plumiDifferentiation: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P1.4 Differentiation, 2019–2025, with its mark scheme and examiner’s report.
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All 38 questions on Differentiation, as a list
- June 2025, AS Pure 1 (P1), Q2 (5 marks): The curve C has equation y x x 2 4 3 5 2 (a) Find d d y x writing your answer in simplest form. The point P lies on C. Given that • the x coordinate of P is 2 k
- 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), Q5 (10 marks): y = 1 2 x 4 – 3 + 10 2x x ≠ 0 (a) Find y x d ∫ writing the answer in simplest form. (b) (i) Find d d y x writing the answer in simplest form. (ii) Hence find th
- 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), Q5 (8 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. The curve C has equation y x x 4 2 9 3
- 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), Q9 (10 marks): O C x y Figure 4 Figure 4 shows a sketch of the curve C with equation y = f(x), where f(x) = ( )( ) x x x 5 3 4 20 2 (a) Deduce the range of values of x for whi
- June 2024, AS Pure 1 (P1), Q7 (8 marks): The curve C has equation y = f(x) where f(x) = 2x 3 – kx 2 + 14x + 24 and k is a constant. (a) Find, in simplest form, (i) f′(x) (ii) f′′(x) The curve with equa
- 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), Q3 (6 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. y = x 3 + 96 x + 5 x > 0 (a) Find d d
- June 2024 (R), AS Pure 1 (P1), Q10 (10 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. The curve C has equation y = 2 3 x 3 –
- January 2024, AS Pure 1 (P1), Q3 (7 marks): The curve C has equation y x x x 5 8 2 0 3 2 > (a) Find d d y x writing your answer in simplest form. The point P(2, 4) lies on C. (b) Find an equation for the
- 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), Q1 (5 marks): Given that y x x x 5 3 7 3 2 x > 0 find, in simplest form, (a) d d y x (b) d d 2 2 y x
- 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), Q4 (7 marks): In this question you must show all stages of your working. (a) Write y x x x 5 8 2 3 3 in the form y = Ax p + Bx q where A, B, p and q are constants to be found
- 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), Q1 (5 marks): A curve C has equation y = 2 + 10x 1 2 – 2x 3 2 x > 0 (a) Find d d y x giving your answer in simplest form. (b) Hence find the exact value of the gradient of th
- October 2022, AS Pure 1 (P1), Q1 (6 marks): The curve C has equation y x x x = − + 3 2 4 17 x > 0 (a) Find d d y x , giving your answer in simplest form. The point R 2 13 2 , lies on C. (b) Find
- 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 =
- October 2022, AS Pure 1 (P1), Q9 (14 marks): O P l M C x y Figure 3 Figure 3 shows a sketch of the curve C with equation y = 1 2 x2 – 10x + 22 (a) Write 1 2 x2 – 10x + 22 in the form a(x + b) 2 + c where a
- 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
- June 2022, AS Pure 1 (P1), Q10 (12 marks): y O l C B A x Figure 5 Figure 5 shows a sketch of the curve C with equation y = 2 7 x3 + 1 7 x2 − 5 2 x + k where k is a constant. (a) Find d d y x The line l,
- 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), Q2 (5 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. A curve has equation y = 3x 5 + 4x 3 –
- October 2021, AS Pure 1 (P1), Q6 (10 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. A curve C has equation y = f(x) where
- 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), Q1 (8 marks): The curve C has equation y x x x x = + + − > 2 3 4 8 3 5 0 (a) Find d d y x, giving your answer in simplest form. The point P (4, 3) lies on C. (b) Find the equ
- January 2021, AS Pure 1 (P1), Q1 (8 marks): A curve has equation y x x x x = − − + > 2 5 3 2 7 0 3 2 (a) Find, in simplest form, d d y x The point P lies on the curve and has x coordinate 1 2 (b) Find an
- January 2021, AS Pure 1 (P1), Q7 (9 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. f ( ) x x x x = − − > 2 3 5 0 (a) Solv
- October 2020, AS Pure 1 (P1), Q8 (11 marks): The curve C has equation y = (x – 2)(x – 4) 2 (a) Show that d d y x = 3x 2 – 20x + 32 The line l1 is the tangent to C at the point where x = 6 (b) Find the equa
- January 2020, AS Pure 1 (P1), Q3 (6 marks): P(3,16) O y x Figure 1 Figure 1 shows part of the curve with equation y = x2 + 3x – 2 The point P(3,16) lies on the curve. (a) Find the gradient of the tangent
- January 2020, AS Pure 1 (P1), Q9 (6 marks): In this question you must show all stages of your working. . Solutions relying on calculator technology are not acceptable. A curve has equation . y x x x = + >
- June 2019, AS Pure 1 (P1), Q1 (6 marks): The curve C has equation y x x = − + 1 8 24 1 3 (a) Find d d y x , giving the answer in its simplest form. The point P í OLHVRQC. (b) Find the equation
- 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
- June 2019, AS Pure 1 (P1), Q10 (10 marks): A curve has equation y = f(x), where f(x) = (xí x 2 The curve touches the x-axis at the point P and crosses the x-axis at the point Q. (a) State the coo
- January 2019, AS Pure 1 (P1), Q6 (7 marks): (Solutions based entirely on graphical or numerical methods are not acceptable.) Given f (x) = 2x 5 2 − 40x + 8 x > 0 (a) solve the equation f ʹ (x) = 0 (b) sol
- 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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