Edexcel C1 — Question 2 5 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndices and Surds
TypeRationalize denominator simple
DifficultyModerate -0.8 This is a straightforward C1 surds question requiring basic expansion and rationalizing the denominator. Part (a) is simple FOIL expansion, and part (b) is a standard rationalization technique. Both are routine textbook exercises with no problem-solving insight required, making it easier than average but not trivial since it requires careful algebraic manipulation.
Spec1.02b Surds: manipulation and rationalising denominators

Given that \((2 + \sqrt{7})(4 - \sqrt{7}) = a + b\sqrt{7}\), where \(a\) and \(b\) are integers,
  1. find the value of \(a\) and the value of \(b\). [2]
Given that \(\frac{2 + \sqrt{7}}{4 + \sqrt{7}} = c + d\sqrt{7}\) where \(c\) and \(d\) are rational numbers,
  1. find the value of \(c\) and the value of \(d\). [3]

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]}}