plumiThe binomial series: Edexcel International GCSE Further Maths questions
Edexcel International GCSE Further Maths past-paper questions on 6 The binomial series, 2019–2025, with mark schemes and examiner’s reports where available.
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All 22 questions on The binomial series, as a list
- June 2025, Paper 1, Q6 (8 marks): 1 x 2 6 (a) Show that where A and B are integers to be found. x A 4 1 B (2) (b) Hence expand 4 − x in ascending powers of x up to and including the term in x3 G
- November 2024, Paper 1, Q6 (12 marks): (a) Show that 1 a a bx 2 2 1 where a and b are positive integers. 4 bx 4 (2) a The expansion of in ascending powers of x can be written as 4 + bx P + Qx + Rx 2
- June 2024 (R), Paper 1, Q2 (8 marks): Given that 1 5 1 x x 2 ... 3 36 n is the binomial expansion, in ascending powers of x, of 1 Ax where A and n are rational numbers, (a) find the value of A and t
- June 2024 (R), Paper 2, Q2 (5 marks): 2 (a) Expand in ascending powers of x up to and including the term in x3 x 1 + 3 Express each coefficient as a fraction in its simplest terms where appropriate.
- June 2024, Paper 2, Q7 (7 marks): 3 7 (a) Expand 1 x in ascending powers of x up to and including the term in x6 2 2 4 Express each coefficient as an exact fraction in its lowest terms. (3) kx 2
- November 2023, Paper 1, Q9 (11 marks): 1 9 (a) Expand 1 8 x 2 in ascending powers of x, up to and including the term in x6 2 giving each coefficient as an integer. (3) a bx g x 2 where a and b are pr
- June 2023 (R), Paper 1, Q9 (14 marks): 1 9 (a) Expand 1 2 x in ascending powers of x up to and including the term in x3 3 expressing each coefficient as a fraction in its lowest terms. (3) (b) Find t
- June 2023, Paper 2, Q7 (11 marks): 3 x 7 (a) Expand 1 in ascending powers of x up to and including the term in x3 3 Where appropriate express each coefficient as an exact fraction in its lowest t
- January 2023 (R), Paper 2, Q1 (6 marks): 8 x 1 (a) Expand 1 + in ascending powers of x up to and including the term in x3 4 Give each coefficient in its simplest terms. (3) (b) Use your expansion with
- January 2023, Paper 1, Q6 (7 marks): 1 1 3 can be expressed in the form p(1 + qx) 3 where p and q 6 Given that (8 + 3x) are constants, (a) find the value of p and the value of q (2) 1 3 in ascendin
- June 2022 (R), Paper 2, Q9 (9 marks): 3 in the form a(1 – bx)–3 9 (a) Write − x 3 ( 3 ) where a and b are fractions in their lowest terms. (2) 3 in ascending powers of x up to and including the term
- June 2022, Paper 1, Q5 (11 marks): –1 can be expressed in the form p (1 + qx) –1 where p and q 5 Given that (2 + 3x) are constants, (a) find the value of p and the value of q (2) –1 in ascending
- January 2022 (R), Paper 1, Q5 (8 marks): f (x) = (1 + ax) n where n > 2 (a) Write down the expansion of f (x) in ascending powers of x up to and including the term in x3 Give each coefficient in terms
- January 2022, Paper 1, Q9 (11 marks): 1 9 (a) Expand x in ascending powers of x up to and including the term in x 3 − 1 2 Simplify each term as far as possible. (3) 1 5 6 (b) Show that = 12 0 96 . S
- November 2021, Paper 2, Q10 (13 marks): 1 3 x 2 10 (a) Show that 1 3 9 3 x (2) 3 (b) Hence expand - x in ascending powers of x up to and including the term in x3 9 3 expressing each coefficient as an
- June 2021, Paper 1, Q5 (10 marks): (a) Expand (1 + ax)n in ascending powers of x up to and including the term in x3 Express each coefficient of x in terms of a and n where a and n are constants a
- November 2020 (R), Paper 1, Q5 (8 marks): (a) Expand 1 − x in ascending powers of x up to and including the term in x3 Give each coefficient as an exact fraction in its lowest terms. (3) (b) Using your
- November 2020, Paper 2, Q3 (5 marks): (a) Expand (1 + px)–5 p ≠ 0 in ascending powers of x, up to and including the term in x4 Give each term in its simplest form. (3) The coefficient of xr in the e
- January 2020 (R), Paper 2, Q9 (10 marks): 1 9 Given that can be written as p(1 − qx)–3 − x ( 2 ) 3 (a) find the value of p and the value of q. (2) 1 (b) Expand in ascending powers of x up to and includi
- January 2020, Paper 1, Q9 (8 marks): (a) Expand 1 − x in ascending powers of x up to and including the term in x3, 4 giving each coefficient as an integer. (3) (b) Use your expansion with a suitabl
- June 2019 (R), Paper 2, Q6 (8 marks): 1 6 Given that 9 − x can be expressed in the form p(1 + qx) 2 where p and q are constants (a) find the value of p and the value of q. (2) (b) Hence expand 9 − x
- June 2019, Paper 1, Q10 (14 marks): (a) Expand (1+ 2x2)≥ in ascending powers of x up to and including the term in r*, expressing each coefficient as an exact fraction in its lowest terms. (3) (b)
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