The curve C has equation y = x(x - 2)(x - 4).
(a) Sketch C, showing where it meets the coordinate axes.
(b) Find the total area of the regions bounded by C and the x-axis between x = 0 and x = 4.
From Paper 2: Pure Mathematics 2
57 marks
(a) Express (x + 11)/((x + 3)(x - 1)2) in partial fractions.
(b) Hence find the exact value of ∫23 (x + 11)/((x + 3)(x - 1)2) dx, giving your answer in the form a + bln 3/5.
From Paper 2: Pure Mathematics 2
68 marks
(a) Find ∫ x2 ex dx.
(b) Hence find the exact value of ∫01 x2 ex dx.
From Paper 2: Pure Mathematics 2
710 marks
(a) Find the particular solution of dy/dx = (y + 1)cos x, given that y = 2 when x = 0. Give your answer in the form y = f(x).
(b) Find the exact maximum and minimum values of y.
From Paper 2: Pure Mathematics 2
1212 marks
(a) Use the substitution u = x + 1 to find the exact value of ∫03 x√(x + 1) dx.
(b) Use the trapezium rule with 3 strips to estimate the same integral.
(c) Find the percentage error in your estimate and explain why the trapezium rule gives an overestimate here.
Score 0 / 51 · 0 of 6 marked
This paper is written by Plasmo in the style of the Edexcel A-Level Maths exam. It is not a past paper and is not produced or endorsed by the exam board.