| Exam Board | AQA |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Easy -1.2 This is a routine C1 surds question requiring standard techniques: simplifying surds (√8 = 2√2), rationalizing simple denominators, and multiplying by conjugates. Both parts follow textbook procedures with no problem-solving insight needed, making it easier than average but not trivial due to the algebraic manipulation required in part (b). |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \(5\sqrt{8} = 10\sqrt{2}\) \(\frac{6}{\sqrt{2}} = \frac{6\sqrt{2}}{2}\) (\(= 3\sqrt{2}\)) Answer \(= 13\sqrt{2}\) | B1, M1, A1 | Or \(\frac{5\sqrt{16+6}}{\sqrt{2}}\) gets B1; then M1 for rationalising; and A1 answer \(n = 13\) |
| 3 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{\sqrt{2}+2}{3\sqrt{2}-4} \cdot \frac{3\sqrt{2}+4}{3\sqrt{2}+4}\) Numerator \(= 6 + 6\sqrt{2} + 4\sqrt{2} + 8\) Denominator \(= 18 - 16\) (\(= 2\)) Final answer \(= 5\sqrt{2} + 7\) | M1, m1, B1, A1 | Multiplying top & bottom by \(\pm(3\sqrt{2}+4)\); Multiplying out (condone one slip); CSO; AG |
| 4 | ||
| 7 |
## Part (a)
$5\sqrt{8} = 10\sqrt{2}$ $\frac{6}{\sqrt{2}} = \frac{6\sqrt{2}}{2}$ ($= 3\sqrt{2}$) Answer $= 13\sqrt{2}$ | B1, M1, A1 | Or $\frac{5\sqrt{16+6}}{\sqrt{2}}$ gets B1; then M1 for rationalising; and A1 answer $n = 13$
| | 3 |
## Part (b)
$\frac{\sqrt{2}+2}{3\sqrt{2}-4} \cdot \frac{3\sqrt{2}+4}{3\sqrt{2}+4}$ Numerator $= 6 + 6\sqrt{2} + 4\sqrt{2} + 8$ Denominator $= 18 - 16$ ($= 2$) Final answer $= 5\sqrt{2} + 7$ | M1, m1, B1, A1 | Multiplying top & bottom by $\pm(3\sqrt{2}+4)$; Multiplying out (condone one slip); CSO; AG
| | 4 |
| | 7 |
---3
\begin{enumerate}[label=(\alph*)]
\item Express $5 \sqrt { 8 } + \frac { 6 } { \sqrt { 2 } }$ in the form $n \sqrt { 2 }$, where $n$ is an integer.
\item Express $\frac { \sqrt { 2 } + 2 } { 3 \sqrt { 2 } - 4 }$ in the form $c \sqrt { 2 } + d$, where $c$ and $d$ are integers.
\end{enumerate}
\hfill \mbox{\textit{AQA C1 2008 Q3 [7]}}