Change of Subject Formula

Whenever the subject of a formula is to be changed, the intention is to make the value becoming the subject stand alone and remain on the left hand side of the expression. The methods used to effect this change may be any basic mathematical principles like multiplication, addition, subtraction, division, finding square roots, etc.

Whatever operation that is used to perform the change must be applied to both sides of the expression (formula).

Examples;

1. Make u the subject of the formula; v² = u² + 2as.

Solution

Step 1

Rearrange by bringing “u²” to the LHS of the expression and carrying v² to the RHS of the expression. The reason for this is because you have been instructed to make “u” the subject of the formula according to the question.

-u² = 2as – v²

Note;

Whenever you carry figures from one side of an expression to another, the sign changes to the opposite.

Step 2

Multiply both sides by -1 in order to eliminate the – (minus sign);

u² = 2as + v²

Step 3

Take square root of both sides;

2. Change the subject of the formula below to h;

Solution

Step 1

The target value here is “h”. So in order to make “h” subject, you need to remove the square root by taking square of both sides;

Step 2

Cross multiply both sides;

2Qh = 100p²

Step 3

Divide both sides by 2Q;

Final answer will be;

3. Express S in terms of T, X and K in the formula below;

Solution

Step 1

Remove the square root by taking square of both sides;

Step 2

Split the RHS expression apart to make it easier for you to solve. See below;

Step 3

Expand (2X) ² and remove the square root;

Note; raise to power of 2 can easily cancel square root. This is why: (2 × ½ gives 1 where ½ is the mathematical interpretation of square root)

Step 4

Cross multiply both sides;

4SX² X 1 = T² X K

4SX² = KT²

Step 5

Divide both sides by 4X² because you need “S” to be alone;

Lastly, we need to find S when T = 8, X = 2 and K = 3. The only way to do this is by substituting for T, X and K respectively in our new formula.

S = 3 × 4
Note; 16 goes in 64 gives 4

S = 12. (Answer)

Practice these questions below;

1. Make d the subject of the formula below; 

2. Make m the subject of the expression below;

3. Make v the subject of the relation;

4. Given that v² = u² + 2as, express a in terms of u, v and s. Hence, find the value of a when u = 15, v = 20 and s = 5.

5. An expression is given as

Make R the subject of the formula and find R when K = 20, q = 15 and D = 6.