plumiIntegration: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P3.5 Integration, 2019–2025, with its mark scheme and examiner’s report.
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All 23 questions on Integration, as a list
- June 2025, Pure 3 (P3), Q5 (4 marks): Find (i) sin2 3x x d ∫ (ii) x x x ( ) 2 3 2 4 d
- June 2025 (A), Pure 3 (P3), Q4 (8 marks): R C O x y 2 3 Figure 1 In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Figure 1 shows
- January 2025, Pure 3 (P3), Q4 (9 marks): Given that 4 2 3 8 4 4 3 2 2 2 x x x x Ax B Cx D x (a) (i) find the values of the constants A, B and C (ii) show that D = 0 (b) Hence, using algebraic integrati
- October 2024, Pure 3 (P3), Q9 (14 marks): y x O P l C R Figure 5 Figure 5 shows a sketch of part of the curve C with equation y = f (x) where f (x) = 6 4 2 2 1 2x x x x > – 1 2 (a) Find f′ (x) , giving
- June 2024, Pure 3 (P3), Q2 (7 marks): g( ) x x x x 2 5 8 2 2 (a) Write g (x) in the form Ax B C x 2 where A, B and C are integers to be found. (b) Hence use algebraic integration to show that 8 4 g(
- June 2024, Pure 3 (P3), Q6 (9 marks): y R P l O x Figure 3 In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Figure 3
- January 2024, Pure 3 (P3), Q7 (12 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 x
- October 2023, Pure 3 (P3), Q3 (6 marks): (a) Using the identity for cos (A + B) , prove that cos 2A ≡ 2 cos 2 A – 1 (b) Hence, using algebraic integration, find the exact value of 8 2 12 (5 4cos 3 )d π
- June 2023, Pure 3 (P3), Q3 (7 marks): (i) Find d dx x ln sin 2 3 writing your answer in simplest form. (ii) (a) Find d dx x 3 4 2 6 (b) Hence show that x x x R 3 4 2 0 2 5 d where R is an integer
- January 2023, Pure 3 (P3), Q4 (7 marks): f x x x x x x x x 2 15 35 21 4 3 3 4 3 2 2 (a) Find the values of the constants A, B, C and D such that f x Ax Bx C D x 2 2 3 (b) Hence find, f d x x
- January 2023, Pure 3 (P3), Q8 (5 marks): Find, in simplest form, 2 2 cos sin x x x d
- October 2022, Pure 3 (P3), Q1 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. f(x) = 2 4 15 3 4 3 2 x x x x
- June 2022, Pure 3 (P3), Q3 (6 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Given that k is a positive co
- June 2022, Pure 3 (P3), Q8 (12 marks): T t O v Figure 4 Figure 4 is a graph showing the velocity of a sprinter during a 100 m race. The sprinter’s velocity during the race, v m s –1, is modelled by t
- January 2022, Pure 3 (P3), Q3 (6 marks): (i) Find, in simplest form, ( ) 2 5 7 x x − ∫ d (ii) Show, by algebraic integration, that 3 0 4sin d ln 1 2cos = + ∫ π x x a x where a is a rational constant to
- October 2021, Pure 3 (P3), Q5 (6 marks): (i) Find, by algebraic integration, the exact value of 8 2 3 3 2 4 ( ) x x d (ii) Find, in simplest form, x x x 2 7 3 d
- October 2021, Pure 3 (P3), Q10 (7 marks): O x y a Figure 4 Figure 4 shows a sketch of part of the curve with equation y = (1 + 2 cos 2x)2 (a) Show that (1 + 2 cos 2x)2 ≡ p + q cos 2x + r cos 4x where p,
- June 2021, Pure 3 (P3), Q3 (8 marks): (i) Find 12 2 1 2 x x − ( ) ∫ d giving your answer in simplest form. (ii) (a) Write 4 3 2 x x + + in the form A + B x + 2 where A and B are constants to be foun
- January 2021, Pure 3 (P3), Q1 (3 marks): Find x x x x 2 3 5 2 0 − ∫ d > giving your answer in simplest form.
- January 2021, Pure 3 (P3), Q9 (4 marks): Find (i) 3 2 3 4 5 2 x x x x − − + ∫ d (ii) e e d 2 2 3 1 0 x x x x ( ) − ≠ ∫
- 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), Q9 (14 marks): (a) Given that x x x x x x x P Q x x 4 3 2 2 2 10 3 9 12 4 3 − − + − − − ≡ + + − − > find the value of the constant P and show that Q = 5 The curve C has equati
- January 2020, Pure 3 (P3), Q8 (10 marks): (i) Find, using algebraic integration, the exact value of 2 3 1 3 42 x x − ∫ d giving your answer in simplest form. (ii) h(x) = 2 7 8 1 1 3 2 2 x x x x − + + −
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