| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2013 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Modulus function transformations |
| Difficulty | Moderate -0.8 Part (i) requires straightforward substitution of -x and algebraic manipulation to show f(-x) = -f(x), which is a standard definition check. Part (ii) involves sketching the reflection of a given curve using odd function symmetry (rotational symmetry about origin), which is a routine application of function properties with no problem-solving required. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02u Functions: definition and vocabulary (domain, range, mapping) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(f(-x) = \frac{2(-x)}{1-(-x)^2}\) | M1 | substituting \(-x\) for \(x\) in \(f(x)\) |
| \(= -\frac{2x}{1-x^2} = -f(x)\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| [Graph showing half-turn rotational symmetry about O] | M1 | Recognisable attempt at a half turn rotation about O |
| A1 | Good curve starting from \(x = -4\), asymptote \(x = -1\) shown on graph. (Need not state \(-4\) and \(-1\) explicitly as long as graph is reasonably to scale.) Condone if curve starts to the left of \(x = -4\). |
## Question 7:
### Part (i):
| Answer | Mark | Guidance |
|--------|------|----------|
| $f(-x) = \frac{2(-x)}{1-(-x)^2}$ | M1 | substituting $-x$ for $x$ in $f(x)$ |
| $= -\frac{2x}{1-x^2} = -f(x)$ | A1 | |
### Part (ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| [Graph showing half-turn rotational symmetry about O] | M1 | Recognisable attempt at a half turn rotation about O |
| | A1 | Good curve starting from $x = -4$, asymptote $x = -1$ shown on graph. (Need not state $-4$ and $-1$ explicitly as long as graph is reasonably to scale.) Condone if curve starts to the left of $x = -4$. |
---7 (i) Show algebraically that the function $\mathrm { f } ( x ) = \frac { 2 x } { 1 - x ^ { 2 } }$ is odd.
Fig. 7 shows the curve $y = \mathrm { f } ( x )$ for $0 \leqslant x \leqslant 4$, together with the asymptote $x = 1$.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{28ce1bcc-e9d5-4ae6-98c0-67b5b8c50bc6-4_730_817_431_607}
\captionsetup{labelformat=empty}
\caption{Fig. 7}
\end{center}
\end{figure}
(ii) Use the copy of Fig. 7 to complete the curve for $- 4 \leqslant x \leqslant 4$.
\hfill \mbox{\textit{OCR MEI C3 2013 Q7 [4]}}