| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2011 |
| Session | June |
| Marks | 6 |
| Topic | Indices and Surds |
| Type | Show surd expression equals value |
| Difficulty | Easy -1.2 This question tests basic algebraic manipulation of surds through routine techniques. Part (i) is straightforward expansion of a binomial with surds (2 marks), and part (ii) is a standard rationalizing-the-denominator exercise requiring multiplication by the conjugate. Both are textbook exercises with no problem-solving element, making this easier than average A-level content. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| Attempt to multiply out brackets | M1 | |
| Obtain \(61 - 28\sqrt{3}\) | A1 | [2] |
| Answer | Marks | Guidance |
|---|---|---|
| \(\sqrt{125} = 5\sqrt{5}\) seen | B1 | |
| Multiply numerator and denominator by \(2 - \sqrt{5}\), and expand | M1 | |
| Use of \((2 + \sqrt{5})(2 - \sqrt{5}) = -1\) | A1 | |
| Obtain \(25 - 10\sqrt{5}\) | A1 | [4] |
**Part (i)**
Attempt to multiply out brackets | M1
Obtain $61 - 28\sqrt{3}$ | A1 | [2]
*SC: For answer given without working – B1*
**Part (ii)**
$\sqrt{125} = 5\sqrt{5}$ seen | B1
Multiply numerator and denominator by $2 - \sqrt{5}$, and expand | M1
Use of $(2 + \sqrt{5})(2 - \sqrt{5}) = -1$ | A1
Obtain $25 - 10\sqrt{5}$ | A1 | [4]\begin{enumerate}[label=(\roman*)]
\item Expand and simplify $(7 - 2\sqrt{3})^2$. [2]
\item Show that
$$\frac{\sqrt{125}}{2 + \sqrt{5}} = 25 - 10\sqrt{5}.$$ [4]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2011 Q2 [6]}}