| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Multiple transformations in sequence |
| Difficulty | Moderate -0.8 This question tests standard transformations of trigonometric functions with straightforward recall and application. Part (i) requires knowing that cos(2x) has period 180°, part (ii) involves identifying a horizontal stretch factor 1/2 and vertical translation +1, and part (iii) is routine sketching. All components are textbook exercises requiring minimal problem-solving or insight. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.05f Trigonometric function graphs: symmetries and periodicities |
| Answer | Marks | Guidance |
|---|---|---|
| Period \(180°\) | B1 [1] | Condone \(0 \leq x \leq 180°\) or \(\pi\) |
| Answer | Marks | Guidance |
|---|---|---|
| One-way stretch in \(x\)-direction, scale factor \(\frac{1}{2}\) | M1, A1 | Either way round; condone 'squeeze', 'contract' for M1; stretch used and s.f. \(\frac{1}{2}\) |
| Translation in \(y\)-direction through \(\begin{pmatrix}0\\1\end{pmatrix}\) | M1, A1 [4] | Condone 'move', 'shift' etc for M1; 'translation' used, \(+1\) unit; \(\begin{pmatrix}0\\1\end{pmatrix}\) only is M1 A0 |
| Answer | Marks | Guidance |
|---|---|---|
| Correct shape, touching \(x\)-axis at \(-90°\), \(90°\) | M1 | Correct shape, touching \(x\)-axis at \(-90°\), \(90°\) |
| Correct domain | B1 | |
| \((0, 2)\) marked or indicated (amplitude is 2) | A1 [3] |
## Question 4:
**(i)**
| Period $180°$ | B1 [1] | Condone $0 \leq x \leq 180°$ or $\pi$ |
|---|---|---|
**(ii)**
| One-way stretch in $x$-direction, scale factor $\frac{1}{2}$ | M1, A1 | Either way round; condone 'squeeze', 'contract' for M1; stretch used and s.f. $\frac{1}{2}$ |
|---|---|---|
| Translation in $y$-direction through $\begin{pmatrix}0\\1\end{pmatrix}$ | M1, A1 [4] | Condone 'move', 'shift' etc for M1; 'translation' used, $+1$ unit; $\begin{pmatrix}0\\1\end{pmatrix}$ only is M1 A0 |
**(iii)**
| Correct shape, touching $x$-axis at $-90°$, $90°$ | M1 | Correct shape, touching $x$-axis at $-90°$, $90°$ |
|---|---|---|
| Correct domain | B1 | |
| $(0, 2)$ marked or indicated (amplitude is 2) | A1 [3] | |
---4 (i) State the period of the function $\mathrm { f } ( x ) = 1 + \cos 2 x$, where $x$ is in degrees.\\
(ii) State a sequence of two geometrical transformations which maps the curve $y = \cos x$ onto the curve $y = \mathrm { f } ( x )$.\\
(iii) Sketch the graph of $y = \mathrm { f } ( x )$ for $- 180 ^ { \circ } < x < 180 ^ { \circ }$.
\hfill \mbox{\textit{OCR MEI C3 Q4 [8]}}