Simple Rearranging
What are formulae?
- A formula (plural, formulae) is a mathematical relationship consisting of variables, constants and an equals sign
- You will come across many formulae in your IGCSE course, including
- the formulae for areas and volumes of shapes
- equations of lines and curves
- the relationship between speed, distance and time
- Some examples of formulae you should be familiar with are
- The equation of a straight line
- The area of a trapezium
- Pythagoras' theorem
- The equation of a straight line
- You will also be expected to rearrange formulae that you are not familiar with
How do I rearrange formulae?
- Rearranging formulae can also be called changing the subject
- The subject is the variable (letter) that you want to find out, or get on its own on one side of the formula
- The method for changing the subject is the same as the method used for solving linear equations
- STEP 1
Remove any fractions or brackets- Remove fractions by multiplying both sides by anything on the denominator
- Expand any brackets only if it helps to release the variable, if not it may be easier to leave the bracket there
- STEP 2
Carry out inverse operations to isolate the variable you are trying to make the subject- This works in the same way as with linear equations, however you will create expressions rather than carry out calculations
- For example, to rearrange so that is the subject
- Multiply by 2
- STEP 1
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- Expanding the bracket will not help here as we would end up with the subject appearing twice, so instead divide by the whole expression
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- You can now rewrite this with the subject () on the left hand side
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How do I rearrange formulae that include powers or roots?
- If the formula contains a power of n, use the nth root to reverse this operation
- For example to make the subject of
- Divide both sides by first
- For example to make the subject of
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- Then take the 5th root of both sides
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- If n is even then there will be two answers: a positive and a negative
- For example if then
- If the formula contains an nth 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
- For example to make the subject of
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- Divide both sides by
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Exam Tip
- If you are unsure about the order in which you would carry out the inverse operations, try substituting numbers in and reverse the order that you would carry out the substitution
Worked example
Make the subject of the following formulae.
(a)
(b)
(c)
(a)
Get 5x on its own by subtracting 4m from both sides
Get x on its own by dividing both sides by 5
(b)
Remove fractions by multiplying both sides by x
Get x on its own by dividing both sides by 3t
(c)
Get x2 on its own by dividing both sides by 4π
Get x on its own by square-rooting both sides
Use ± to show that there are two possible answers when square-rooting
Use ± to show that there are two possible answers when square-rooting