| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Easy -1.2 Part (a) is trivial application of index laws (squaring removes the square root). Part (b) is a standard rationalizing-the-denominator exercise requiring multiplication by the conjugate—routine technique with no problem-solving required. Both are textbook drill questions worth only 4 marks total, significantly easier than average A-level questions. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(4x\) | B1 | Accept alternatives such as \(x4, 4\times x, x\times 4\) |
| (b) \(\frac{10-7+2\sqrt{7}-5\sqrt{7}}{-3}\) | M1, A1 | For multiplying numerator and denominator by \(2-\sqrt{7}\) and attempting to expand the brackets. There is no requirement to get the expanded numerator or denominator correct—seeing the brackets removed is sufficient. |
| \(-1+\sqrt{7}\) | A1 | All four terms correct (unsimplified) on the numerator OR the correct denominator of -3. Accept \(\sqrt{7}-1, -1+1\sqrt{7}\) and other fully correct simplified forms |
| (4 marks) |
(a) $4x$ | B1 | Accept alternatives such as $x4, 4\times x, x\times 4$
(b) $\frac{10-7+2\sqrt{7}-5\sqrt{7}}{-3}$ | M1, A1 | For multiplying numerator and denominator by $2-\sqrt{7}$ and attempting to expand the brackets. There is no requirement to get the expanded numerator or denominator correct—seeing the brackets removed is sufficient.
$-1+\sqrt{7}$ | A1 | All four terms correct (unsimplified) on the numerator OR the correct denominator of -3. Accept $\sqrt{7}-1, -1+1\sqrt{7}$ and other fully correct simplified forms
| | **(4 marks)**
---Simplify fully
\begin{enumerate}[label=(\alph*)]
\item $(2\sqrt{x})^2$ [1]
\item $\frac{5 + \sqrt{7}}{2 + \sqrt{7}}$ [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2014 Q1 [4]}}