| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Expand and simplify surd expressions |
| Difficulty | Moderate -0.8 Part (a) is a straightforward expansion of a binomial with a surd requiring only FOIL and simplification. Part (b) involves rationalizing denominators and adding fractions, which is slightly more demanding but still a standard C1 technique with clear steps. Both parts are routine exercises testing basic surd manipulation without requiring problem-solving insight. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \((2+\sqrt{3})^2 = 4 + 2 \cdot 2\cdot\sqrt{3} + 3 = 7 + 4\sqrt{3}\) | M1 A1 | Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{x-\sqrt{y}} + \frac{1}{x+\sqrt{y}} = \frac{x+\sqrt{y}+x-\sqrt{y}}{(x-\sqrt{y})(x+\sqrt{y})} = \frac{2x}{x^2-y}\) | M1 A1 | |
| If \(x\) and \(y\) are integers then this is a fraction (not necessarily reduced to lowest terms) | E1 | Statement. Total: 3 |
# Question 7:
## Part (a):
$(2+\sqrt{3})^2 = 4 + 2 \cdot 2\cdot\sqrt{3} + 3 = 7 + 4\sqrt{3}$ | M1 A1 | **Total: 2**
## Part (b):
$\frac{1}{x-\sqrt{y}} + \frac{1}{x+\sqrt{y}} = \frac{x+\sqrt{y}+x-\sqrt{y}}{(x-\sqrt{y})(x+\sqrt{y})} = \frac{2x}{x^2-y}$ | M1 A1 |
If $x$ and $y$ are integers then this is a fraction (not necessarily reduced to lowest terms) | E1 | Statement. **Total: 3**
---7
\begin{enumerate}[label=(\alph*)]
\item Express $( 2 + \sqrt { 3 } ) ^ { 2 }$ in the form $a + b \sqrt { 3 }$ where $a$ and $b$ are integers to be determined.
\item Given that $x$ and $y$ are integers, prove that $\frac { 1 } { x - \sqrt { y } } + \frac { 1 } { x + \sqrt { y } }$ can be written in the form $\frac { p } { q }$ where $p$ and $q$ are both integers.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q7 [5]}}