plumiTrigonometry: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P3.2 Trigonometry, 2019–2025, with its mark scheme and examiner’s report.
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All 30 questions on Trigonometry, as a list
- June 2025, Pure 3 (P3), Q2 (7 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. f (x) = 7 cos x – 24 sin x (a
- June 2025, Pure 3 (P3), Q8 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Prove that tan tan tan ta
- June 2025 (A), Pure 3 (P3), Q5 (10 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A curve C has equation y = 5
- June 2025 (A), Pure 3 (P3), Q7 (10 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Write sin 4θ in the form
- January 2025, Pure 3 (P3), Q8 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (i) Solve, for 0 < θ < π 3 co
- October 2024, Pure 3 (P3), Q1 (5 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Solve, for 0 < θ 360° , the
- October 2024, Pure 3 (P3), Q5 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Show that sin 3x can be w
- June 2024, Pure 3 (P3), Q4 (9 marks): f (x) = 8 sin x cos x + 4 cos 2 x – 3 (a) Write f (x) in the form a sin 2 x + b cos 2x + c where a, b and c are integers to be found. (b) Use the answer to part
- June 2024, Pure 3 (P3), Q7 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Given that 2 sin (x + 45°
- January 2024, Pure 3 (P3), Q9 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Show that the equation 3s
- October 2023, Pure 3 (P3), Q8 (8 marks): (a) Prove that 2 cosec 2 2θ (1 – cos 2θ) ≡ 1 + tan 2 θ (b) Hence solve for 0 < x < 360° , where x ≠ (90n)° , n ∈ , the equation 2 cosec 2 2x (1 – cos 2x) = 4
- June 2023, Pure 3 (P3), Q5 (7 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (i) Solve, for 0 < x < π x x
- June 2023, Pure 3 (P3), Q9 (10 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Show that cos sin sin cos
- January 2023, Pure 3 (P3), Q2 (6 marks): f x x x cos sin 2 (a) Express f (x) in the form where R and α are constants, R > 0 and Give the exact value of R and give the value of α, in radians, to 3 decim
- January 2023, Pure 3 (P3), Q5 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Prove that (b) Hence solv
- October 2022, Pure 3 (P3), Q8 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Express 8 sin x − 15 cos
- October 2022, Pure 3 (P3), Q9 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Given that cos 2θ − sin 3θ ≠
- June 2022, Pure 3 (P3), Q7 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Show that the equation 2
- June 2022, Pure 3 (P3), Q9 (9 marks): M x O y Figure 5 In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Figure 5 sho
- January 2022, Pure 3 (P3), Q2 (5 marks): (a) Show that the equation 8 cos θ = 3 cosec θ can be written in the form sin 2θ = k where k is a constant to be found. (b) Hence find the smallest positive sol
- January 2022, Pure 3 (P3), Q9 (8 marks): In this question you must show detailed reasoning. Solutions relying entirely on calculator technology are not acceptable. (i) Solve, for 0 < x π, the equatio
- October 2021, Pure 3 (P3), Q4 (7 marks): In this question you should show detailed reasoning. Solutions relying entirely on calculator technology are not acceptable. (a) Show that the equation 2 sin(θ
- June 2021, Pure 3 (P3), Q2 (9 marks): (a) Show that 1 2 2 2 −cos sin x x º k tan x x ¹ (90n)° n where k is a constant to be found. (b) Hence solve, for 0 < θ < 90° ( ) 9 1 cos2 2sin 2 θ θ − = 2
- June 2021, Pure 3 (P3), Q9 (8 marks): (a) Express 12 sin x − 5 cos x in the form Rsin (x − α), where R and α are constants, R > 0 and 0 < α < 2 π . Give the exact value of R and give the value of α
- January 2021, Pure 3 (P3), Q7 (9 marks): (a) Prove that sin 2 cos2 cosec cos sin 2 + ≡ ≠ ∈ x x nπ x x n x x Z (b) Hence solve, for 2 2 π π θ − < < 2 sin 4 cos4 7 3cot 2 cos2 sin 2 θ θ θ θ θ + + = givin
- October 2020, Pure 3 (P3), Q1 (5 marks): Solve, for 0 x < 360°, the equation 2 cos 2 x = 7 cos x giving your solutions to one decimal place. (Solutions based entirely on graphical or numerical method
- October 2020, Pure 3 (P3), Q5 (8 marks): (a) Show that sin 3x ≡ 3 sin x − 4 sin3 x (b) Hence find, using algebraic integration, 3 3 0 sin d π x x ∫
- October 2020, Pure 3 (P3), Q7 (9 marks): (a) Express cos x + 4 sin x in the form R cos (x − α) where R > 0 and 0 < α < 2 π Give the exact value of R and give the value of α, in radians, to 3 decimal pl
- January 2020, Pure 3 (P3), Q5 (8 marks): (a) Use the substitution t = tan x to show that the equation 12 tan 2x + 5 cot x sec2 x = 0 can be written in the form 5t 4 – 24t2 – 5 = 0 (b) Hence solve, for
- January 2020, Pure 3 (P3), Q9 (7 marks): f(θ) = 5 cos θ – 4 sin θ θ ∈ (a) Express f(θ) in the form R cos (θ + α), where R and α are constants, R > 0 and 0 < α < 2 π. Give the exact value of R and giv
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