Edexcel ALevel Maths, Pure Paper 1, June 2019 Question Walkthroughs

Pure Paper 1, 2019, Q1f(x) = 3x^3 + 2ax^2 – 4x + 5a
Given that (x + 3) is a factor of f(x), find the value of the constant a. 

Pure Paper 1, 2019, Q2Figure 1 shows a plot of part of the curve with equation y = cos x where x is measured in radians. Diagram 1, on the opposite page, is a copy of Figure 1.
(a) Use Diagram 1 to show why the equation cos x − 2x − 1/2 = 0 has only one real root, giving a reason for your answer. Given that the root of the equation is alpha, and that alpha is small, b) use the small angle approximation for cos x to estimate the value of alpha to 3 decimal places. 