3 }$, where $c$ and $d$ are integers.
\hfill \mbox{\textit{OCR MEI C1 2016 Q5 [5]}}