Edexcel Mathematics Specimen paper · Paper 2 · Question 2 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

Specimen paper · Paper 2 · Question 2 · 5 marks

2. (a) Given that θ is small, use the small angle approximation for cos θ to show that 1 + 4 cos θ + 3 cos2 θ ≈ 8 – 5θ^2 Adele uses θ = 5° to test the approximation in part (a). Adele’s working is shown below. (3) Using my calculator, 1 + 4 cos (5°) + 3 cos2 (5°) = 7.962, to 3 decimal places. Using the approximation 8 – 5θ^2 gives 8 – 5(5)2 = –117 Therefore, 1 + 4 cos θ + 3 cos2θ θ ≈ 8 – 5θ^2 is not true for θ = 5° (b) (i) Identify the mistake made by Adele in her working. (ii) Show that 8 – 5θ^2 can be used to give a good approximation to 1 + 4 cos θ + 3 cos2 for an angle of size 5°"

Lesson: Introduction to Differentiation and First Principles (Polynomials)