| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2022 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Find period or state transformations |
| Difficulty | Moderate -0.3 This is a straightforward transformation question requiring students to identify a horizontal stretch of tan x from a graph, state the period, and solve a basic equation. Part (a) involves reading the period from the graph (likely 90° instead of 180°), part (b) is immediate from part (a), and part (c) requires solving tan(kx) = 1 which gives standard angles (45°, 135°, etc.) scaled appropriately. While multi-part, each step uses routine techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.05f Trigonometric function graphs: symmetries and periodicities1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(y = \tan(ax°)\) | B1 | For any \(a \neq 1\) with no other transformation |
| \(y = \tan\left(\frac{3}{2}x°\right)\) | B1 | o.e. SC 1 for just \(f\left(\frac{3}{2}x\right)\) o.e. seen |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(120°\) | B1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| DR: \(\arctan 1 = 45°\), \(x = \frac{2}{3} \times 45° = 30°\) | M1 | Complete method for solving their \(y=1\) leading to at least one root. Do not allow where their \(y = \tan x\) |
| function is periodic with period \(120°\) | M1 | Appropriate use of the periodicity of their \(y\) or \(\tan x\) leading to at least one more root |
| roots are \(30°, 150°, 270°\) | B1 | cao. Allow for all roots seen and no extras in \([0°, 360°]\). Ignore values outside this range |
## Question 5:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $y = \tan(ax°)$ | B1 | For any $a \neq 1$ with no other transformation |
| $y = \tan\left(\frac{3}{2}x°\right)$ | B1 | o.e. SC 1 for just $f\left(\frac{3}{2}x\right)$ o.e. seen |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $120°$ | B1 | cao |
### Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| DR: $\arctan 1 = 45°$, $x = \frac{2}{3} \times 45° = 30°$ | M1 | Complete method for solving their $y=1$ leading to at least one root. Do not allow where their $y = \tan x$ |
| function is periodic with period $120°$ | M1 | Appropriate use of the periodicity of their $y$ or $\tan x$ leading to at least one more root |
| roots are $30°, 150°, 270°$ | B1 | cao. Allow for all roots seen and no extras in $[0°, 360°]$. Ignore values outside this range |
---5 Part of the graph of $y = f ( x )$ is shown below. The graph is the image of $y = \tan x ^ { \circ }$ after a stretch in the $x$-direction.\\
\includegraphics[max width=\textwidth, alt={}, center]{7af62e61-c67f-4d05-b6b9-c1a110345812-4_791_1022_1014_244}
\begin{enumerate}[label=(\alph*)]
\item Find the equation of the graph.
\item Write down the period of the function $\mathrm { f } ( x )$.
\item In this question you must show detailed reasoning.
Find all the roots of the equation $\mathrm { f } ( x ) = 1$ for $0 ^ { \circ } \leqslant x ^ { \circ } \leqslant 360 ^ { \circ }$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 1 2022 Q5 [6]}}