plumiInduction: matrices, recurrences and inequalities: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 1.3 Induction: matrices, recurrences and inequalities, 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.
All papers
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 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 PDFLoading the question…
Open the full PDF
All 12 questions on Induction: matrices, recurrences and inequalities, as a list
- June 2025, Core Pure 2, Q3 (12 marks): Given A 1 5 0 2 (a) prove by mathematical induction that, for n ∈ An n n 1 5 2 1 0 2 (6) Given B 1 0 0 1 (b) describe fully the singl
- June 2025, Further Pure 2, Q4 (9 marks): A sequence is defined by un+2 = 6un+1 – 8un n 1 u1 = 399.6 u2 = 798.4 (a) Prove by induction that, for n ∈ un = 200(2 n) – 1 10 (4 n) (6) (b) Hence determin
- June 2023, Core Pure 1, Q4 (5 marks): Prove by induction that for n ∈ 1 2 0 1 1 2 0 1 n n (5)
- June 2023, Core Pure 2, Q6 (6 marks): Given that y = e 2x sinh x prove by induction that for n ∈ d d e n n x n n y x x x 2 3 1 2 3 1 2 sinh cosh (6)
- June 2023, Further Pure 2, Q3 (9 marks): In a model for the number of subscribers to a new social media channel it is assumed that • each week 20% of the subscribers at the start of the week cancel the
- June 2022, Core Pure 2, Q3 (11 marks): M = 3 0 1 a where a is a constant (a) Prove by mathematical induction that, for n ∈ M n = 3 2 3 1 0 1 n n a ( ) − (6) Triangle T has
- June 2022, Further Pure 2, Q3 (8 marks): A B C Figure 1 There are three lily pads on a pond. A frog hops repeatedly from one lily pad to another. The frog starts on lily pad A, as shown in Figure 1. In
- June 2022, AS Core Pure, Q7 (6 marks): Prove by mathematical induction that, for n ∈ − − = − − + 5 9 4 7 1 6 9 4 1 6 n n n n n (6)
- November 2021, Further Pure 2, Q6 (6 marks): A recurrence system is defined by un+2 = 9(n + 1) 2 un − 3un+1 n 1 u1 = −3, u2 = 18 Prove by induction that, for n ∈ , un = (−3) n n! (6)
- November 2020, AS Further Pure 2, Q4 (10 marks): Sam borrows £10 000 from a bank to pay for an extension to his house. The bank charges 5% annual interest on the portion of the loan yet to be repaid. Immediate
- June 2018, AS Core Pure, Q8 (12 marks): (i) Prove by induction that for n + 5 8 2 3 4 1 8 2 1 4 − − = + − − n n n n n (6) (ii) Prove by induction that for n + f (n) = 4n + 1 +
- June 2018, AS Further Pure 2, Q3 (10 marks): 3 A tree at the bottom of a garden needs to be reduced in height. The tree is known to increase in height by 15 centimetres each year. On the first day of every
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.