OCR C3 — Question 3 7 marks

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicModulus function
TypeTransformations of modulus graphs from given f(x) sketch
DifficultyStandard +0.3 This is a standard C3 transformations question requiring students to apply well-rehearsed rules: reflecting negative parts for |f(x)|, horizontal scaling and vertical stretching for 3f(2x), and identifying translations for part (b). The transformations are routine textbook exercises with no novel problem-solving required, making it slightly easier than average.
Spec1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations

3. \includegraphics[max width=\textwidth, alt={}, center]{14ec6709-e1cb-42d7-af99-91365e50e4fc-1_535_810_877_406} The diagram shows the curve \(y = \mathrm { f } ( x )\) which has a maximum point at \(( - 3,2 )\) and a minimum point at \(( 2 , - 4 )\).
  1. Showing the coordinates of any stationary points, sketch on separate diagrams the graphs of
    1. \(y = | \mathrm { f } ( x ) |\),
    2. \(y = 3 \mathrm { f } ( 2 x )\).
  2. Write down the values of the constants \(a\) and \(b\) such that the curve with equation \(y = a + \mathrm { f } ( x + b )\) has a minimum point at the origin \(O\).

3.\\
\includegraphics[max width=\textwidth, alt={}, center]{14ec6709-e1cb-42d7-af99-91365e50e4fc-1_535_810_877_406}

The diagram shows the curve $y = \mathrm { f } ( x )$ which has a maximum point at $( - 3,2 )$ and a minimum point at $( 2 , - 4 )$.
\begin{enumerate}[label=(\alph*)]
\item Showing the coordinates of any stationary points, sketch on separate diagrams the graphs of
\begin{enumerate}[label=(\roman*)]
\item $y = | \mathrm { f } ( x ) |$,
\item $y = 3 \mathrm { f } ( 2 x )$.
\end{enumerate}\item Write down the values of the constants $a$ and $b$ such that the curve with equation $y = a + \mathrm { f } ( x + b )$ has a minimum point at the origin $O$.
\end{enumerate}

\hfill \mbox{\textit{OCR C3  Q3 [7]}}