CAIE A-Level Mathematics 2.6.3 Iteration formulae
Practise rearranging equations into iteration formulae, then applying x_{n+1}=F(x_n) until the root is justified.
- Syllabus
- 2028–2030
- Course
- Mathematics 9709
- Level
- AS
Exam points
- 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
2.6.3—Iteration formulae question 1
[Maximum number: 3]
Use an iterative formula, based on the equation in part (b), to find the root correct to 3 significant figures. Give the result of each iteration to 5 significant figures.
Use iteration process correctly at least once
M1
Obtain final answer 1.58
A1
Final answer required to exactly 3 sf .
Show sufficient iterations to 5 sf to justify answer or show a sign change in
interval [1.575, 1.585]
A1
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