Edexcel IAL P4 Coordinate Geometry (parametric) Questions
Parametric curves and conversion to Cartesian form.
- P4 · Pure Mathematics 4
- Calculator allowed
- 30 practice questions
What the questions test
The 30 P4 coordinate geometry (parametric) practice questions cover:
Worked example 1
A curve $C$ has parametric equations $x = \sin \theta$ and $y = \cos 2\theta$ for $0 \le \theta \le \pi$. Find the exact coordinates of the points where $C$ intersects the line $y = x$.
Mark scheme
- M1 for setting $x = y$, resulting in $\sin \theta = \cos 2\theta$.
- M1 for substituting the double angle formula: $\sin \theta = 1 - 2\sin^2 \theta$.
- M1 for rearranging into a quadratic $2\sin^2 \theta + \sin \theta - 1 = 0$ and factorising $(2\sin \theta - 1)(\sin \theta + 1) = 0$.
- A1 for finding valid solutions for $\sin \theta$: $\sin \theta = \frac{1}{2}$ (rejecting $\sin \theta = -1$ since $0 \le \theta \le \pi$).
- A1 for calculating the corresponding $(x, y)$ coordinates: $(\frac{1}{2}, \frac{1}{2})$.
Worked example 2
A curve has parametric equations $x = t^2 - t$ and $y = t^3 - 3t$. Find the exact coordinates of the points where the curve crosses the x-axis.
Mark scheme
- M1 for setting $y = 0$ to find x-axis intersections: $t^3 - 3t = 0$.
- M1 for factorising $t(t^2 - 3) = 0$.
- A1 for finding the parameter values $t = 0, \sqrt{3}, -\sqrt{3}$.
- M1 for substituting these values of $t$ back into $x = t^2 - t$.
- A1 for the exact coordinates: $(0,0)$, $(3-\sqrt{3}, 0)$, and $(3+\sqrt{3}, 0)$.
FAQ
What coordinate geometry (parametric) is in Edexcel IAL P4?
Parametric curves and conversion to Cartesian form.
Is P4 a calculator paper?
Yes, a calculator is allowed in P4, but method marks are only given for working you write down.
How are P4 coordinate geometry (parametric) questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.