| Exam Board | AQA |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Simplify numerical surds |
| Difficulty | Easy -1.8 This is a very routine C1 question testing basic surd manipulation: part (a) is difference of two squares yielding 5-4=1, and part (b) requires simplifying surds to 2√2 + 3√2 = 5√2. Both are standard textbook exercises requiring only direct application of memorized techniques with no problem-solving. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \((\sqrt{5})^2 + 2\sqrt{5} - 2\sqrt{5} - 4 = 1\) | M1 | Multiplying out difference of two squares attempted |
| A1 | 2 | Full marks for correct answer/no working |
| Answer | Marks | Guidance |
|---|---|---|
| \(\sqrt{8} = 2\sqrt{2}\); \(\sqrt{18} = 3\sqrt{2}\) | M1 | Either correct |
| Answer \(= 5\sqrt{2}\) | A1 | 2 |
## 1(a)
$(\sqrt{5})^2 + 2\sqrt{5} - 2\sqrt{5} - 4 = 1$ | M1 | Multiplying out difference of two squares attempted
| A1 | 2 | Full marks for correct answer/no working
## 1(b)
$\sqrt{8} = 2\sqrt{2}$; $\sqrt{18} = 3\sqrt{2}$ | M1 | Either correct
Answer $= 5\sqrt{2}$ | A1 | 2 | Full marks for correct answer/no working
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\begin{enumerate}[label=(\alph*)]
\item Simplify $( \sqrt { 5 } + 2 ) ( \sqrt { 5 } - 2 )$.
\item Express $\sqrt { 8 } + \sqrt { 18 }$ in the form $n \sqrt { 2 }$, where $n$ is an integer.
\end{enumerate}
\hfill \mbox{\textit{AQA C1 2006 Q1 [4]}}