Exam-style question
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In an iterative-method question, what should be checked when using x_(n+1) = g(x_n)?.
- A.Show the recurrence, starting value, successive approximations and any sign of convergence or failure.
- B.Use one iteration only and assume it is the exact root.
- C.Avoid recording the starting value because it is not part of the method.
- D.Draw a histogram instead of a cobweb or staircase diagram.
Model answer
What a good answer should say
- The correct answer is Show the recurrence, starting value, successive approximations and any sign of convergence or failure.
- This is the best choice because it names the A-level method being tested and explains the mathematical check needed for this objective.
This answer is tied to the objective: I2 Solve equations approximately using simple iterative methods; draw associated cobweb and staircase diagrams; solve equations using the Newton-Raphson method and other recurrence relations of the form x_(n+1) = g(x_n); understand how such methods can fail..
Explanation
Why this works
Use the explanation to connect the worked answer back to I2 Solve equations approximately using simple iterative methods; draw associated cobweb and staircase diagrams; solve equations using the Newton-Raphson method and other recurrence relations of the form x_(n+1) = g(x_n); understand how such methods can fail..
Show the recurrence, starting value, successive approximations and any sign of convergence or failure. is correct.
It is specific to the learning objective, keeps the method visible, and avoids the generic shortcut described by the distractors.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: application.
- Check the operation, notation, units, and final answer form against the question before moving on.
Common mistake
No common mistake is linked to this question yet.