| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2021 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Forward transformation (single point, multiple transformations) |
| Difficulty | Easy -1.2 This is a straightforward recall and application question testing basic function transformations and gradient function interpretation. Part (a) requires direct application of standard transformation rules (vertical shift, horizontal stretch/shift, inverse function), while part (b) involves reading information from a derivative graph using well-rehearsed connections (stationary points where g'=0, decreasing where g'<0, inflection where g' has turning points). All parts are routine textbook exercises with no problem-solving or novel insight required. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence1.02w Graph transformations: simple transformations of f(x)1.07a Derivative as gradient: of tangent to curve1.07f Convexity/concavity: points of inflection1.07n Stationary points: find maxima, minima using derivatives1.07o Increasing/decreasing: functions using sign of dy/dx |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| (i) \((2, 9)\) | B1 | Correct coordinate; and no others |
| (ii) \((1, 12)\) | B1 | Correct \(x\)-coordinate; if more than one solution given award B1 if either coordinate is consistent in all solutions |
| B1 | Correct \(y\)-coordinate | |
| (iii) \((6, 2)\) | B1 | Correct coordinate; and no others |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| (i) \(x = -2,\ x = 4\) | B1 | Both \(x\)-coordinates correct and no others; ignore any attempt at \(y\) values |
| (ii) \(x < -2\) | B1 | Correct inequality and no others; allow \(\leq\); could be written in set notation |
| (iii) \(x = 4\) | B1 | Correct \(x\)-coordinate and no others; ignore any attempt at \(y\) values |
# Question 5:
## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| (i) $(2, 9)$ | B1 | Correct coordinate; and no others |
| (ii) $(1, 12)$ | B1 | Correct $x$-coordinate; if more than one solution given award B1 if either coordinate is consistent in all solutions |
| | B1 | Correct $y$-coordinate |
| (iii) $(6, 2)$ | B1 | Correct coordinate; and no others |
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| (i) $x = -2,\ x = 4$ | B1 | Both $x$-coordinates correct and no others; ignore any attempt at $y$ values |
| (ii) $x < -2$ | B1 | Correct inequality and no others; allow $\leq$; could be written in set notation |
| (iii) $x = 4$ | B1 | Correct $x$-coordinate and no others; ignore any attempt at $y$ values |
---5
\begin{enumerate}[label=(\alph*)]
\item The graph of the function $y = \mathrm { f } ( x )$ passes through the point $P$ with coordinates (2, 6), and is a one-one function. State the coordinates of the point corresponding to $P$ on each of the following curves.
\begin{enumerate}[label=(\roman*)]
\item $\quad y = \mathrm { f } ( x ) + 3$
\item $\quad y = 2 \mathrm { f } ( 3 x - 1 )$
\item $y = \mathrm { f } ^ { - 1 } ( x )$
\end{enumerate}\item \\
\includegraphics[max width=\textwidth, alt={}, center]{6b766f5c-8533-4e0c-bb10-0d9949dc777b-5_494_739_806_333}
The diagram shows part of the graph of $y = \mathrm { g } ^ { \prime } ( x )$. This is the graph of the gradient function of $y = \mathrm { g } ( x )$. The graph intersects the $x$-axis at $x = - 2$ and $x = 4$.
\begin{enumerate}[label=(\roman*)]
\item State the $x$-coordinate of any stationary points on the graph of $y = \mathrm { g } ( x )$.
\item State the set of values of $x$ for which $y = \mathrm { g } ( x )$ is a decreasing function.
\item State the $x$-coordinate of any points of inflection on the graph of $y = \mathrm { g } ( x )$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2021 Q5 [7]}}