GCSE MATHS PRACTICE

GCSE Changing the Subject of a Formula Questions

The subject of a formula is the variable isolated on one side. Rearrange by applying the same inverse operation to both sides, undoing addition or subtraction before multiplication or division where appropriate. Keep brackets around grouped terms in fractions. The last question extends to Higher work with the new subject on both sides; factorise to collect it.

Updated 12 October 2026

Worked example

Make x the subject of y = 3x + 7.

Subtract 7 from both sides: y − 7 = 3x.
Divide both sides by 3: x = y − 73.
The whole expression y − 7 is divided by 3. Check with x = 4: y = 19 and (19 − 7) ÷ 3 = 4.

Answer: x = y − 73

Practice questions

1
Make x the subject of y = x + a.
2
Make t the subject of v = u + at. Assume a ≠ 0.
3
Make t the subject of v = dt. Assume t ≠ 0 and v ≠ 0.
4
Higher: make x the subject of y = ax + bx + c. Assume x + c ≠ 0 and y ≠ a.

Show answers

1. x = y − a
2. t = v − ua
3. t = dv
4. x = b − cyy − a

Common mistakes

Dividing only one term — A fraction bar applies to the whole numerator.
Changing only one side — Every operation must preserve equality.
Dividing by zero — State restrictions when dividing by a variable or variable expression.

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GCSE MATHS PRACTICE

GCSE Changing the Subject of a Formula Questions

Updated 12 October 2026

Worked example

Make x the subject of y = 3x + 7.

Subtract 7 from both sides: y − 7 = 3x.
Divide both sides by 3: x = y − 73.
The whole expression y − 7 is divided by 3. Check with x = 4: y = 19 and (19 − 7) ÷ 3 = 4.

Answer: x = y − 73

Practice questions

1
Make x the subject of y = x + a.
2
Make t the subject of v = u + at. Assume a ≠ 0.
3
Make t the subject of v = dt. Assume t ≠ 0 and v ≠ 0.
4
Higher: make x the subject of y = ax + bx + c. Assume x + c ≠ 0 and y ≠ a.

Show answers

1. x = y − a
2. t = v − ua
3. t = dv
4. x = b − cyy − a

Common mistakes

Dividing only one term — A fraction bar applies to the whole numerator.
Changing only one side — Every operation must preserve equality.
Dividing by zero — State restrictions when dividing by a variable or variable expression.

GCSE Changing the Subject of a Formula Questions

Worked example

Practice questions

Common mistakes

Related resources

GCSE Changing the Subject of a Formula Questions

Worked example

Practice questions

Common mistakes

Related resources