| Exam Board | AQA |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2014 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Polar coordinates |
| Type | Convert Cartesian to polar equation |
| Difficulty | Standard +0.8 This is a Further Maths polar coordinates question requiring manipulation of the conversion formulas (r² = x² + y², x = r cos θ) and algebraic rearrangement to eliminate r and θ. While the steps are systematic, it requires careful handling of substitutions and rearranging to the specific form requested, making it moderately challenging but still a standard FP3 exercise. |
| Spec | 4.09a Polar coordinates: convert to/from cartesian |
## Question 3
[4 marks]
M1: Use $r(4 - 3\cos\theta) = 4$ and $x = r\cos\theta$
M1: Rearrange to $r = \frac{4}{4 - 3\cos\theta}$
M1: Eliminate parameter using $\cos\theta = \frac{x}{r}$ and $r^2 = x^2 + y^2$
A1: Correct Cartesian equation $y^2 = f(x)$ in required form3 A curve has polar equation $r ( 4 - 3 \cos \theta ) = 4$. Find its Cartesian equation in the form $y ^ { 2 } = \mathrm { f } ( x )$.\\[0pt]
[4 marks]
\hfill \mbox{\textit{AQA FP3 2014 Q3 [4]}}