| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Moderate -0.8 This is a straightforward surds question testing basic algebraic manipulation: part (a) requires simple expansion of brackets, and part (b) requires rationalizing the denominator—both standard C1 techniques with no problem-solving insight needed. Easier than average but not trivial since part (b) involves multiple steps. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
Given that $(2 + \sqrt{7})(4 - \sqrt{7}) = a + b\sqrt{7}$, where $a$ and $b$ are integers,
\begin{enumerate}[label=(\alph*)]
\item find the value of $a$ and the value of $b$. [2]
\end{enumerate}
Given that $\frac{2 + \sqrt{7}}{4 + \sqrt{7}} = c + d\sqrt{7}$ where $c$ and $d$ are rational numbers,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the value of $c$ and the value of $d$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q2 [5]}}