| Exam Board | AQA |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Simplify numerical surds |
| Difficulty | Easy -1.3 This is a straightforward surd manipulation question requiring only basic rules: simplifying √12 = 2√3, multiplying/dividing surds, and expanding a binomial. All parts are routine C1 exercises with no problem-solving element, making it easier than average but not trivial since students must correctly apply multiple surd rules. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \(xy = 6\) | B1 | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{y}{x} = \frac{2\sqrt{3}}{\sqrt{3}}\) or \(\sqrt{\frac{12}{3}}\) or \(\sqrt{\frac{4}{1}}\) or \(\frac{\sqrt{12}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = 2\) | M1 | |
| A1 | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| \(x^2 + 2xy + y^2\) or \((\sqrt{3} + 2\sqrt{3})^2\) correct | M1 | |
| Correct with 2 of \(x^2, y^2, 2xy\) simplified | A1 | |
| \(3 + 2\sqrt{36} + 12\) or \(3^2 \times 3\) or \((\sqrt{3})^2 = 27\) | A1 | 3 |
**2(a)**
| $xy = 6$ | B1 | 1 | B0 for $\sqrt{36}$ or $\pm 6$ |
**2(b)**
| $\frac{y}{x} = \frac{2\sqrt{3}}{\sqrt{3}}$ or $\sqrt{\frac{12}{3}}$ or $\sqrt{\frac{4}{1}}$ or $\frac{\sqrt{12}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = 2$ | M1 | | Allow M1 for $\pm 2$ |
| | A1 | 2 | |
**2(c)**
| $x^2 + 2xy + y^2$ or $(\sqrt{3} + 2\sqrt{3})^2$ correct | M1 | |
| Correct with 2 of $x^2, y^2, 2xy$ simplified | A1 | |
| $3 + 2\sqrt{36} + 12$ or $3^2 \times 3$ or $(\sqrt{3})^2 = 27$ | A1 | 3 | or $(\sqrt{3} + \sqrt{12})(\sqrt{3} + \sqrt{12})$ expanded as 4 terms – no more than one slip Correct but unsimplified – one more step |
---2 It is given that $x = \sqrt { 3 }$ and $y = \sqrt { 12 }$.\\
Find, in the simplest form, the value of:
\begin{enumerate}[label=(\alph*)]
\item $x y$;
\item $\frac { y } { x }$;
\item $( x + y ) ^ { 2 }$.
\end{enumerate}
\hfill \mbox{\textit{AQA C1 2008 Q2 [6]}}