: Edexcel past-paper questions pack
Back to the topic page

Binomial expansion

Past-paper questions pack

Name
Class
Date set
Date due
Score/ 98

Questions are numbered; the mark schemes (the answer key) follow on separate pages so the question pages can be handed out alone. www.mathsaleveltutor.com

Edexcel AS and A-level Maths past-paper questions since June 2018 · 33 parts, 98 marks · mark schemes follow the questions · www.mathsaleveltutor.com · Questions and mark schemes © Pearson Education Ltd

1. June 2025 · AS Paper 1 · Q14(a) · 2 marks
14. In this question you must show detailed reasoning. f (x) = (1 + kx) where k is a constant. Given that the first 3 terms, in ascending powers of x, of the binomial series expansion of f (x) are 1 + 8kx + px where p is a constant, (a) find p in terms of k. (2)
2. June 2025 · AS Paper 1 · Q14(b) · 5 marks
2 f (x) x ≠ 0 ; g (x) = a :9 x where a is a constant. Given that the first 3 terms, in ascending powers of x, of the series expansion of g (x) are – 2 x – 21 – 90x (b) find the possible pairs of values of a and k. (5)
3. June 2024 · Paper 1 · Q2(a) · 3 marks
2. (a) Find, in ascending powers of x, the first four terms of the binomial expansion of / x giving each term in simplest form. (3)
4. June 2024 · Paper 1 · Q2(b) · 1 marks
(b) Give a reason why x = – 2 9 should not be used in the expansion to find an approximation to (1)
5. June 2024 · AS Paper 1 · Q6(a) · 2 marks
6. The binomial expansion of (1 + ax) up to and including the term in x 2 is 1 – 15 2 x + kx where a and k are constants. (a) Show that a = – 5 (2)
6. June 2024 · AS Paper 1 · Q6(b) · 2 marks
(b) Hence find the value of k (2)
7. June 2024 · AS Paper 1 · Q6(c) · 2 marks
Using the expansion and making your method clear, < (c) find an estimate for the value of 17 87 , giving your answer to 4 decimal places. ;: (2)
8. June 2023 · AS Paper 1 · Q14 · 5 marks
14. Find, in simplest form, the coefficient of x5 in the expansion of (5)
9. June 2023 · Paper 2 · Q13(a) · 4 marks
13. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Find the first three terms, in ascending powers of x, of the binomial expansion of (3 + x) –2 writing each term in simplest form. (4)
10. June 2023 · Paper 2 · Q13(b) · 4 marks
(b) Using the answer to part (a) and using algebraic integration, estimate the value of 0.4 ∫ x d x (3 + x ) 0.2 giving your answer to 4 significant figures. (4)
11. June 2022 · AS Paper 1 · Q6(a) · 4 marks
6. (a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of x - giving each term in simplest form. (4)
12. June 2022 · AS Paper 1 · Q6(b) · 2 marks
x - x x = - f ( ) x (b) Find the coefficient of x2 in the series expansion of f(x), giving your answer as a simplified fraction. (2)
13. June 2022 · Paper 2 · Q7(a) · 4 marks
7. (a) Find the first four terms, in ascending powers of x, of the binomial expansion of - x writing each term in simplest form. (4)
14. June 2022 · Paper 2 · Q7(b) · 1 marks
A student uses this expansion with x = 1 9 to find an approximation for Using the answer to part (a) and without doing any calculations, (b) state whether this approximation will be an overestimate or an underestimate of giving a brief reason for your answer. (1)
15. Oct 2021 · AS Paper 1 · Q8(a) · 4 marks
8. g(x) = (2 + ax) 8 where a is a constant Given that one of the terms in the binomial expansion of g(x) is 3402x (a) find the value of a. (4)
16. Oct 2021 · AS Paper 1 · Q8(b) · 3 marks
Using this value of a, (b) find the constant term in the expansion of + + ax ( ) x (3)
17. Oct 2021 · Paper 1 · Q9(b) · 7 marks
(b) (i) Use binomial expansions to show that, in ascending powers of x f(x) = p + qx + rx2 + … where p, q and r are simplified fractions to be found. (ii) Find the range of values of x for which this expansion is valid. (7)
18. Oct 2020 · Paper 1 · Q1(a) · 3 marks
1. (a) Find the first four terms, in ascending powers of x, of the binomial expansion of ( ) + x giving each term in simplest form. (3)
19. Oct 2020 · Paper 1 · Q1(b) · 2 marks
(b) Explain how you could use x = 1 32 in the expansion to find an approximation for There is no need to carry out the calculation. (2)
20. Oct 2020 · AS Paper 1 · Q6(a) · 3 marks
6. (a) Find the first 4 terms, in ascending powers of x, in the binomial expansion of (1 + kx)10 where k is a non-zero constant. Write each coefficient as simply as possible. (3)
21. Oct 2020 · AS Paper 1 · Q6(b) · 3 marks
Given that in the expansion of (1 + kx)10 the coefficient x3 is 3 times the coefficient of x, (b) find the possible values of k. (3)
22. Oct 2020 · Paper 2 · Q4 · 3 marks
4. In the binomial expansion of (a + 2x) 7 where a is a constant the coefficient of x4 is 15 120 Find the value of a. (3)
23. June 2019 · Paper 1 · Q4(a) · 4 marks
4. (a) Find the first three terms, in ascending powers of x, of the binomial expansion of 4 -x giving each coefficient in its simplest form. (4)
24. June 2019 · Paper 1 · Q4(b)(i) · 1 marks
The expansion can be used to find an approximation to Possible values of x that could be substituted into this expansion are: Ɣ x = –14 because = = x - Ɣ x = 2 because = = x - Ɣ x = -1 2 because = = x - (b) Without evaluating your expansion, (i) state, giving a reason, which of the three values of x should not be used (1)
25. June 2019 · Paper 1 · Q4(b)(ii) · 1 marks
(ii) state, giving a reason, which of the three values of x would lead to the most accurate approximation to (1)
26. June 2019 · AS Paper 1 · Q8(a) · 4 marks
8. (a) Find the first 3 terms, in ascending powers of x, of the binomial expansion of x ⎛ ⎞ + ⎝⎜ ⎠⎟ giving each term in its simplest form. (4)
27. June 2019 · AS Paper 1 · Q8(b) · 1 marks
(b) Explain how you could use your expansion to estimate the value of 1.925 You do not need to perform the calculation. (1)
28. June 2018 · AS Paper 1 · Q11(a) · 4 marks
11. (a) Find the first 3 terms, in ascending powers of x, of the binomial expansion of x ⎛ ⎞ - ⎝⎜ ⎠⎟ giving each term in its simplest form. (4)
29. June 2018 · Paper 1 · Q11(a) · 6 marks
+ x 11. (a) Use binomial expansions to show that + x - x » - x (6)
30. June 2018 · AS Paper 1 · Q11(b) · 2 marks
x ⎛ ⎞ f(x) = (a + bx) 2 - , where a and b are constants ⎝⎜ ⎠⎟ Given that the first two terms, in ascending powers of x, in the series expansion of f(x) are 128 and 36x, (b) find the value of a, (2)
31. June 2018 · Paper 1 · Q11(b) · 1 marks
A student substitutes x = 1 2 into both sides of the approximation shown in part (a) in an attempt to find an approximation to (b) Give a reason why the student should not use x = 1 (1)
32. June 2018 · AS Paper 1 · Q11(c) · 2 marks
(c) find the value of b. (2)
33. June 2018 · Paper 1 · Q11(c) · 3 marks
(c) Substitute x = 1 11 into + x x x = + - - x to obtain an approximation to 6 . Give your answer as a fraction in its simplest form. (3)

