CAIE A-Level Mathematics 2.6.3 Iteration formulae

CAIE A-Level Mathematics 2.6.3 Iteration formulae
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise rearranging equations into iteration formulae, then applying x_{n+1}=F(x_n) until the root is justified.

How this is tested

  • show a rearrangement gives the required x_{n+1}=F(x_n) form before iterating
  • use the initial value, record iterations to the stated accuracy and give the final root
  • check calculator mode when trig functions appear in the iteration formula

Question 3(c)

[Maximum number: 3]

（c）Use an iterative formula，based on the equation in part（b），to find the x－coordinate of the point of intersection correct to 3 decimal places．Give the result of each iteration to 5 decimal places．