| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2018 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Calculate intersection coordinates algebraically |
| Difficulty | Standard +0.8 Part (i) is routine sketching. Part (ii) requires solving 4cos x = 2sin x algebraically, converting to tan x = 2, then finding the y-coordinate in exact form involving √5, which demands careful manipulation. Part (iii) tests conceptual understanding of periodicity beyond rote application. This is above-average difficulty due to the exact form requirement and the conceptual reasoning component, but remains accessible to strong AS students. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05g Exact trigonometric values: for standard angles1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs1.05o Trigonometric equations: solve in given intervals |
I'd be happy to help clean up the mark scheme, but the content you've provided appears to be incomplete. The sections show:
- Question 5: (i), (ii), and (iii) are listed
- But there are no actual marking points, annotations (M1, A1, B1, etc.), or guidance notes included
Could you please provide the full mark scheme content with the actual marking criteria and annotations? Once you share that, I'll format it clearly with proper LaTeX conversion for mathematical symbols.5 (i) Sketch the graphs of $y = 4 \cos x$ and $y = 2 \sin x$ for $0 ^ { \circ } \leqslant x \leqslant 180 ^ { \circ }$ on the same axes.\\
(ii) Find the exact coordinates of the point of intersection of these graphs, giving your answer in the form (arctan $a , k \sqrt { b }$ ), where $a$ and $b$ are integers and $k$ is rational.\\
(iii) A student argues that without the condition $0 ^ { \circ } \leqslant x \leqslant 180 ^ { \circ }$ all the points of intersection of the graphs would occur at intervals of $360 ^ { \circ }$ because both $\sin x$ and $\cos x$ are periodic functions with this period. Comment on the validity of the student's argument.
\hfill \mbox{\textit{OCR MEI AS Paper 1 2018 Q5 [7]}}