plumiIntegration: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P1.5 Integration, 2019–2025, with its mark scheme and examiner’s report.
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All 35 questions on Integration, as a list
- June 2025, AS Pure 1 (P1), Q3 (5 marks): Find x x x 3 3 2 d writing your answer in simplest form.
- June 2025, AS Pure 1 (P1), Q8 (11 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A curve has equation y = f (x
- June 2025 (A), AS Pure 1 (P1), Q10 (10 marks): The curve C has equation y = f (x) . Given that • f ′ (x) = k x x ( ) −3 5 where k is a constant • the point P with x coordinate 4 lies on C • the equation of t
- January 2025, AS Pure 1 (P1), Q1 (4 marks): Find 8 6 2 5 3 3 x x x x d giving your answer in simplest form.
- January 2025, AS Pure 1 (P1), Q6 (10 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 =
- October 2024, AS Pure 1 (P1), Q3 (9 marks): In this question you must show all stages of your working. f(x) = ( ) x x + 5 2 x > 0 (a) Find ∫f(x) dx (b) (i) Show that when f′(x) = 0 3 10 25 0 2 x x (ii) He
- October 2024, AS Pure 1 (P1), Q8 (7 marks): A curve C has equation y = f(x). The point P with x coordinate 3 lies on C Given • f′(x) = 4x 2 + kx + 3 where k is a constant • the normal to C at P has equati
- June 2024, AS Pure 1 (P1), Q1 (3 marks): Find 10 3 2 7 4 3 x x x d giving each term in simplest form.
- June 2024, AS Pure 1 (P1), Q10 (10 marks): The curve C has equation y = f(x) where x > 0 Given that • f′(x) = 6x – 2 1 3 2 2 x x x • the point P(4, 12) lies on C (a) find the equation of the normal to C
- June 2024 (R), AS Pure 1 (P1), Q1 (4 marks): Find 1 2 3 4 3x x x d writing your answer in simplest form.
- June 2024 (R), AS Pure 1 (P1), Q8 (11 marks): A curve C with equation y = f (x) passes through the point R(4, 13). Given that f′ (x) = 2(x – 3)(3x + 2) (a) use integration to find f (x), giving your answer
- January 2024, AS Pure 1 (P1), Q1 (5 marks): Find ( )( )( ) 2 5 3 2 2 5 x x x x d writing your answer in simplest form.
- January 2024, AS Pure 1 (P1), Q10 (8 marks): In this question you must show all stages of your working. The curve C has equation y = f (x), x > 0 Given that • the point P 2, 8 2 lies on C • f'( ) x x k x 4
- October 2023, AS Pure 1 (P1), Q7 (10 marks): The curve C has equation y = f(x) where x > 0 Given that • fʹ(x) = 4 10 7 4 2 1 2 1 2 x x x • the point P(4, –1) lies on C (a) (i) find the value of the gradien
- June 2023, AS Pure 1 (P1), Q8 (10 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Find the equation of the
- January 2023, AS Pure 1 (P1), Q3 (5 marks): Find 4 3 2 5 2 x x x + ∫ d giving your answer in simplest form.
- January 2023, AS Pure 1 (P1), Q11 (8 marks): A curve C has equation y = f(x), x > 0 Given that • f′′(x) = 4x + 1 x • the point P has x coordinate 4 and lies on C • the tangent to C at P has equation y = 3x
- October 2022, AS Pure 1 (P1), Q2 (7 marks): Given that (x – 5)(2x + 1)(x + 3) ≡ ax3 + bx2 –32x – 15 where a and b are constants, (a) find the value of a and the value of b. (b) Hence find ( )( )( ) x x x
- October 2022, AS Pure 1 (P1), Q5 (9 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 2022, AS Pure 1 (P1), Q1 (4 marks): Find 10 6 3 5 3 2 x x x x + − ∫ d giving your answer in simplest form.
- June 2022, AS Pure 1 (P1), Q7 (9 marks): The curve C has equation y = f(x), x > 0 Given that • f′(x) = 2 x + A x2 + 3 , where A is a constant • f′′(x) = 0 when x = 4 (a) find the value of A. Given also
- January 2022, AS Pure 1 (P1), Q1 (4 marks): Find 8 5 2 3 1 3 4 x x x − − ∫ d giving each term in simplest form.
- January 2022, AS Pure 1 (P1), Q6 (11 marks): The curve C has equation y = f(x) where x > 0 Given that • f′(x) = ( ) x x x + 3 2 • the point P(4, 20) lies on C (a) (i) find the value of the gradient at P (i
- October 2021, AS Pure 1 (P1), Q1 (5 marks): Find 12 1 6 3 2 3 4 x x x x + − ∫ d giving each term in simplest form.
- October 2021, AS Pure 1 (P1), Q10 (7 marks): A curve has equation y = f(x), x > 0 Given that • fʹ(x) = ax – 12x 1 3 , where a is a constant • fʹʹ(x) = 0 when x = 27 • the curve passes through the point (1,
- June 2021, AS Pure 1 (P1), Q4 (6 marks): Find ( )( ) 3 2 5 4 x x x x + − ∫ d writing each term in simplest form.
- June 2021, AS Pure 1 (P1), Q6 (8 marks): The curve C has equation y = f(x), x > 0 Given that ● C passes through the point P (8, 2) ● fʹ(x) = 32 3 3 2 2 3 x x + −( ) (a) find the equation of the tangent
- January 2021, AS Pure 1 (P1), Q9 (11 marks): (i) Find ( ) 3 2 4 2 x x x + ∫ d x > 0 giving your answer in simplest form. (ii) A curve C has equation y = f(x). Given ● fʹ(x) = x2 + ax + b where a and b are
- October 2020, AS Pure 1 (P1), Q9 (6 marks): A curve with equation y = f(x) passes through the point (9, 10). Given that f′(x) = 27x 2 – 21 5 2 3x x x − x > 0 find f(x), fully simplifying each term.
- January 2020, AS Pure 1 (P1), Q1 (4 marks): Find, in simplest form, 8 3 1 2 5 3x x x − − ∫ d
- January 2020, AS Pure 1 (P1), Q11 (11 marks): A curve has equation y = f(x), where . f ʹʹ(x) = 6 0 3x x x + > The point P(4, –50) lies on the curve. Given that fʹ(x) = –4 at P, (a) find the equation of the
- June 2019, AS Pure 1 (P1), Q4 (5 marks): Find 4 1 2 2x x x + ∫ d giving the answer in its simplest form.
- June 2019, AS Pure 1 (P1), Q8 (9 marks): The curve C with equation y = f(x), x 0, passes through the point P *LYHQWKDWIމ x) = 4 x íí 8 3 2x (a) find the equation of the normal to C at P
- January 2019, AS Pure 1 (P1), Q1 (4 marks): Find ∫ − + 2 3 1 2 5 3 3 x x x d simplifying your answer.
- January 2019, AS Pure 1 (P1), Q12 (9 marks): The curve with equation y = f ( x ), x > 0, passes through the point P(4, −2). Given that d d y x x x x = − − 3 10 1 2 (a) find the equation of the tangent to t
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