| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2008 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Determine if inverse exists |
| Difficulty | Moderate -0.8 This question tests basic definitions and recognition of even/odd functions through straightforward substitution. Part (i) requires recall of standard definitions, while part (ii) involves routine checking of f(-x) vs f(x) for three functions with no complex algebraic manipulation needed. This is simpler than average A-level questions which typically require multi-step problem-solving. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping) |
3
\begin{enumerate}[label=(\roman*)]
\item State the algebraic condition for the function $\mathrm { f } ( x )$ to be an even function.\\
What geometrical property does the graph of an even function have?
\item State whether the following functions are odd, even or neither.\\
(A) $\mathrm { f } ( x ) = x ^ { 2 } - 3$\\
(B) $\mathrm { g } ( x ) = \sin x + \cos x$\\
(C) $\mathrm { h } ( x ) = \frac { 1 } { x + x ^ { 3 } }$
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 2008 Q3 [5]}}