plumiCoordinate systems: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP1.4 Coordinate systems, 2019–2025, with its mark scheme and examiner’s report.
Paper
All papers
Exam
All years
All 21 questions on Coordinate systems, as a list
- June 2025, Further Pure 1 (FP1), Q4 (8 marks): The rectangular hyperbola C has equation xy = 81 The point P t t 9 9 , , t ≠ 0, lies on C. (a) Use calculus to show that the normal to C at P has equation ty
- June 2025, Further Pure 1 (FP1), Q9 (4 marks): R O P Q y x Directrix Focus Figure 1 Figure 1 shows a sketch of a parabola C. The point P lies on C at a distance 5 units from the focus of C. The points Q and
- January 2025, Further Pure 1 (FP1), Q6 (9 marks): The rectangular hyperbola H has equation xy = 100 The point P t t 10 10 , , where t ≠ 0, lies on H. (a) Use calculus to show that the normal to H at P has equ
- January 2025, Further Pure 1 (FP1), Q9 (8 marks): The parabola C has equation y x 2 1 2 = The point P t t 2 8 4 , , where t ≠ 0, lies on C. (a) Use calculus to show that the tangent to C at P has equation 8
- June 2024, Further Pure 1 (FP1), Q9 (13 marks): The rectangular hyperbola H has equation xy = c 2 where c is a positive constant. The point P ct c t , , where t > 0, lies on H (a) Use calculus to show that
- January 2024, Further Pure 1 (FP1), Q3 (6 marks): The hyperbola H has equation xy = c 2 where c is a positive constant. The point P ct c t , , where t > 0, lies on H. The tangent to H at P meets the x-axis at
- January 2024, Further Pure 1 (FP1), Q7 (7 marks): The parabola C has equation y x 2 4 3 = The point P t t 1 3 2 3 2, , where t ≠ 0, lies on C. (a) Use calculus to show that the normal to C at P has equation
- June 2023, Further Pure 1 (FP1), Q3 (7 marks): The rectangular hyperbola H has Cartesian equation xy = 9 The point P with coordinates 3 3 t t , , where t ≠ 0, lies on H (a) Use calculus to determine an equ
- June 2023, Further Pure 1 (FP1), Q8 (13 marks): The point P(2p 2, 4p) lies on the parabola with equation y 2 = 8x (a) Show that the point Q 2 4 2 p p , , where p ≠ 0, lies on the parabola. (b) Show that
- January 2023, Further Pure 1 (FP1), Q6 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The rectangular hyperbola H h
- January 2023, Further Pure 1 (FP1), Q8 (11 marks): A parabola C has equation y ax 2 4 = where a is a positive constant. The point S is the focus of C The line l1 with equation y = k where k is a positive constan
- June 2022, Further Pure 1 (FP1), Q6 (11 marks): The parabola C has equation y2 = 36x The point P(9t 2, 18t), where t ≠ 0 , lies on C (a) Use calculus to show that the normal to C at P has equation y + tx = 9t
- January 2022, Further Pure 1 (FP1), Q3 (5 marks): The parabola C has equation y 2 = 18x The point S is the focus of C (a) Write down the coordinates of S The point P, with y > 0, lies on C The shortest distance
- January 2022, Further Pure 1 (FP1), Q7 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The rectangular hyperbola H h
- October 2021, Further Pure 1 (FP1), Q6 (8 marks): The curve H has equation xy = a 2 x > 0 where a is a positive constant. The line with equation y = kx, where k is a positive constant, intersects H at the point
- October 2021, Further Pure 1 (FP1), Q8 (10 marks): The parabola C has equation y 2 = 20x The point P on C has coordinates (5p 2, 10p) where p is a non‑zero constant. (a) Use calculus to show that the tangent to
- June 2021, Further Pure 1 (FP1), Q4 (8 marks): A rectangular hyperbola H has equation xy = 25 The point P t t t 5 5 0 , , , ≠ is a general point on H. (a) Show that the equation of the tangent to H
- June 2021, Further Pure 1 (FP1), Q6 (16 marks): The parabola C has Cartesian equation y2 = 8x The point P(2p2, 4p) and the point Q(2q2, 4q), where p, q ≠ 0, p ≠ q, are points on C. (a) Show that an equation o
- January 2021, Further Pure 1 (FP1), Q8 (14 marks): The hyperbola H has Cartesian equation xy = 25 The parabola P has parametric equations x = 10t2, y = 20t The hyperbola H intersects the parabola P at the point
- October 2020, Further Pure 1 (FP1), Q5 (9 marks): The rectangular hyperbola H has equation xy = 64 The point P p p 8 8 , , where p ≠ 0, lies on H. (a) Use calculus to show that the normal to H at P has
- October 2020, Further Pure 1 (FP1), Q7 (10 marks): The parabola C has equation y2 = 4ax, where a is a positive constant. The line l with equation 3x – 4y + 48 = 0 is a tangent to C at the point P. (a) Show that
Questions, mark schemes and examiner’s reports are © Pearson Edexcel, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every Edexcel International A Level Further Maths paper.
Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.