plumiFurther calculus (option): Edexcel A‑Level Further Maths questions
Every Edexcel A-Level Further Maths exam question on FP.2 Further calculus (option), 2018–2025, with its mark scheme and examiner’s report.
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![June 2019 Further Pure 2, question 5: I x x n n n = ∈ ∫cosec d ] (a) Prove that, for n . 2 I n n I x x n n n n = − − − − − − 2 1 1 2 2 cosec cot (4) (b) Hence show that 2 6 3 56 cosec d 3 135 π π x](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/9fm0-4a-jun19-05-qp.webp)
All 20 questions on Further calculus (option), 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 2025, Further Pure 2, Q6 (8 marks): I x x n n 4 2 0 2 d (a) Prove that, for n 1 I n n I n n 8 2 1 1 (4) (b) Using the result from part (a) and showing all stages of your working, determine the
- June 2025, Further Pure 2, Q8 (10 marks): 60 cm 10 cm x y O C Figure 1 Figure 2 Figure 1 shows a satellite dish. Figure 2 shows a sketch of the curve C with equation y 2 = Ax 0 x 10 where A is a pos
- June 2024, Further Pure 1, Q3 (6 marks): Use L’Hospital’s rule to show that lim sin x x x 0 1 1 0 (6)
- 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 2024, Further Pure 2, Q6 (11 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. I nx x x n n cos( ) sin d 1
- June 2024, Further Pure 2, Q8 (13 marks): bell section y x = 9 2 1 9 e 9 2 O 9 x y Figure 1 Figure 2 Figure 1 shows a French horn with a detachable bell section. The shape of the bell section can be mod
- June 2023, Further Pure 2, Q8 (7 marks): (a) Prove that for n 1 I a n I n n n 2 1 4 where a is a constant to be determined. (4) (b) Hence determine the exact value of (3)
- June 2023, Further Pure 2, Q10 (12 marks): y x O C Figure 2 A solid playing piece for a board game is modelled by rotating the curve C, shown in Figure 2, through 2π radians about the x-axis. The curve C
- 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
- June 2022, Further Pure 2, Q9 (7 marks): 2 0 sin 2 d π n nI x x =∫ (a) Prove that for n 2 In = n n −1 In – 2 (4) (b) Hence determine the exact value of 2 5 5 0 64sin cos d π x x x ∫ (3)
- June 2022, Further Pure 2, Q10 (12 marks): Figure 2 O y C Figure 3 x Figure 2 shows a picture of a plant pot. The plant pot has • a flat circular base of radius 10 cm • a height of 15 cm Figure 3 shows a
- 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 2021, Further Pure 2, Q7 (15 marks): In this question you must show all stages of your working. You must not use the integration facility on your calculator. In = t t t n∫ + 4 5 2 d n 0 (a) Show
- November 2020, Further Pure 1, Q1 (5 marks): Use l’Hospital’s Rule to show that 2 sin (e cos(3 ) e) 3 lim tan(2 ) 2 π x x x x → − − = − (5)
- 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
- November 2020, Further Pure 2, Q7 (8 marks): In = ∫(4 – x2) –n dx n > 0 (a) Show that, for n > 0 I x n x n n I n n n + = − + − 1 2 8 4 2 1 8 ( ) (5) (b) Find I2 (3)
- 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 = + + + (
- June 2019, Further Pure 2, Q5 (8 marks): I x x n n n = ∈ ∫cosec d ] (a) Prove that, for n . 2 I n n I x x n n n n = − − − − − − 2 1 1 2 2 cosec cot (4) (b) Hence show that 2 6 3 56 cosec d 3 135 π π x
- June 2019, Further Pure 2, Q8 (13 marks): A B C D 5 cm Figure 1 Figure 1 shows the vertical cross section of a child’s spinning top. The point A is vertically above the point B and the height of the spi
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