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Edexcel A‑Level Further Maths questions by topic

Every question from every Edexcel A-Level Further Maths paper, 2018–2025, question by question. Filter by topic, paper or year, open the mark scheme under any question, and download a set as a PDF.

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824 questions

  1. Q1

    June 2025 · Core Pure 1

    6 marks
    The whole paper ↗
    June 2025 Core Pure 1, question 1: M     3 6 0 3 1 2 a a a where a is a constant (a) Determine the values of a for which the matrix M is singular. (3) Given that matrix M is non-singular and

  2. Q2

    June 2025 · Core Pure 1

    5 marks
    The whole paper ↗
    June 2025 Core Pure 1, question 2: In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Determine the exact values of

  3. Q3

    June 2025 · Core Pure 1

    5 marks
    The whole paper ↗
    June 2025 Core Pure 1, question 3: The complex number z a b i where a and b are real constants. Given that z z* is purely imaginary, (a) show that a b 2 2 = (2) Given also that zz* = 50 (b) deter

  4. Q4

    June 2025 · Core Pure 1

    8 marks
    The whole paper ↗
    June 2025 Core Pure 1, question 4: (a) Determine the general solution of the differential equation d d d d e 2 2 3 4 4 2 y x y x y x giving your answer in the form y = f (x) (5) Given that y = 5

  5. Q5

    June 2025 · Core Pure 1

    5 marks
    The whole paper ↗
    June 2025 Core Pure 1, question 5: Use the method of differences to prove that for n > 2 4 1 2 2 1 1 r r n pn q n n n where p and q are constants to be determined. (5)

  6. Q6

    June 2025 · Core Pure 1

    5 marks
    The whole paper ↗
    June 2025 Core Pure 1, question 6: f (z) = z3 + az2 + bz + c where a, b and c are real constants The roots of the equation f (z) = 0 are z1, z2 and z3 When plotted on an Argand diagram, the point

  7. Q7

    June 2025 · Core Pure 1

    8 marks
    The whole paper ↗
    June 2025 Core Pure 1, question 7: (a) Express 2 10 9 22 2 3 3 2 2 x x x x x in partial fractions. (4) (b) Hence, show that 2 10 9 22 2 3 2 27 4 6 3 3 2 2 0 1 x x x x x x d ln ϖ (4)

  8. Q8

    June 2025 · Core Pure 1

    12 marks
    The whole paper ↗
    June 2025 Core Pure 1, question 8: A rambler starts a walk at the bottom of a hill at 10 am. The rambler walks all the way to the top of the hill and then turns around and walks back down to the

  9. Q9

    June 2025 · Core Pure 1

    9 marks
    The whole paper ↗
    June 2025 Core Pure 1, question 9: (i) The curves with equations y x = 3 4 sinh and y x tanh 1 5 intersect at just one point P (a) Use algebra to show that the x coordinate of P satisfies the equ

  10. Q10

    June 2025 · Core Pure 1

    12 marks
    The whole paper ↗
    June 2025 Core Pure 1, question 10: (a) Given that, for n ∈ z z n n n 1 2cos θ z z n n n 1 2isin θ show that 8 4 4 2 3 4 sin cos cos θ θ θ (5) O y R x Figure 1 Figure 2 Figure 1 shows the central

  11. Q1

    June 2025 · Core Pure 2

    6 marks
    The whole paper ↗
    June 2025 Core Pure 2, question 1: In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Given that z 2 2 3i and w 1 3

  12. Q2

    June 2025 · Core Pure 2

    8 marks
    The whole paper ↗
    June 2025 Core Pure 2, question 2: An archer shoots an arrow towards a target. In a model • the arrow is a particle • the flight path of the arrow is a straight line • the target is part of a pla

  13. Q3

    June 2025 · Core Pure 2

    12 marks
    The whole paper ↗
    June 2025 Core Pure 2, question 3: Given A   1 5 0 2 (a) prove by mathematical induction that, for n ∈ An n n       1 5 2 1 0 2 (6) Given B    1 0 0 1 (b) describe fully the singl

  14. Q4

    June 2025 · Core Pure 2

    10 marks
    The whole paper ↗
    June 2025 Core Pure 2, question 4: (i) z a b 1 i and z c d 2 i where a, b, c and d are real constants. Given that • b d > • z z 1 2 + is real • z1 13 = • z2 5 = • Re z z 2 1 2 show that a = 2 and

  15. Q5

    June 2025 · Core Pure 2

    4 marks
    The whole paper ↗
    June 2025 Core Pure 2, question 5: Three planes are defined by the following equations 2 3 3 3 2 4 x y z x py z q x y z where p and q are constants. Given that the planes form a sheaf, determine

  16. Q6

    June 2025 · Core Pure 2

    8 marks
    The whole paper ↗
    June 2025 Core Pure 2, question 6: The quartic equation 2 5 6 0 4 3 2 x Ax Ax x where A is a real constant, has roots , , and (a) Determine the value of 3 3 3 3    (3) Given that 2 2 2 2 3 4 

  17. Q7

    June 2025 · Core Pure 2

    12 marks
    The whole paper ↗
    June 2025 Core Pure 2, question 7: A O C B Initial line Figure 1 The curve C shown in Figure 1 has polar equation r a 1 sinθ ϖ θ ϖ where a is a constant. The tangents to C at the points A and B a

  18. Q8

    June 2025 · Core Pure 2

    8 marks
    The whole paper ↗
    June 2025 Core Pure 2, question 8: Given that y x x = cos sinh x (a) show that d d 4 4 y x ky = where k is a constant to be determined. (5) (b) Hence determine the first three non-zero terms of t

  19. Q9

    June 2025 · Core Pure 2

    7 marks
    The whole paper ↗
    June 2025 Core Pure 2, question 9: Given that y x = arcsin3 −1 3 1 3   x (a) determine d d y x in terms of x (2) The curve C has equation y x cos arcsin3 −1 3 1 3   x (b) Determine d d y x gi

  20. Q1

    June 2025 · Further Pure 1

    6 marks
    The whole paper ↗
    June 2025 Further Pure 1, question 1: (a) Given that y = e cosec2x complete the table below with the value of y corresponding to x = 2, giving your answer to 2 decimal places. x 1.5 1.75 2 2.25 2.5

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