plumiFurther algebra and functions: Edexcel A‑Level Further Maths questions
Every Edexcel A-Level Further Maths exam question on CP.4 Further algebra and functions, 2018–2025, with its mark scheme and examiner’s report.
Find questions824
All 32 questions on Further algebra and functions, as a list
- June 2025, Core Pure 1, Q5 (5 marks): 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)
- June 2025, Core Pure 2, Q6 (8 marks): 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
- June 2025, Core Pure 2, Q8 (8 marks): 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
- June 2025, Further Pure 1, Q4 (8 marks): y x 15 2e (a) Show that d d e e e 2 2 2 2 2 30 15 3 2 y x x x x (3) (b) Hence determine the Maclaurin series expansion for y, in ascending powers of x, up to an
- June 2025, AS Core Pure, Q8 (7 marks): The first n triangular numbers are 1, 3, 6, 10, ... , 1 2 n(n + 1) where n is a positive integer. (a) Use the standard results for 2 1 n r r and 1 n r r to show
- June 2025, AS Core Pure, Q11 (7 marks): In this question you must show detailed reasoning. f(x) = x 3 – 21x 2 + Ax – 91 where A is a real constant The roots of f(x) = 0 are α, α + 3β and α + 6β where
- June 2024, Core Pure 1, Q2 (8 marks): The roots of the equation 2 3 12 7 0 3 2 x x x are α, β and γ Without solving the equation, (a) write down the value of each of α + β + γ αβ + αγ + βγ αβγ (1) (
- June 2024, Core Pure 2, Q2 (8 marks): f(x) = tanh 1 3 6 3 2 x x x < (a) Show that f′(x) = – 1 2 3 x + (4) (b) Hence determine f′′(x) (1) (c) Hence show that the Maclaurin series for f(x), up
- June 2024, Core Pure 2, Q4 (6 marks): Use the method of differences to show that 2 4 6 30 5 6 1 r r n an b n n r n where a and b are integers to be determined. (6)
- June 2024, AS Core Pure, Q1 (9 marks): The cubic equation 2 3 5 7 0 3 2 x x x has roots α, β and γ. Without solving the equation, determine the exact value of (i) α 2 + β 2 + γ 2 (3) (ii) 3 3 3 α β γ
- June 2024, AS Core Pure, Q3 (10 marks): (a) Use the standard results for summations to show that, for all positive integers n, r r n n n an b r n 2 1 1 1 12 1 2 where a and b are integers to be dete
- June 2023, Core Pure 1, Q1 (5 marks): The cubic equation x 3 – 7x 2 – 12x + 6 = 0 has roots α, β and γ. Without solving the equation, determine a cubic equation whose roots are (α + 2), (β + 2) and
- June 2023, Core Pure 1, Q7 (12 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Explain why, for n ∈ 1 2 2 1
- June 2023, Core Pure 2, Q2 (6 marks): (a) Write down the Maclaurin series of e x, in ascending power of x, up to and including the term in x 3 (1) (b) Hence, without differentiating, determine the M
- June 2023, Further Pure 1, Q6 (12 marks): y = ln(e 2x cos 3x) – 1 2 < x < 1 2 (a) Show that d d y x x 2 3 3 tan (2) (b) Determine d d 4 4 y x (3) (c) Hence determine the first 3 non-zero terms in ascend
- June 2023, AS Core Pure, Q8 (8 marks): (a) Use the standard results for r n 1 r 2 and r n 1 r to show that, for all positive integers n, ( ) ( ) 2 1 3 1 2 2 1 r n an r n where a is a constant to be d
- June 2023, AS Core Pure, Q10 (12 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (i) The quartic equation z 4 + 5z 2 –
- June 2022, Core Pure 1, Q4 (7 marks): (a) Use the method of differences to prove that for n > 2 ln ln r r n n r n + − ≡ + ( ) =∑ 1 1 1 2 2 (4) (b) Hence find the exact value of ln
- June 2022, Core Pure 2, Q6 (10 marks): The cubic equation 4x 3 + px 2 – 14x + q = 0 where p and q are real positive constants, has roots α, β and γ Given that α 2 + β 2 + γ 2 = 16 (a) show that p = 1
- June 2022, Core Pure 2, Q9 (8 marks): y = cosh n x n 5 (a) (i) Show that d d 2 2 y x = n 2 cosh n x – n(n – 1)cosh n – 2 x (4) (ii) Determine an expression for d d 4 4 y x (2) (b) Hence determine
- June 2022, AS Core Pure, Q4 (9 marks): The roots of the quartic equation 3x4 + 5x3 − 7x + 6 = 0 are α, β, γ and δ Making your method clear and without solving the equation, determine the exact value
- June 2022, AS Core Pure, Q5 (12 marks): (a) Use the standard summation formulae to show that, for n ∈ , 3 17 25 2 2 1 r r n n An B r n − − ( ) = − − ( ) =∑ where A and B are integers to be determine
- November 2021, Core Pure 1, Q2 (7 marks): (a) Use the Maclaurin series expansion for cos x to determine the series expansion of cos2 3 x in ascending powers of x, up to and including the term i
- November 2021, Core Pure 1, Q3 (6 marks): The cubic equation ax 3 + bx 2 – 19x – b = 0 where a and b are constants, has roots α, β and γ The cubic equation w 3 – 9w 2 – 97w + c = 0 where c is a constant
- November 2021, Core Pure 2, Q3 (6 marks): f (x) = arcsin x −1 x 1 (a) Determine the first two non-zero terms, in ascending powers of x, of the Maclaurin series for f (x) , giving each coefficient in
- November 2021, Core Pure 2, Q4 (9 marks): In this question you may assume the results for r r n 3 1 =∑ , r r n 2 1 =∑ and r r n =∑ 1 (a) Show that the sum of the cubes of the first n positive odd number
- November 2020, AS Core Pure, Q5 (7 marks): r (r + 2) (r + 1) Figure 2 A block has length (r + 2) cm, width (r + 1) cm and height r cm, as shown in Figure 2. In a set of n such blocks, the first block has
- November 2020, AS Core Pure, Q9 (6 marks): The cubic equation 3x3 + x2 – 4x + 1 = 0 has roots α, β, and γ. Without solving the cubic equation, (a) determine the value of 1 1 1 α β γ + + (3) (b) find a cu
- June 2019, Core Pure 1, Q4 (5 marks): Prove that, for n ], n . 1 1 2 3 2 3 0 r r r n a n b c n n r n + ( ) + ( ) + ( ) = + ( ) + ( ) + ( ) + ( ) =∑ where a, b and cDUHLQWHJHUVWREHIRXQG (5)
- June 2019, Core Pure 2, Q2 (8 marks): The roots of the equation x3 – 2x2 + 4x – 5 = 0 are p, q and r. Without solving the equation, find the value of (i) 2 p + 2 q + 2 r (ii) ( p – 4)(q – 4)(r – 4)
- June 2018, AS Core Pure, Q2 (5 marks): The cubic equation z3 – 3z2 + z + 5 = 0 has roots α, β and γ. Without solving the equation, find the cubic equation whose roots are (2α + 1), (2β + 1) and (2γ +
- June 2018, AS Core Pure, Q6 (10 marks): (a) Use the standard results for r r r n r n 2 1 1 = = ∑ ∑ and to show that ( ) 3 2 1 2 6 3 1 2 1 2 r n n n r n − = − − =∑ for all positive integers n. (5
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 A-Level Further Maths paper.
Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.