| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| 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 This is a straightforward two-part question testing basic surd manipulation. Part (a) requires simple squaring of a surd expression, while part (b) is a standard rationalizing the denominator exercise using conjugates. Both are routine textbook exercises requiring only direct application of learned techniques with no problem-solving or insight needed. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | \(4x\) | B1 |
| (b) | \(\frac{10-7+2\sqrt{7}-5\sqrt{7}}{-3}\) | M1, A1 |
| \(-1+\sqrt{7}\) | A1 | All four terms correct (unsimplified) on the numerator OR the correct denominator of \(-3\). Correct answer \(-1+\sqrt{7}\). Accept \(\sqrt{7}-1\), \(-1+1\sqrt{7}\) and other fully correct simplified forms. |
(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 $-3$. Correct answer $-1+\sqrt{7}$. Accept $\sqrt{7}-1$, $-1+1\sqrt{7}$ and other fully correct simplified forms.
---\begin{enumerate}
\item Simplify fully\\
(a) $( 2 \sqrt { } x ) ^ { 2 }$\\
(b) $\frac { 5 + \sqrt { 7 } } { 2 + \sqrt { 7 } }$\\
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2014 Q1 [4]}}