plumiTrigonometry: Edexcel A‑Level Maths questions
Every Edexcel A-Level Maths exam question on P.5 Trigonometry, 2019–2025, with its mark scheme and examiner’s report.
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All 41 questions on Trigonometry, as a list
- June 2025, Pure 1, Q14 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Show that sin(x + 30°) + 3 cos(x +
- June 2025, Pure 1, Q15 (9 marks): O D C B A Figure 4 Figure 4 shows the plan view for the design of a stage. The shape of this design consists of a sector of a circle AOB joined to a rectangle O
- June 2025, Pure 2, Q4 (5 marks): A B C R D 13 cm 6.4 cm 8 cm Not to scale Figure 1 The shape ABCD, shown in Figure 1, consists of a triangle ABD containing a sector ABC of a circle with centre
- June 2025, Pure 2, Q6 (6 marks): In this question you must show detailed reasoning. (a) Given that x is small and in radians, use the small angle approximation for cos θ to show that 1 – cos 2
- June 2025, AS Pure, Q8 (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 x 90°, the e
- June 2024, Pure 1, Q11 (4 marks): A O R B C Figure 4 Figure 4 shows the design of a badge. The shape ABCOA is a semicircle with centre O and diameter 10 cm. OB is the arc of a circle with centre
- June 2024, Pure 1, Q12 (11 marks): (a) Express 140 cos θ – 480 sin θ in the form K cos(θ + α) where K > 0 and 0 < α < 90° State the value of K and give the value of α, in degrees, to 2 decimal pl
- June 2024, Pure 2, Q5 (3 marks): Given that θ is small and in radians, use the small angle approximations to find an approximate numerical value of tan 2 1 cos3 θ θ θ (3)
- June 2024, Pure 2, Q8 (7 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Prove that o 1 1 2tan sec
- June 2024, AS Pure, Q4 (5 marks): 140° (x + 3) cm x cm (x – 2) cm 30° A B C D Figure 1 Figure 1 shows a sketch of triangle ABD and triangle BCD Given that • ADC is a straight line • BD = (x + 3)
- June 2024, AS Pure, Q13 (9 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 si
- June 2023, Pure 1, Q4 (5 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The curve C has equation y =
- June 2023, Pure 1, Q8 (10 marks): FRONT OF STAGE Diagram NOT accurately drawn A O G 27.6 m 2.3 rad D E F B C 15 m BACK OF STAGE Figure 1 Figure 1 shows the plan view of a stage. The plan view sh
- June 2023, Pure 2, Q8 (6 marks): (a) Express 2 cos θ + 8 sin 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 give the value of α in
- June 2023, Pure 2, Q14 (7 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 2023, AS Pure, Q3 (4 marks): North C A B Figure 1 Figure 1 is a sketch showing the position of three phone masts, A, B and C. The masts are identical and their bases are assumed to lie in t
- June 2023, AS Pure, Q12 (9 marks): In this question you must show detailed reasoning. Solutions relying entirely on calculator technology are not acceptable. (a) Show that the equation 4 5 tan co
- June 2022, Pure 1, Q14 (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 − 60°
- June 2022, Pure 1, Q15 (10 marks): A 0.8 rad h r r F E D C B Figure 5 A company makes toys for children. Figure 5 shows the design for a solid toy that looks like a piece of cheese. The toy is mo
- June 2022, Pure 2, Q9 (5 marks): H O t H Figure 4 Figure 5 Figure 4 shows a sketch of a Ferris wheel. The height above the ground, H m, of a passenger on the Ferris wheel, t seconds after the w
- June 2022, Pure 2, Q15 (10 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Given that the first three terms of a
