Iteration
AQA GCSE Maths revision on Iteration. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
When using an iterative formula to find a root of an equation, what does a 'convergent' sequence represent?
- A) The values get closer to a specific limit
- B) The values fluctuate between two points
- C) The values increase towards infinity
- D) The values remain exactly the same
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Answer: The values get closer to a specific limit
In iteration, convergence occurs when the output of each step gets progressively closer to the actual root of the equation. If the sequence diverges, the values move further away from the root, making the method fail to find a solution.
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Question 2
If an iterative formula produces a sequence that grows larger with every step, what term is used to describe this behaviour?
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Answer: Divergence
Divergence happens when the iterative process fails to home in on the solution. Instead of settling on a single value, the outputs move towards infinity or oscillate uncontrollably.
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Question 3
A student is asked to solve x^3 + x - 5 = 0 using iteration. They rearrange it to x = 5 - x^3. Why is this a poor choice of rearrangement?
- A) The rearrangement does not lead to convergence
- B) The equation has no real roots
- C) The student should have used the quadratic formula instead
- D) Iteration only works for linear equations
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Answer: The rearrangement does not lead to convergence
To solve x = g(x), the gradient of the function g(x) must be less than 1 near the root for the method to converge. Choosing the wrong rearrangement can cause the sequence to spiral away from the target value, failing to reach the root.
Want to test yourself on the remaining cards for this topic?
13 more questions on Iteration — plus mistakes tracking and spaced repetition across the whole Maths spec.