Chapter 19: Iteration and Rearranging formulae

Iteration

• You can find exact answers to quadratic equations by completing the square or using the quadratic formula
• It can be trickier to find exact answers to more complicated equations, like those involving cubes ot square roots
• You can use iteration to find numerical answers to a given degree of accuracy

Iteration formula

• Here is a cubic function: f(x) = x^3 - 5x + 3
• The roots of this function occur when f(x) = 0
• These are the points where the graph of y = f(x) crosses the x-axis
• You can use an iteration formula to find the roots
• Here is an iteration formula for this function
  • x(n+1) = 3/5x(n) - 3
• If you have to use an iteration formula to find a root or solve an equation, you will usually be given it in the exam

Using a calculator

• The ans button enters the answer to the previous calculation
• This is exactly what you need for speedy iterations
• In the worked example on the left you could use these keys for each new line of working
  • + 2 = ans

Rearranging formulae

• Most formulae have one letter on its own on one side of the formula
• This letter is called the subject of the formula
• Changing the subject of a formula is like solving an equation
• You have to do the same thing to both sides of the formula until you have the new letter on its own on one side

Harder formulae

• If the letter you need appears twice in the formula you need to factorise
  • Group all the terms with that letter on one side of the formula and all the other terms on the other side
  • Factorise so the letter only appears once
  • Divide by everything in thr bracket to get the letter on its own