Edexcel A‑Level Maths questions by topic

June 2025 Pure 1, question 1: The point P(6, –4) lies on the curve with equation y = f(x), x ∈  Find the point to which P is mapped when the curve with equation y = f(x) is transformed to t

June 2025 Pure 1, question 2: 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 1, question 3: The first three terms of an arithmetic sequence are 6k, 10 and 2k where k is a constant. (a) Find the value of k. (2) (b) Hence find the value of the sum of the

June 2025 Pure 1, question 4: Given that • f(x) = 2x 3 + 3x 2 – 16x + 16 • f(–4) = 0 (a) write f(x) in the form (x + a) Q(x) where a is a constant and Q(x) is a quadratic expression. (3) (b)

June 2025 Pure 1, question 5: (a) Express 2.89 0 1.44 2 lim δx x δx x as an integral. (1) (b) Hence show that 2.89 0 1.44 2 lim δx x δx k x where k is an integer to be found. (Solutions rely

June 2025 Pure 1, question 6: A scientist is monitoring the flight of sea birds after they leave their nests on a cliff. The height above the sea, h metres, of one of the birds is modelled b

June 2025 Pure 1, question 7: O 2 –1 –75 5 C x y Figure 1 Figure 1 shows a sketch of a curve C with equation y = f(x), where f(x) is a quartic expression in x. The curve • has maximum turnin

June 2025 Pure 1, question 8: A student was asked to prove that the square of any number can be expressed in the form 5n or 5n ± 1 where n ∈  The start of the student’s proof is shown in th

June 2025 Pure 1, question 9: O T t v Figure 2 A racing car is driven along a straight road. Figure 2 shows a graph of the speed of the car as it travels along the road. The car starts from

June 2025 Pure 1, question 10: Given that • PQ → = 2i + 8j – 2k • QR → = 6i + 6k (a) find PR →. (2) (b) Hence show that triangle PQR is both right-angled and isosceles. (4)

June 2025 Pure 1, question 11: In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The value of a car, £V, is mo

June 2025 Pure 1, question 12: O Q C l x y Figure 3 Figure 3 shows a sketch of the curve C with equation y = 15 2 3 3 x x x ( )( ) x ≠ – 3 2 x ≠ 3 and the straight line l with equation y = 2x

June 2025 Pure 1, question 13: In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Show that x x x ( ) 2 1 2 25 3 0 2 d (

June 2025 Pure 1, question 14: In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Show that sin(x + 30°) + 3 cos(x +

June 2025 Pure 1, question 15: O D C B A Figure 4 Figure 4 shows the plan view for the design of a stage. The shape of this design consists of a sector of a circle AOB joined to a rectangle O

June 2025 Pure 1, question 16: O 1 C R x y 3 Figure 5 Figure 5 shows a sketch of the curve C with equation y = 1 4 2 2 x x − 0 &lt; x &lt; 2 The region R, shown shaded in Figure 5, is bounded by C,