AQA C1 2006 June — Question 4 6 marks

Exam BoardAQA
ModuleC1 (Core Mathematics 1)
Year2006
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndices and Surds
TypeExpand and simplify surd expressions
DifficultyEasy -1.2 This is a straightforward surd manipulation question requiring only routine algebraic expansion and simplification. Part (a) involves basic FOIL expansion with surds, and part (b) requires recognizing that √75 = 5√3 and √27 = 3√3, then simplifying—both are standard textbook exercises with no problem-solving insight needed.
Spec1.02b Surds: manipulation and rationalising denominators

4
  1. Express \(( 4 \sqrt { 5 } - 1 ) ( \sqrt { 5 } + 3 )\) in the form \(p + q \sqrt { 5 }\), where \(p\) and \(q\) are integers.
  2. Show that \(\frac { \sqrt { 75 } - \sqrt { 27 } } { \sqrt { 3 } }\) is an integer and find its value.

4
\begin{enumerate}[label=(\alph*)]
\item Express $( 4 \sqrt { 5 } - 1 ) ( \sqrt { 5 } + 3 )$ in the form $p + q \sqrt { 5 }$, where $p$ and $q$ are integers.
\item Show that $\frac { \sqrt { 75 } - \sqrt { 27 } } { \sqrt { 3 } }$ is an integer and find its value.
\end{enumerate}

\hfill \mbox{\textit{AQA C1 2006 Q4 [6]}}