plumiThe t-formulae: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 1.1 The t-formulae, 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.
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All 13 questions on The t-formulae, 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 2025, AS Further Pure 1, Q1 (9 marks): In this question you must show all stages of your working. Solutions based entirely on calculator technology are not acceptable. The surface temperature of the
- 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
- June 2023, AS Further Pure 1, Q2 (7 marks): (a) Use the substitution t x tan 2 to show that the equation 3 cos x – 2 sin x = 1 can be written in the form 2t 2 + 2t – 1 = 0 (3) (b) Hence solve, for –1
- June 2022, Further Pure 1, Q2 (7 marks): During 2029, the number of hours of daylight per day in London, H, is modelled by the equation H = 0.3 sin x 60 – 4 cos x 60 + 11.5 0 x < 365 where x is
- June 2022, AS Further Pure 1, Q3 (7 marks): (a) Use t = tan 2 θ to show that, where both sides are defined 29 21sec 20 21tan θ θ − − ≡ 5 2 2 5 t t + + (4) (b) Hence, again using t = tan 2 θ , prove that,
- 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
- November 2020, AS Further Pure 1, Q3 (11 marks): (i) Use the substitution t x = tan 2 to prove that cot tan cosec , 2 x x x x nπ n + = ≠ Z ∈ (2) (ii) H metres Figure 1 An engineer models
- 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
- June 2019, AS Further Pure 1, Q1 (9 marks): (a) Write down the t-formula for sin x. (1) (b) Use the answer to part (a) (i) to find the exact value of sin x when tan x 2 2 ⎛ ⎝⎜ ⎞ ⎠⎟= (ii) to show that cos
- June 2018, AS Further Pure 1, Q1 (7 marks): (a) Use the substitution t = tan x 2 to show that the equation 5 sin x + 12 cos x = 2 can be written in the form 7t 2 − 5t − 5 = 0 (3) (b) Hence solve
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