| Exam Board | AQA |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Easy -1.2 Part (a) is trivial recall of index laws. Part (b) is a standard rationalizing denominator exercise requiring multiplication by conjugate and simplification—routine C1 technique with no problem-solving insight needed, though the algebra requires care. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \(27\) | B1 | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{4\sqrt{3} + 3\sqrt{7}}{3\sqrt{3} + \sqrt{7}} \times \frac{3\sqrt{3} - \sqrt{7}}{3\sqrt{3} - \sqrt{7}}\) | M1 | |
| (Numerator =) \(36 + 9\sqrt{21} - 4\sqrt{21} - 21\) | m1 | expanding numerator condone one slip or omission |
| (Denominator =) \(20\) | B1 | must be seen as denominator |
| \(\frac{15 + 5\sqrt{21}}{20}\) | ||
| \(= \frac{3 + \sqrt{21}}{4}\) | A1cso | \(m = 3, n = 4\) condone \(\frac{3}{4} + \frac{\sqrt{21}}{4}\) |
**2(a)**
$27$ | B1 | 1
**2(b)**
$\frac{4\sqrt{3} + 3\sqrt{7}}{3\sqrt{3} + \sqrt{7}} \times \frac{3\sqrt{3} - \sqrt{7}}{3\sqrt{3} - \sqrt{7}}$ | M1 |
(Numerator =) $36 + 9\sqrt{21} - 4\sqrt{21} - 21$ | m1 | expanding numerator condone one slip or omission
(Denominator =) $20$ | B1 | must be seen as denominator
$\frac{15 + 5\sqrt{21}}{20}$ | |
$= \frac{3 + \sqrt{21}}{4}$ | A1cso | $m = 3, n = 4$ condone $\frac{3}{4} + \frac{\sqrt{21}}{4}$ | 4
---2
\begin{enumerate}[label=(\alph*)]
\item Simplify $( 3 \sqrt { 3 } ) ^ { 2 }$.
\item Express $\frac { 4 \sqrt { 3 } + 3 \sqrt { 7 } } { 3 \sqrt { 3 } + \sqrt { 7 } }$ in the form $\frac { m + \sqrt { 21 } } { n }$, where $m$ and $n$ are integers.
\end{enumerate}
\hfill \mbox{\textit{AQA C1 2011 Q2 [5]}}