Mark schemes

Each mark scheme shows the whole question; the parts on this topic are the ones listed above.

June 2025 · AS Paper 1 · Q14
Mark scheme June 2025 Paper 1 Q14(b)
June 2024 · Paper 1 · Q2
Mark scheme June 2024 Paper 1 Q2(b)
June 2024 · AS Paper 1 · Q6
Mark scheme June 2024 Paper 1 Q6(c)
June 2023 · AS Paper 1 · Q14
Mark scheme June 2023 Paper 1 Q14
June 2023 · Paper 2 · Q13
Mark scheme June 2023 Paper 2 Q13(b)
June 2022 · AS Paper 1 · Q6
Mark scheme June 2022 Paper 1 Q6(b)
June 2022 · Paper 2 · Q7
Mark scheme June 2022 Paper 2 Q7(b)
Oct 2021 · AS Paper 1 · Q8
Mark scheme Oct 2021 Paper 1 Q8(b)
Oct 2021 · Paper 1 · Q9
Mark scheme Oct 2021 Paper 1 Q9(b)
Oct 2020 · Paper 1 · Q1
Mark scheme Oct 2020 Paper 1 Q1(b)
Oct 2020 · AS Paper 1 · Q6
Mark scheme Oct 2020 Paper 1 Q6(b)
Oct 2020 · Paper 2 · Q4
Mark scheme Oct 2020 Paper 2 Q4
June 2019 · Paper 1 · Q4
Mark scheme June 2019 Paper 1 Q4(b)(ii)
June 2019 · AS Paper 1 · Q8
Mark scheme June 2019 Paper 1 Q8(b)
June 2018 · AS Paper 1 · Q11
Mark scheme June 2018 Paper 1 Q11(c)
June 2018 · Paper 1 · Q11
Mark scheme June 2018 Paper 1 Q11(c)