| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 1 (Further AS Paper 1) |
| Year | 2019 |
| Session | June |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Polar coordinates |
| Type | Sketch polar curve |
| Difficulty | Moderate -0.3 This is a straightforward polar coordinates question requiring recognition that r = k/sin θ is equivalent to r sin θ = k (a horizontal line y = k), then sketching it and identifying the perpendicular distance. While it's a Further Maths topic, it tests basic recall and interpretation rather than problem-solving, making it slightly easier than average. |
| Spec | 4.09b Sketch polar curves: r = f(theta) |
| Answer | Marks |
|---|---|
| 4(a) | Draws a horizontal line above the point O, parallel to the initial line. |
| Answer | Marks | Guidance |
|---|---|---|
| A deliberate curve, e.g. parabolic, is B0. | 1.1b | B1 |
| Answer | Marks |
|---|---|
| 4(b) | States the correct minimum distance as k |
| Answer | Marks | Guidance |
|---|---|---|
| 𝜃𝜃 𝜃𝜃 = 2 | 1.1b | B1 |
| 𝑘𝑘−0 𝑘𝑘−0 = 𝑘𝑘 Total | 2 | |
| Q | Marking instructions | AO |
Question 4:
--- 4(a) ---
4(a) | Draws a horizontal line above the point O, parallel to the initial line.
Ignore a vertical axis through O.
Ignore an extension of the initial line.
Accept a freehand ‘straight’ line – mark intention.
A deliberate curve, e.g. parabolic, is B0. | 1.1b | B1
--- 4(b) ---
4(b) | States the correct minimum distance as k
Treat an answer of as two responses, one correct and one incorrect (B0).
Condone
𝑘𝑘 = 0
Ignore any value of , e.g.
𝑟𝑟 = 𝑘𝑘
𝜋𝜋
Must be simplified, e.g. is B0, but is B1.
𝜃𝜃 𝜃𝜃 = 2 | 1.1b | B1 | k
𝑘𝑘−0 𝑘𝑘−0 = 𝑘𝑘 Total | 2
Q | Marking instructions | AO | Marks | Typical solutionThe line $L$ has polar equation
$$r = \frac{k}{\sin \theta}$$
where $k$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\item Sketch $L$. [1 mark]
\item State the minimum distance between $L$ and the point $O$. [1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 1 2019 Q4 [2]}}