| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Transformations of functions |
| Difficulty | Moderate -0.8 Part (i) is a straightforward algebraic verification requiring substitution of -x and simplification to show f(-x) = -f(x), which is routine recall. Part (ii) tests understanding of odd function symmetry (rotational symmetry about origin) but requires only graphical reflection, not calculation. Both parts are below average difficulty for C3, involving standard definitions with minimal problem-solving. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping) |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (i) | 2(x) |
| Answer | Marks |
|---|---|
| 1x2 | MM11 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | substitutin –x for x in f(x) | |
| (ii) | 4 1 1 4 | M1 |
| Answer | Marks |
|---|---|
| [2] | Recognisable attempt at a half turn rotation about O |
Question 1:
1 | (i) | 2(x)
f(x)
1(x)2
2x
f(x)
1x2 | MM11
A1
[2] | substitutin –x for x in f(x)
(ii) | 4 1 1 4 | M1
A1
[2] | Recognisable attempt at a half turn rotation about O
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.\begin{enumerate}[label=(\roman*)]
\item Show algebraically that the function $\text{f}(x) = \frac{2x}{1-x^2}$ is odd. [2]
Fig. 7 shows the curve $y = \text{f}(x)$ for $0 \leq x < 4$, together with the asymptote $x = 1$.
\includegraphics{figure_7}
\item Use the copy of Fig. 7 to complete the curve for $-4 \leq x \leq 4$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 Q1 [4]}}