Rearranging Formulae (Edexcel GCSE Maths: Foundation)

What are formulae?

• A formula is a rule, definition or relationship between different quantities, written in shorthand using letters (variables)
  • They include an equals sign
• Some examples you should be familiar with are:
  • The equation of a straight line
    • 
  • The area of a trapezium
    • 
  • Pythagoras' theorem
    • 

How do I rearrange formulae?  

• The letter (variable) that is on its own on one side is called the subject
  • y  is the subject of y = mx + c
• To make a different letter the subject, we need to rearrange the formula
  • This is also called changing the subject
• The method is as follows:
  • First, remove any fractions
    • Multiply both sides by the lowest common denominator
  • Then use inverse (opposite) operations to get the variable on its own
    • This is similar to solving equations
• For example, make  the subject of 
  • First remove fractions
    • Multiply both sides by 2
      
  • Then get  on its own
    • Subtract 6 from both sides
      
    • Divide both sides by 5
      
  • There may be more than one correct way to write an answer
    • The following are acceptable alternative forms 
      
      
      
      

Should I expand brackets?

• Expand brackets if it releases the variable you want from inside the brackets
  • If not, you can leave them in
• To make the subject of 
  • is inside the brackets, so expand
    • 
  • Rearrange
    • 
       

• To make  the subject of 
  • is not inside the brackets, so you do not need to expand
  • Instead, divide both sides by the bracket
    • 

How do I rearrange formulae where the subject appears on both sides?  

• If the subject appears on both sides, you will need bring those terms to the same side
  • Then you can continue to rearrange as usual
    • E.g.
    • Expand the bracket
      
    • Remove the  term from the left hand side by subtracting
      
    • Add  to both sides
      
    • Rewrite with  on the left hand side
      

How do I rearrange formulae that include powers or roots?  

• If the formula contains a power of n, use the n th root to reverse this operation 
  
  • For example to make  the subject of 
    • Divide both sides by first 

• • • Then take the 5th root of both sides

• If n is even then there will be two answers: a positive and a negative
  • For example if then
• If the formula contains an n th root, reverse this operation by raising both sides to the power of n
  
  • For example to make  the subject of  
    • Raise both sides to the power of 3 first

• • • Divide both sides by