plumiTaylor series and Leibnitz's theorem: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 2.1 Taylor series and Leibnitz's theorem, 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.
Questions from
Paper
All papers
Exam
All years
Loading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDF
All 6 questions on Taylor series and Leibnitz's theorem, as a list
- June 2025, Further Pure 1, Q6 (11 marks): (i) Use L’Hospital’s Rule to show that lim cos sin x x x x 0 1 7 9 49 18 (4) (ii) y = x 2e 3x (a) Use Leibnitz’s theorem to show that, for k ∈ d d e k k k x y
- June 2024, Further Pure 1, Q5 (9 marks): y x x = e3 sin (a) Use Leibnitz’s theorem to show that d d e e 4 4 3 3 28 96 y x x x x x sin cos (6) (b) Hence express d d 4 4 y x in the form 3e sin x R x wher
- June 2022, Further Pure 1, Q8 (10 marks): 2 ( ) f ( ) ( ) f ( ) f ( ) ( )f ( ) f ( ) ( ! ( f ) ) 2! = − − = + − + + + + ′ ′′ … … r r The Taylor series expansion of x about x a is giv
- November 2021, Further Pure 1, Q6 (12 marks): 2 ( ) f ( ) ( ) f ( ) f ( ) ( )f ( ) f ( ) ( ! ( f ) ) 2! = − − = + − + + + + ′ ′′ … … r r The Taylor series expansion of x about x a is giv
- November 2020, Further Pure 1, Q4 (8 marks): f (x) = x4 sin(2 x) Use Leibnitz’s theorem to show that the coefficient of (x − π)8 in the Taylor series expansion of f (x) about π is 3 315 aπ bπ + where a and
- June 2019, Further Pure 1, Q2 (4 marks): Given that k is a real non-zero constant and that y = x3 sin kx use Leibnitz’s theorem to show that d d 5 5 2 2 3 2 2 2 y x k x A k x kx B k x C k kx = + + + (
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? Edexcel A-Level Further Maths past papers.
The Plumi iPad app also offers exam-style questions with AI feedback on your handwritten working.