Coordinate systems questions

Practice questions covering coordinate systems from this specification. Attempt the questions below; real-paper references for this topic are being imported.

Questions to attempt

6 questions on Coordinate systems, each with its mark scheme and worked method. Reveal the answer when you have had a go.

FP1-4.1 · Cartesian and parametric equations for the parabola and rectangular hyperbola, ellipse and hyperbola.
Q1
ORIGINAL
Years 1 and 2
Years 1 and 2: this holds AS subject content and content the exam board adds beyond it for the full A-level.
1.
The rectangular hyperbola $xy=16$ is met by the line $y=x-6$ . Find the coordinates of the two points of intersection and the corresponding values of the parameter $t$ in $\left(4t,\,\dfrac4t\right)$ .
(5)
(Total for Question 1 is 5 marks)
FP1-4.1 · Cartesian and parametric equations for the parabola and rectangular hyperbola, ellipse and hyperbola.
Q2
ORIGINAL
Years 1 and 2
Years 1 and 2: this holds AS subject content and content the exam board adds beyond it for the full A-level.
2.
A parabola has parametric equations $x=5t^2$ , $y=10t$ . Find its Cartesian equation and the value of $a$ in the standard form $y^2=4ax$ .
(3)
(Total for Question 2 is 3 marks)
FP1-4.2 · The focus-directrix properties of the parabola, ellipse and hyperbola, including the eccentricity.
Q3
ORIGINAL
Years 1 and 2
Years 1 and 2: this holds AS subject content and content the exam board adds beyond it for the full A-level.
3.
Find the eccentricity, the foci and the directrices of the hyperbola $\dfrac{x^2}{9}-\dfrac{y^2}{16}=1$ .
(4)
(Total for Question 3 is 4 marks)
FP1-4.2 · The focus-directrix properties of the parabola, ellipse and hyperbola, including the eccentricity.
Q4
ORIGINAL
Years 1 and 2
Years 1 and 2: this holds AS subject content and content the exam board adds beyond it for the full A-level.
4.
State the coordinates of the focus and the equation of the directrix of the parabola $y^2=16x$ .
(2)
(Total for Question 4 is 2 marks)
FP1-4.3 · Tangents and normals to these curves.
Q5
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
5.
Show that the normal to the parabola $y^2=4ax$ at the point $\left(at^2,2at\right)$ has equation $y+tx=2at+at^3$ .
(4)
(Total for Question 5 is 4 marks)
FP1-4.4 · Loci problems.
Q6
ORIGINAL
Years 1 and 2
Years 1 and 2: this holds AS subject content and content the exam board adds beyond it for the full A-level.
6.
The chord $PQ$ of the parabola $y^2=4ax$ subtends a right angle at the vertex $O$ . Show that $PQ$ passes through the fixed point $(4a,0)$ .
(6)
(Total for Question 6 is 6 marks)

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Printable question pack — FP1-4 Coordinate systems (Further Pure 1)All 40 questions across 4 specification points — 34 more than the 6 above — with the full mark scheme. Guest accessible · browser print.

FP1-4 Coordinate systems (Further Pure 1) revision notes

Real-paper references

Real-paper references for this module are being imported — the questions above are the site's own, exam-faithful, marked.

Reference rows contain series, paper, question number, marks and classification metadata only. Pearson's question papers open on Pearson's own website.

Questions to attempt

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