Determine the missing quantities in your study schedule with Beyond Revision and tuition-style posts like this one on changing the subject of a formula.

The best way to learn and improve is to get right into it so let’s start with a simple exercise.
Getting Started on Changing the Subject of a Formula
The inverse of an operation will undo the operation.
The following examples contain everything you need to know about changing the subject of a formula.
This is very similar to solving linear equations so you may want to revise the two topics together.
Make π the subject of π₯ = 4π + π¦.
Making π the subject means we want a formula in the form π = _. We do this by using inverse operations to manipulate the formula until we have π on its own.
First, we want to get the term including π on its own. We can do this by subtracting π¦ from both sides.
π₯ = 4π + π¦ | ||
– π¦ | – π¦ | |
π₯ – π¦ = 4π | ||
Γ· 4 | Γ· 4 | |
It doesnβt matter that we have π on the right-hand side rather than the left-hand side. Both sides of the formula are equal, so π is the subject of this formula. If you prefer, you can swap the sides and write the formula as π = but there is no need to.
Make π the subject of – π = π
This example is very similar to example 3. The key difference is the order in which we perform our manipulation. In this case, π is divided by 3 and then π is subtracted. To change the subject, we need to undo each of these in reverse order.
+ π | + π | |
Γ 3 | Γ 3 | |
π = 3(π + π) |
Make π the subject of = π
This example is very similar to example 2. The key difference is the order in which we perform our manipulation. In this case, we subtract π and then divide by 3. To change the subject we need to undo each of these in reverse order.
Γ 3 | Γ 3 | |
π – π = 3π | ||
+ π | + π | |
π = 3π + π |
Make π₯ the subject of π =
This time, we need to start by eliminating the square root.
π = | ||
_2 | _2 | |
π2 = π₯2 – 3π | ||
+ 3π | + 3π | |
π2 + 3π = π₯2 | ||
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