Edexcel ALevel Maths October 2021  Question Walkthroughs

Pure Paper 2, 2021, Q1In an arithmetic series
• the first term is 16 • the 21st term is 24 (a) Find the common difference of the series. (b) Hence find the sum of the first 500 terms of the series. 

Pure Paper 2, 2021, Q2The functions f and g are defined by f (x) = 7 – 2x^2, g (x) = 3x / (5x – 1)
(a) State the range of f b) Find gf (1.8) (c) Find g^–1(x) 

Pure Paper 2, 2021, Q3Using the laws of logarithms, solve the equation log3 (12y + 5) – log3 (1 – 3y) = 2


Pure Paper 2, 2021, Q4Given that θ is small and measured in radians, use the small angle approximations to show that 4 sin θ/2 + 3 cos2 θ = a + bθ + cθ^2 where a, b and c are integers to be found.


Pure Paper 2, 2021, Q5The curve C has equation y = 5x^4 – 24x^3 + 42x^2 – 32x + 11
(a) Find (i) dy/dx (ii) dy^2/d^2x (b) (i) Verify that C has a stationary point at x = 1 (ii) Show that this stationary point is a point of inflection, giving reasons for your answer. 

Pure Paper 2, 2021, Q6The 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 r • sector OFE is congruent to sector OAB • ODC is a sector of a circle centre O and radius 2r • AOF is a straight line Given that the size of angle COD is θ radians, (a) write down, in terms of θ, the size of angle AOB b) Show that the area of the logo is 1/2 r^2 (3θ + π) (c) Find the perimeter 