plumiCoordinate systems and conics: Edexcel A‑Level Further Maths questions
Every Edexcel A-Level Further Maths exam question on FP.4 Coordinate systems and conics, 2018–2025, with its mark scheme and examiner’s report.
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All 20 questions on Coordinate systems and conics, as a list
- June 2025, Further Pure 1, Q8 (7 marks): The ellipse E has equation x y 2 2 64 36 1 The line l has equation y = mx + c where m and c are constants. (a) Show that the x coordinates of the points of inte
- June 2025, AS Further Pure 1, Q5 (9 marks): The parabola C has equation y 2 = 16x The point P (4t 2 , 8t) lies on C. (a) Show that an equation for the tangent to C at P is yt – x = 4t 2 (3) The line l pas
- June 2024, Further Pure 1, Q6 (6 marks): The ellipse E has equation x y 2 2 25 9 1 The hyperbola H has equation x a y b 2 2 2 2 1 where a and b are positive constants. Given that • the eccentricity of
- June 2024, Further Pure 1, Q8 (8 marks): The parabola P has equation y 2 = 4ax, where a is a positive constant. The point A at at 2 2 , , where t ≠ 0, lies on P. (a) Use calculus to show that an equati
- June 2024, AS Further Pure 1, Q5 (9 marks): The parabola C has equation y 2 = 16x The point P on C has y coordinate p, where p is a positive constant. (a) Show that an equation of the tangent to C at P is
- June 2023, Further Pure 1, Q4 (12 marks): The ellipse E has equation x y 2 2 16 9 1 (a) Determine the exact value of the eccentricity of E (2) The points P(4 cos θ, 3 sin θ) and Q(4 cos θ, –3 sin θ) lie
- June 2023, AS Further Pure 1, Q3 (5 marks): The rectangular hyperbola H has equation xy = c 2 where c is a positive constant. The line l has equation x – 2y = c The points P and Q are the points of inters
- June 2023, AS Further Pure 1, Q6 (8 marks): The parabola C has equation y 2 = 4ax where a is a positive constant. The point P(at 2, 2at) , t ≠ 0, lies on C The normal to C at P is parallel to the line wit
- June 2022, Further Pure 1, Q1 (7 marks): An ellipse has equation x y 2 2 16 4 1 and eccentricity e 1 A hyperbola has equation x a y b 2 2 2 2 1 and eccentricity e 2 Given that e 1 × e 2 = 1 (a) show th
- June 2022, Further Pure 1, Q5 (9 marks): The rectangular hyperbola H has equation xy = 36 (a) Use calculus to show that the equation of the tangent to H at the point P 6 6 t t , is yt 2 + x = 12t (3
- June 2022, AS Further Pure 1, Q4 (9 marks): The parabola C has equation y2 = 10x The point F is the focus of C. (a) Write down the coordinates of F. (1) The point P on C has y coordinate q , where q > 0 (
- November 2021, Further Pure 1, Q1 (5 marks): The ellipse E has equation x y 2 2 36 20 1 + = Find (a) the coordinates of the foci of E, (3) (b) the equations of the directrices of E. (2)
- November 2021, Further Pure 1, Q5 (9 marks): The parabola C has equation y 2 = 32x and the hyperbola H has equation x y 2 2 36 9 1 − = (a) Write down the equations of the asymptotes of H. (1) The line l1 i
- November 2020, Further Pure 1, Q5 (7 marks): The ellipse E has equation x y 2 2 36 16 1 + = The points S and S ′ are the foci of E. (a) Find the coordinates of S and S ′ (3) (b) Show that for any point P o
- November 2020, Further Pure 1, Q7 (14 marks): The points P(9p2, 18p) and Q(9q2, 18q) , p ≠ q , lie on the parabola C with equation y2 = 36x The line l passes through the points P and Q (a) Show that an equa
- November 2020, AS Further Pure 1, Q4 (7 marks): y P O S x C Figure 2 Figure 2 shows a sketch of the parabola C with equation y2 = 4ax, where a is a positive constant. The point S is the focus of C and the poi
- June 2019, Further Pure 1, Q4 (8 marks): The parabola C has equation y 2 = 16x The distinct points P( p2, 4p) and Q(q2, 4q) lie on C, where pq The tangent to C at P and the tangent to C at Q
- June 2019, Further Pure 1, Q8 (14 marks): The hyperbola H has equation x y 2 2 16 9 1 − = The line l1 is the tangent to H at the point P(4cosh ș, 3sinh ș). The line l1 meets the x-axis at the point A. T
- June 2019, AS Further Pure 1, Q5 (10 marks): A B x y O l R P H Figure 2 Figure 2 shows a sketch of part of the rectangular hyperbola +with equation xy c x = > 2 0 where c is a positive constant. The point
- June 2018, AS Further Pure 1, Q5 (10 marks): The rectangular hyperbola H has equation xy = c2, where c is a non-zero constant. The point P cp c p p H , ≠ , where , lies on . 0 (a) Use calculus to
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