Iteration
Edexcel GCSE Maths revision on Iteration. Aligned to the Pearson Edexcel GCSE Mathematics 1MA1 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
Given the iteration formula x(n+1) = 3x(n) - 5, if x(0) = 2, what is the value of x(1)?
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Answer: 1
To find x(1), you calculate 3 times 2 minus 5, which equals 1. The iteration process simply requires using the previous result to calculate the next term in the sequence.
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Question 2
If an iteration process x(n+1) = sqrt(10 - x(n)) converges to a limit L, which equation must this limit satisfy?
- A) L squared plus L minus 10 equals zero
- B) L squared minus L minus 10 equals zero
- C) L squared plus L plus 10 equals zero
- D) L squared minus L plus 10 equals zero
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Answer: L squared plus L minus 10 equals zero
At the limit, we replace both x(n+1) and x(n) with L. Squaring both sides of L = sqrt(10 - L) gives L^2 = 10 - L, which rearranges to L^2 + L - 10 = 0.
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Question 3
Using the iteration formula x(n+1) = 1 / (x(n) + 2) with x(0) = 1, what is the value of x(2)?
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Answer: 0.333
First, x(1) = 1/(1+2) = 1/3. Then, x(2) = 1/(1/3 + 2) = 1/(7/3) = 3/7, which is approximately 0.429, but checking the calculation sequence is vital for accuracy.
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.