Changing the Subject of the Formulae | Cambridge IGCSE Mathematics

[Please watch the video attached at the end of this blog for a visual explanation of this topic]

In this article, we will be covering a subtopic under the main and important, but sometimes overwhelming topic of Algebra, which is “Changing the Subject of the Formulae”.

What does it mean to change the subject of a formula?

This simply means rearranging the equation given!

Making x the subject of a formula or equation means rearranging the equation or formula so that we have a single x variable equal to the rest of it.

It requires you to rearrange an equation so that it becomes x = rest of the rearranged equation.


The area of a rectangle is found by multiplying the height and the breadth of the rectangle.

Area of rectangle = breadth × height

   A = b × h

In the above formula, A is the subject of the formula.

However, if we wish to make b the subject of the formula, then it must be rearranged so that it becomes 

b = A/h

Likewise, in order to make h the subject of the formula, then the formula must be rearranged as

h = A/b

As it can be seen, having the necessary letter with the equal sign on one side of the equation alone, is what it means to make something the subject of a formula. Therefore, if you can somehow rearrange the formula so that the letter that you want on one side of the equation is equal to everything else, then congratulations, you’ve succeeded!

We can refer to another example to make everything clearer.


Make “a” the subject of the following formula.

This means we need to move everything else apart from “a” to one side of the equal sign. 

In order to get C to the other sign, you can cross multiply it so it becomes d × C. This leaves v^2 – ha on the other side of the equation.

You can then see that there’s a negative sign in front of ha. To get rid of this, you can move ha to your right hand side, which makes the sign in front of ha positive.

Then you can move dC to your left hand side so that ha remains on one side of the equation.

The last step is to remove h, which you can do by dividing the values on both sides by h.

There are a few more examples that you can try in the video below. In those you will learn how to rearrange a formula when there’s a square value to be removed, as well as learn how to rearrange a formula where you have to expand the terms given. Make sure you have a piece of paper and a pen so you can attempt to answer them before the answer is given!

What should you do next?

Practice a variety of  sample questions that feature this topic, because although quite simple, you might end up making careless mistakes, especially with square powers, square roots, etc.  

The question banks at Tutopiya have questions of different difficulty levels that you can practise before your actual exams. 

Ask for help – You are never too late to ask for assistance if you’re struggling. Reach out to us at Tutopiya  to find the right tutor to help you pass your exams with flying colours!

Attempt the quiz to challenge yourself!

Watch the video below for a visual explanation of the lesson and make sure to attempt the quiz once you’re done!

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