| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2022 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Multiple choice transformation |
| Difficulty | Moderate -0.8 Part (a) requires visual identification of function types from graphs using standard definitions (one-one, many-one, inverse), which is straightforward recall and pattern recognition. Part (b) is a routine exercise finding the range of 1/x over a restricted domain, requiring only substitution of endpoints. Both parts are below average difficulty 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 existence |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Table with rows 1–5: Row 1: Many-one \(\checkmark\); Row 2: Not a function \(\checkmark\); Row 3: One-one \(\checkmark\), Own inverse \(\checkmark\); Row 4: One-one \(\checkmark\); Row 5: Many-one \(\checkmark\) | B4 | B4 for all 5 rows correct; B3 for 3 or 4 rows correct; B2 for 2 rows correct; B1 for 1 row correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\geq\frac{1}{2}\) | B1 | \(\geq\frac{1}{2}\) soi, no top limit (except \(\infty\)). Allow \(>\frac{1}{2}\). Allow \(f(x)\) or \(\frac{1}{x}\) or any letter or none for 1st B1 |
# Question 6:
## Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Table with rows 1–5: Row 1: Many-one $\checkmark$; Row 2: Not a function $\checkmark$; Row 3: One-one $\checkmark$, Own inverse $\checkmark$; Row 4: One-one $\checkmark$; Row 5: Many-one $\checkmark$ | B4 | B4 for all 5 rows correct; B3 for 3 or 4 rows correct; B2 for 2 rows correct; B1 for 1 row correct |
## Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\geq\frac{1}{2}$ | B1 | $\geq\frac{1}{2}$ soi, no top limit (except $\infty$). Allow $>\frac{1}{2}$. Allow $f(x)$ or $\frac{1}{x}$ or any letter or none for 1st B1 |6
\begin{enumerate}[label=(\alph*)]
\item The diagrams show five different graphs. In each case the whole of the graph is shown.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{cb83836f-753f-4b3a-99e8-a18aff0f49ff-06_376_382_310_306}
\captionsetup{labelformat=empty}
\caption{Fig. 1.1}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{cb83836f-753f-4b3a-99e8-a18aff0f49ff-06_376_378_310_842}
\captionsetup{labelformat=empty}
\caption{Fig. 1.2}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{cb83836f-753f-4b3a-99e8-a18aff0f49ff-06_378_378_310_1379}
\captionsetup{labelformat=empty}
\caption{Fig. 1.3}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{cb83836f-753f-4b3a-99e8-a18aff0f49ff-06_378_382_872_306}
\captionsetup{labelformat=empty}
\caption{Fig. 1.4}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{cb83836f-753f-4b3a-99e8-a18aff0f49ff-06_378_378_872_845}
\captionsetup{labelformat=empty}
\caption{Fig. 1.5}
\end{center}
\end{figure}
Place ticks in the boxes in the table in the Printed Answer Booklet to indicate, for each graph, whether it represents a one-one function, a many-one function, a function that is its own inverse or it does not represent a function. There may be more than one tick in some rows or columns of the table.
\item A function f is defined by $\mathrm { f } ( x ) = \frac { 1 } { x }$ for the domain $\{ x : 0 < x \leqslant 2 \}$.
State the range of f , giving your answer in set notation.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2022 Q6 [6]}}