OCR C1 — Question 1 3 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSolving quadratics and applications
TypeAlgebraic identity, find constants
DifficultyModerate -0.8 This is a straightforward algebraic manipulation question requiring expansion of two squared brackets and collection of like terms. The substitution aspect (treating √x as a variable) is implicit and routine. It's easier than average as it's purely mechanical algebra with no problem-solving required, though slightly more involved than the most basic index law recall.
Spec1.02b Surds: manipulation and rationalising denominators1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

  1. \(\quad \mathrm { f } ( x ) = ( \sqrt { x } + 3 ) ^ { 2 } + ( 1 - 3 \sqrt { x } ) ^ { 2 }\).
Show that \(\mathrm { f } ( x )\) can be written in the form \(a x + b\) where \(a\) and \(b\) are integers to be found.

\begin{enumerate}
  \item $\quad \mathrm { f } ( x ) = ( \sqrt { x } + 3 ) ^ { 2 } + ( 1 - 3 \sqrt { x } ) ^ { 2 }$.
\end{enumerate}

Show that $\mathrm { f } ( x )$ can be written in the form $a x + b$ where $a$ and $b$ are integers to be found.\\

\hfill \mbox{\textit{OCR C1  Q1 [3]}}