plumiFurther coordinate systems: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP3.2 Further coordinate systems, 2019–2025, with its mark scheme and examiner’s report.
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All 16 questions on Further coordinate systems, as a list
- June 2025, Further Pure 3 (FP3), Q9 (12 marks): The hyperbola H has equation x y 2 2 64 49 − = 1 and eccentricity e. (a) Show that e = 113 8 The point (8 sec θ, 7 tan θ), where 0 2 π θ < < , lies on H. (b) Us
- January 2025, Further Pure 3 (FP3), Q2 (6 marks): The hyperbola H has equation kx 2 – y 2 = 9 where k is a positive constant. Given that the point (6, 0) is a focus of H (a) determine the value of k. (b) Hence
- January 2025, Further Pure 3 (FP3), Q7 (12 marks): The ellipse E has equation x a y b a b 2 2 2 2 1 0 > > The point P(a cos θ, b sin θ) lies on E where 0 2 π θ < < (a) Use calculus to show that an equation of th
- June 2024, Further Pure 3 (FP3), Q1 (6 marks): The hyperbola H has • foci with coordinates 13 2 0 , • directrices with equations x = ± 72 13 • eccentricity e Determine (a) the value of e (b) an equation
- June 2024, Further Pure 3 (FP3), Q6 (9 marks): The ellipse E has equation x y 2 2 25 9 1 The line l is the normal to E at the point P (5 cos θ, 3 sin θ) where 0 < θ < 2 π (a) Using calculus, show that an equ
- January 2024, Further Pure 3 (FP3), Q3 (11 marks): The ellipse E has equation x y b 2 2 2 49 1 where b is a constant and 0 < b < 7 The eccentricity of the ellipse is e (a) Write down, in terms of e only, (i) the
- June 2023, Further Pure 3 (FP3), Q6 (13 marks): The ellipse E has equation x y 2 2 16 9 1 The point P(4 cos θ, 3 sin θ) lies on E. (a) Use calculus to show that an equation of the tangent to E at P is 3x cos
- January 2023, Further Pure 3 (FP3), Q2 (6 marks): A hyperbola H has equation x a y a 2 2 2 5 1 where is a positive constant The line with equation x = 4 3 is a directrix of H (a) Write down an equation of the o
- January 2023, Further Pure 3 (FP3), Q9 (13 marks): The ellipse E has equation x y 2 2 9 9 The foci of E are F1 and F2 (a) (i) Determine the coordinates of F1 and the coordinates of F2 (ii) Write down the equatio
- June 2022, Further Pure 3 (FP3), Q9 (10 marks): The ellipse E has equation x y 2 2 9 4 1 + = The line l has equation y = kx – 3, where k is a constant. Given that E and l meet at 2 distinct points P and Q (a)
- January 2022, Further Pure 3 (FP3), Q8 (13 marks): The ellipse E has equation x y 2 2 9 4 1 + = (a) Determine the eccentricity of E (b) Hence, for this ellipse, determine (i) the coordinates of the foci, (ii) th
- October 2021, Further Pure 3 (FP3), Q3 (9 marks): The ellipse E has equation x2 64 + y2 36 = 1 The line l is the normal to E at the point P (8 cos θ , 6 sin θ). (a) Using calculus, show that an equation for l i
- October 2021, Further Pure 3 (FP3), Q7 (11 marks): A hyperbola H has equation x a 2 2 − y2 25 = 1 where a is a positive constant. The eccentricity of H is e. (a) Determine an expression for e2 in terms of a. The
- June 2021, Further Pure 3 (FP3), Q8 (14 marks): The hyperbola H has equation 4x 2 − y 2 = 4 (a) Write down the equations of the asymptotes of H. (b) Find the coordinates of the foci of H. The point P(sec θ, 2
- January 2021, Further Pure 3 (FP3), Q9 (12 marks): The ellipse E has equation x y 2 2 25 16 1 + = The point P lies on the ellipse and has coordinates (5 cos θ, 4 sin θ) where 0 < θ < 2 π The line l is the normal
- October 2020, Further Pure 3 (FP3), Q5 (12 marks): The hyperbola H has equation x y 2 2 25 4 1 − = The line l has equation y = mx + c, where m and c are constants. Given that l is a tangent to H, (a) show that 2
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