| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core (Further Pure Core) |
| Year | 2023 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Polar coordinates |
| Type | Sketch polar curve |
| Difficulty | Standard +0.8 This Further Maths polar curves question requires understanding when r=0 and r is minimized, identifying loop formation (where r<0), and working with trigonometric equations. While systematic, it demands conceptual understanding of polar coordinate behavior beyond routine A-level, particularly recognizing the inner loop corresponds to negative r values. |
| Spec | 4.09a Polar coordinates: convert to/from cartesian4.09b Sketch polar curves: r = f(theta) |
| Answer | Marks | Guidance |
|---|---|---|
| 7 | (a) | A: r = a , = 0 |
| Answer | Marks |
|---|---|
| C: r = 3a , = 3/2 | B1 |
| Answer | Marks |
|---|---|
| [3] | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| 1.1 | or = 2𝜋 | |
| 7 | (b) | 1 |
| Answer | Marks |
|---|---|
| 6 6 | M1 |
| Answer | Marks |
|---|---|
| [3] | 3.1a |
| Answer | Marks |
|---|---|
| 1.1 | (cid:2869) (cid:2869) (cid:2869) (cid:2869) |
Question 7:
7 | (a) | A: r = a , = 0
B: r = a , = /2
C: r = 3a , = 3/2 | B1
B1
B1
[3] | 1.1
1.1
1.1 | or = 2𝜋
7 | (b) | 1
sin𝜃 >
2
1 5
𝜋, 𝜋
6 6
1 5
𝜋 < 𝜃 < 𝜋
6 6 | M1
A1
A1
[3] | 3.1a
1.1
1.1 | (cid:2869) (cid:2869) (cid:2869) (cid:2869)
Allow sin𝜃 = (or < or ≤ or ≥ )
(cid:2870) (cid:2870) (cid:2870) (cid:2870)
both
condone for <7 The diagram below shows the curve with polar equation $r = a ( 1 - 2 \sin \theta )$ for $0 \leqslant \theta \leqslant 2 \pi$, where $a$ is a positive constant.\\
\includegraphics[max width=\textwidth, alt={}, center]{76631941-3cd5-4b3e-a7e4-27b8f991975a-4_634_865_486_239}
The curve crosses the initial line at A , and the points B and C are the lowest points on the two loops.
\begin{enumerate}[label=(\alph*)]
\item Find the values of $r$ and $\theta$ at the points A , B and C .
\item Find the set of values of $\theta$ for the points on the inner loop (shown in the diagram with a broken line).
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Pure Core 2023 Q7 [6]}}