Iterative Methods (AQA GCSE Maths): Quizzes

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Iterative Methods
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What is the key idea behind iterative methods?

Each result feeds into next calculation

What does a sign change between two values tell you about an equation equal to zero?

A solution exists between those values

For x23x1=0x^2 - 3x - 1 = 0, at x=1x = -1 you get 3 and at x=0x = 0 you get -1. What does this mean?

Solution exists between x=1x = -1 & x=0x = 0

When should you use iterative methods instead of standard algebraic techniques?

When equations are too complex to solve

In the decimal search method, what do you do after finding a sign change?

Narrow the interval & increase precision

If a solution lies between -1.5 and -1.6, what precision would you test next?

2 decimal places: -1.50, -1.51, -1.52...

What is the first step in the iteration machine method?

Rearrange equation with xx on one side

In iteration, what is x0x_0?

The starting value

When do you stop iterating?

When consecutive values round to same no.

What is a key issue with rearrangement in iteration machines?

Not all rearrangements converge

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