plumiWeierstrass substitution: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 2.3 Weierstrass substitution, 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 Weierstrass substitution, as a list
- June 2025, Further Pure 1, Q5 (8 marks): (a) Use the substitution t x tan 2 to show that 1 1 4 1 1 2 2 cosec d d x x t t t t (3) (b) Hence show that 1 1 1 2 cosec d x x B x
- June 2024, Further Pure 1, Q7 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Use the substitution t = tan 2
- June 2023, Further Pure 1, Q5 (8 marks): (a) Show that the substitution t x tan 2 transforms the integral 1 d 2sin cos 5 x x x into the integral 2 1 d 3 2 2 t t t (4) (b) Hence determine 1 d 2sin
- November 2021, Further Pure 1, Q2 (10 marks): (i) Use the substitution t = tan x 2 to prove the identity sin cos sin cos x x x x − + + − 1 1 ≡ sec x + tan x x ≠ 2 nπ n (5) (ii) Use the substitution t =
- November 2020, Further Pure 1, Q8 (16 marks): f ( ) sin cos x x x = + − 3 13 6 5 Using the substitution t = tan x 2 (a) show that f ( x ) can be written in the form 3 1 2 3 1 6 2 2 ( ) ( ) + + + t
- June 2019, Further Pure 1, Q5 (8 marks): 1 d 0 4cos 3sin 4 π I x x x x = − ∫ < < Use the substitution t x = ⎛ ⎝⎜ ⎞ ⎠⎟ tan 2 to show that I x x k = + ⎛ ⎝⎜⎞ ⎠⎟ − ⎛ ⎝⎜⎞ ⎠⎟ ⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ + 1 5 2 2 1
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.