plumiBinomial expansion (positive n): AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on D.1 Binomial expansion (positive n), 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 9 questions on Binomial expansion (positive n), as a list
- June 2025, Paper 3, Q6 (4 marks): The first four terms in ascending powers of x of the binomial expansion of (2 – 3x)5 are given by 32 + px + qx2 – 1080x3 where p and q are constants. 6 (a) Find
- June 2024, Paper 1, Q8 (5 marks): (a) Find the first three terms, in ascending powers of x, in the expansion of (2 + kx)5 where k is a positive constant. [3 marks] 8 (b) Hence, given that the co
- June 2023, Paper 1, Q1 (1 mark): Find the coefficient of x7 in the expansion of (2x − 3)7 Circle your answer. [1 mark] −2187 −128 2 128 d
- June 2022, Paper 2, Q5 (6 marks): The binomial expansion of (2 + 5x)4 is given by (2 + 5x)4 = A + 160x + Bx2 + 1000x3 + 625x4 5 (a) Find the value of A and the value of B. [2 marks] 5 (b) Show t
- November 2021, Paper 3, Q4 (5 marks): (a) Show that the first three terms, in descending powers of x, of the expansion of (2x − 3)10 are given by 1024x10 + px9 + qx8 where p and q are integers to be
- November 2020, Paper 2, Q3 (3 marks): Find the coefficient of x2 in the binomial expansion of 2x − 3 x 8 [3 marks]
- November 2020, Paper 3, Q7 (7 marks): (a) Using nCr = n! r!(n − r)! show that nC2 = n(n − 1) 2 [2 marks] 7 (b) (i) Show that the equation 2 × nC4 = 51 × nC2 simplifies to n2 − 5n − 300 = 0 [3 marks]
- June 2019, Paper 3, Q2 (1 mark): Find the value of 100! 98! × 3! Circle your answer. [1 mark] 50 147 1650 3300 161 700
- June 2018, Paper 2, Q2 (1 mark): Find the coefficient of x2 in the expansion of (1 + 2x)7 Circle your answer. [1 mark] 42 4 21 84
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