| Exam Board | AQA |
|---|---|
| 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 -1.3 This is a straightforward C1 question testing basic surd manipulation: part (a) is simple squaring of a surd (routine recall), and part (b) requires standard rationalization of the denominator by multiplying by the conjugate, followed by simplification. All steps are textbook procedures with no problem-solving or insight required, making it easier than average. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(45\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\frac{\ast\ast+\sqrt{5}}{7+3\sqrt{5}} \times \frac{7-3\sqrt{5}}{7-3\sqrt{5}}\) | M1 | |
| Numerator \(= 315+7\sqrt{5}-135\sqrt{5}-15\) | A1 | At least this far |
| Denominator \(= 49+21\sqrt{5}-21\sqrt{5}-45 = 4\) | B1 | Must be seen as denominator |
| \(\frac{300-128\sqrt{5}}{4} = 75-32\sqrt{5}\) | A1cso |
## Question 2:
### Part (a)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $45$ | B1 | |
### Part (b)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{\ast\ast+\sqrt{5}}{7+3\sqrt{5}} \times \frac{7-3\sqrt{5}}{7-3\sqrt{5}}$ | M1 | |
| Numerator $= 315+7\sqrt{5}-135\sqrt{5}-15$ | A1 | At least this far |
| Denominator $= 49+21\sqrt{5}-21\sqrt{5}-45 = 4$ | B1 | Must be seen as denominator |
| $\frac{300-128\sqrt{5}}{4} = 75-32\sqrt{5}$ | A1cso | |
---2
\begin{enumerate}[label=(\alph*)]
\item Simplify $( 3 \sqrt { 5 } ) ^ { 2 }$.
\item Express $\frac { ( 3 \sqrt { 5 } ) ^ { 2 } + \sqrt { 5 } } { 7 + 3 \sqrt { 5 } }$ in the form $m + n \sqrt { 5 }$, where $m$ and $n$ are integers.\\[0pt]
[4 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA C1 2016 Q2 [5]}}