plumiCoordinate geometry: Edexcel A‑Level Maths questions
Every Edexcel A-Level Maths exam question on P.3 Coordinate geometry, 2019–2025, with its mark scheme and examiner’s report.
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All 29 questions on Coordinate geometry, as a list
- June 2025, Pure 1, Q2 (5 marks): The circle C has equation (x + 3) 2 + (y – 4) 2 = 24 (a) (i) State the coordinates of the centre of C. (ii) Find the radius of C writing your answer as a fully
- June 2025, Pure 2, Q5 (7 marks): The curve C has parametric equations x t 1 2 y = 5(t + 2) 4 t ∈ The point P with x coordinate –3 lies on C. (a) Find the y coordinate of P. (2) (b) Find a Car
- June 2025, AS Pure, Q2 (5 marks): The line l passes through the points A (–3, 0) and B 5 2 22 , (a) Find the equation of l giving your answer in the form y = mx + c where m and c are constant
- June 2025, AS Pure, Q4 (6 marks): The circle C has equation x 2 + y 2 + 10x – 4y + 1 = 0 (a) Find (i) the coordinates of the centre of C (ii) the exact radius of C (3) The line with equation y =
- June 2024, Pure 2, Q10 (6 marks): O C x y Figure 4 Figure 4 shows a sketch of the curve C with parametric equations x t y t t 3 1 2 1 2 3 The point P with coordinates (4, 2) lies on C. (a
- June 2024, Pure 2, Q14 (8 marks): The circle C1 has equation x y x y 2 2 6 14 33 0 (a) Find (i) the coordinates of the centre of C1 (ii) the radius of C1 (3) A different circle C2 • has centre w
- June 2024, AS Pure, Q10 (8 marks): C P Q l O y x Figure 4 Figure 4 shows a sketch of the circle C • the point P (–1, k + 8) is the centre of C • the point Q (3, k 2 – 2k) lies on C • k is a posit
- June 2023, Pure 1, Q10 (9 marks): A circle C has equation x 2 + y 2 + 6kx – 2ky + 7 = 0 where k is a constant. (a) Find in terms of k, (i) the coordinates of the centre of C (ii) the radius of C
- June 2023, Pure 2, Q9 (7 marks): The curve C has parametric equations x = t 2 + 6t – 16 y = 6 ln(t + 3) t > –3 (a) Show that a Cartesian equation for C is y = A ln (x + B) x > –B where A and B
- June 2023, AS Pure, Q6 (5 marks): The circle C has equation where k is a constant. (a) Find the coordinates of the centre of C. (2) Given that C does not cut or touch the x-axis, (b) find the ra
- June 2023, AS Pure, Q7 (8 marks): The distance a particular car can travel in a journey starting with a full tank of fuel was investigated. • From a full tank of fuel, 40 litres remained in the
- June 2023, AS Pure, Q10 (8 marks): O y x C B A l1 l2 Figure 4 The line l1 has equation y x 3 5 6 The line l2 is perpendicular to l1 and passes through the point B( , ) 8 0 , as shown in the sketc
- June 2022, Pure 1, Q3 (5 marks): A circle has equation x2 + y2 − 10x + 16y = 80 (a) Find (i) the coordinates of the centre of the circle, (ii) the radius of the circle. (3) Given that P is the
- June 2022, Pure 1, Q16 (9 marks): y 4 C R x O Figure 6 Figure 6 shows a sketch of the curve C with parametric equations x = 8 sin2 t y = 2 sin 2t + 3 sin t 0 t π 2 The region R, shown shaded
- June 2022, Pure 2, Q16 (12 marks): y l P C O x Figure 6 Figure 6 shows a sketch of the curve C with parametric equations x = 2 tan t + 1 y = 2 sec 2 t + 3 − 4 π t 3 π The line l is the normal
- June 2022, AS Pure, Q11 (8 marks): C O l y x Figure 3 Figure 3 shows the circle C with equation x2 + y2 – 10x – 8y + 32 = 0 and the line l with equation 2y + x + 6 = 0 (a) Find (i) the coordinate
- November 2021, Pure 1, Q7 (9 marks): The circle C has equation x2 + y2 − 10x + 4y + 11 = 0 (a) Find (i) the coordinates of the centre of C, (ii) the exact radius of C, giving your answer as a simpl
- November 2021, Pure 1, Q13 (3 marks): A curve C has parametric equations x = t t 2 2 5 1 + + y = 4 1 2 t t + t ∈ Show that all points on C satisfy (x − 3) 2 + y2 = 4 (3)
- November 2021, AS Pure, Q15 (9 marks): P l O x y N C Figure 4 Figure 4 shows a sketch of a circle C with centre N(7, 4) The line l with equation y = 1 3 x is a tangent to C at the point P. Find (a) t
- November 2020, Pure 1, Q11 (8 marks): y C2 B A O C1 x Figure 3 Circle C1 has equation x2 + y2 = 100 Circle C2 has equation (x − 15)2 + y2 = 40 The circles meet at points A and B as shown in Figure 3
- November 2020, Pure 2, Q4 (3 marks): In the binomial expansion of (a + 2x) 7 where a is a constant the coefficient of x4 is 15 120 Find the value of a. (3)
- November 2020, Pure 2, Q12 (11 marks): y R O x Figure 3 The curve shown in Figure 3 has parametric equations x = 6 sin t y = 5 sin 2t 0 t 2 π The region R, shown shaded in Figure 3, is bounded by
- November 2020, Pure 2, Q14 (7 marks): A circle C with radius r ● lies only in the 1st quadrant ● touches the x-axis and touches the y-axis The line l has equation 2x + y = 12 (a) Show that the x coo
- November 2020, AS Pure, Q4 (6 marks): In 1997 the average CO2 emissions of new cars in the UK was 190 g/km. In 2005 the average CO2 emissions of new cars in the UK had fallen to 169 g/km. Given A g/
- November 2020, AS Pure, Q11 (9 marks): (i) A circle C1 has equation x2 + y2 + 18x – 2y + 30 = 0 The line l is the tangent to C1 at the point P(–5, 7). Find an equation of l in the form ax + by + c =
- June 2019, Pure 2, Q4 (6 marks): y x O S C2 C1 Figure 2 The curve C1 with parametric equations x FRVt , y = 4 2sin t , 0 - t 2ʌ meets the circle C2 with equation x2 + y2 = 66 at four dist
- June 2019, AS Pure, Q1 (4 marks): The line l1 has equation 2x + 4y – 3 = 0 The line l2 has equation y = mx + 7, where m is a constant. Given that l1 and l2 are perpendicular, (a) find the value
- June 2019, AS Pure, Q4 (5 marks): A tree was planted in the ground. Its height, H metres, was measured t years after planting. Exactly 3 years after planting, the height of the tree was 2.35 met
- June 2019, AS Pure, Q10 (5 marks): A circle C has equation x2 + y2 – 4x + 8y – 8 = 0 (a) Find (i) the coordinates of the centre of C, (ii) the exact radius of C. (3) The straight line with equati
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