- June 2022, AS Pure, Q4 (6 marks): A 60° θ° C B (x + 2) cm 7x cm (3x + 10) cm Figure 1 Figure 1 shows a sketch of triangle ABC with AB = (x + 2) cm, BC = (3x + 10) cm, AC = 7x cm, angle BAC = 60°
- June 2022, AS Pure, Q13 (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 1 cosθ + tan θ
- November 2021, Pure 1, Q10 (8 marks): In this question you should show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Given that 1 + cos 2θ +
- November 2021, Pure 2, Q4 (3 marks): Given that θ is small and measured in radians, use the small angle approximations to show that 4 sin θ 2 + 3 cos2 θ » a + b θ + c θ 2 where a, b and c are integ
- November 2021, Pure 2, Q6 (5 marks): A O r 2r 2r θ r B C D E F Figure 1 The shape OABCDEFO shown in Figure 1 is a design for a logo. In the design • OAB is a sector of a circle centre O and radius
- November 2021, Pure 2, Q15 (11 marks): (a) Express 2cos θ – sin θ in the form R cos (θ + α), where R > 0 and 0 < α < π 2 Give the exact value of R and the value of α in radians to 3 decimal places. (
- November 2021, AS Pure, Q7 (5 marks): A parallelogram PQRS has area 50 cm 2 Given • PQ has length 14 cm • QR has length 7 cm • angle SPQ is obtuse find (a) the size of angle SPQ, in degrees, to 2 de
- November 2021, AS Pure, Q12 (9 marks): In this question you should show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (i) Solve, for 0 < θ 450°
- November 2020, Pure 1, Q6 (7 marks): (a) Express sin x + 2 cos x in the form R sin (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 in ra
- November 2020, Pure 1, Q11 (8 marks): y C2 B A O C1 x Figure 3 Circle C1 has equation x2 + y2 = 100 Circle C2 has equation (x − 15)2 + y2 = 40 The circles meet at points A and B as shown in Figure 3
- November 2020, Pure 1, Q12 (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 cosec θ − sin θ
- November 2020, Pure 2, Q10 (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 cos 3 A ≡ 4 cos
- November 2020, AS Pure, Q5 (6 marks): Not to scale A B C D 27° Figure 1 Figure 1 shows the design for a structure used to support a roof. The structure consists of four steel beams, AB, BD, BC and A
- November 2020, AS Pure, Q9 (8 marks): P(c, d) y O x Figure 3 Figure 3 shows part of the curve with equation y = 3 cos x°. The point P(c, d) is a minimum point on the curve with c being the smallest
- June 2019, Pure 1, Q6 (8 marks): (a) Solve, for –180° - ș - 180°, the equation 5 sin 2ș= 9 tan ș giving your answers, where necessary, to one decimal place. [6ROXWLRQVEDVHGHQWLUHO\RQJUDSKL
- June 2019, Pure 1, Q14 (7 marks): The curve C, in the standard Cartesian plane, is defined by the equation x = 4 sin 2\ 4 4 π π y − < < The curve C passes through the origin O (a) Find th
- June 2019, Pure 2, Q3 (3 marks): O 5 cm B A 40° Figure 1 Figure 1 shows a sector AOB of a circle with centre O, radius 5 cm and angle AOB = 40° The attempt of a student to find the area of the
- June 2019, Pure 2, Q12 (7 marks): (a) Prove cos3 sin θ θ + sin3 cos θ θ {FRWș ș z (90n)°, n ] (4) (b) Hence solve, for 90° ș 180°, the equation cos3 sin θ θ + sin3 cos θ θ = 4 giving any
- June 2019, AS Pure, Q6 (6 marks): A 3x cm 2x cm 60q B C Figure 1 Figure 1 shows a sketch of a triangle ABC with AB = 3x cm, AC = 2x cm and angle CAB = 60q Given that the area of triangle ABC is
- June 2019, AS Pure, Q12 (7 marks): (a) Show that 2 10sin 7cos 2 3 2cos θ θ θ − + + Ł±FRVș (4) (b) Hence, or otherwise, solve, for 0 - x 360q, the equation 10 7 2 3 2 2 sin cos cos x x x −
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