Rearrange a formula so a different letter sits alone on one side, undoing operations one at a time. It is on Foundation and Higher, aimed at grade 5. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Changing the subject is solving an equation for a different letter. Inverse operations, one at a time, with the new subject ending up on its own on the left. From v=u+at, v−u=at, then t=av−u. If the new subject appears twice, factorise it out first: ax+bx=x(a+b).
Roots and squares: square both sides to undo a square root; square-root both sides (and remember ± if the question wants both) to undo a square. Fractions: multiply through by the denominator. Check by substituting numbers into both versions of the formula.
Do the inverse operations in reverse order, both sides. Roots: square after isolating the root. Fractions: multiply through by the denominator. Always finish with the letter alone on the left.
Objectives
Make x the subject of y = mx + c.
Make x the subject when the constant is subtracted.
Make x the subject of y = x/n and of y = n − x.
Key points
Identify which operations are being done to the new subject, and in what order.
Undo them in reverse order using inverse operations on both sides.
Deal with a squared subject by square rooting at the end, and a square-rooted subject by squaring.
Handle a subject that is being divided by something, or is in the denominator, by multiplying through.
Worked examples
Example 1
Make x the subject of y=3x+7.
2 marks
Subtract 7 from both sides: y - 7 = 3x.
Divide both sides by 3: x = (y-7)/3.
The rearranged formula is x = (y-7)/3.
Answer: (y-7)/3
Common slips
Slip: Divide only y by 3. Every term on that side must be divided by 3, including the 7. Subtracting 7 first is simpler.
Slip: Tom wrote 3y+7. You must divide by the coefficient 3, not multiply.
Slip: Conclude x = 3y+7. Subtracting 7 then dividing by 3 gives (y-7)/3.
Example 2
Make x the subject of y=2x-5.
2 marks
Add 5 to both sides: y + 5 = 2x.
Divide both sides by 2: x = (y+5)/2.
The rearranged formula is x = (y+5)/2.
Answer: (y+5)/2
Common slips
Slip: Subtract 5 from both sides. The formula subtracts 5, so the inverse operation is adding 5.
Slip: Una subtracted 5 again to get (y-5)/2. Adding 5 undoes the subtraction.
Slip: Conclude x = (y-5)/2. Adding 5 then dividing by 2 gives (y+5)/2.
Example 3
Make x the subject of y=5-x.
3 marks
Add x to both sides to make it positive: y + x = 5.
Subtract y from both sides: x = 5 - y.
The rearranged formula is x = 5-y.
Answer: 5-y
Common slips
Slip: Subtract 5 directly without moving x. Moving -x across the equals sign makes it +x.
Slip: Val wrote x = y - 5. Taking y from 5 leaves 5 - y, not y - 5.
Slip: Conclude x = y-5. Subtracting y from 5 gives x = 5-y.
Questions and answers
GCSE Maths changing the subject of a formula questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
Make x the subject of y=2x+6.
Show answer
Answer: (y-6)/2
Subtract 6 from both sides: y - 6 = 2x.
Divide by 2: x = (y-6)/2.
M1 — Subtract 6 from both sides: y - 6 = 2x.
A1 — Divide by 2: x = (y-6)/2.
Question 2 Easy2 marks
Make x the subject of y=4x+1.
Show answer
Answer: (y-1)/4
Subtract 1 from both sides: y - 1 = 4x.
Divide by 4: x = (y-1)/4.
M1 — Subtract 1 from both sides: y - 1 = 4x.
A1 — Divide by 4: x = (y-1)/4.
Question 3 Medium2 marks
Make x the subject of y=3x-6.
Show answer
Answer: (y+6)/3
Add 6 to both sides: y + 6 = 3x.
Divide by 3: x = (y+6)/3.
M1 — Add 6 to both sides: y + 6 = 3x.
A1 — Divide by 3: x = (y+6)/3.
Question 4 Medium2 marks
Make x the subject of y=4x-8.
Show answer
Answer: (y+8)/4
Add 8 to both sides: y + 8 = 4x.
Divide by 4: x = (y+8)/4.
M1 — Add 8 to both sides: y + 8 = 4x.
A1 — Divide by 4: x = (y+8)/4.
Question 5 Hard2 marks
Make x the subject of y=8-x.
Show answer
Answer: 8-y
Add x to both sides: y + x = 8.
Subtract y: x = 8 - y.
M1 — Add x to both sides: y + x = 8.
A1 — Subtract y: x = 8 - y.
Question 6 Hard2 marks
Make x the subject of y=12-x.
Show answer
Answer: 12-y
Add x to both sides: y + x = 12.
Subtract y: x = 12 - y.
M1 — Add x to both sides: y + x = 12.
A1 — Subtract y: x = 12 - y.
Question 7 Exam-style2 marks
Make x the subject of y = 4x + 8.
Show answer
Answer: (y-8)/4
Subtract 8 from both sides: y - 8 = 4x.
Divide both sides by 4: x = (y-8)/4.
M1 — y - 8 = 4x, or y/4 - 2 = x
A1 — (y-8)/4, or y/4 - 2
Common mistakes
Most lost marks on this topic are one slip.
Multiplying by the gradient instead of dividing
Divide by the gradient after removing the constant
Subtracting a constant that was already subtracted
Add that constant back
Writing y-5 when the formula was 5-x
The two amounts still add to 5, so x = 5-y
Spot the slip
Ada is asked to make x the subject of y = 3x + 7. What should x equal?
(y-7)/3
3y+7
y-7
Show the slip
(y-7)/3 Subtract 7, then divide by 3: x = (y-7)/3.
Exam tips
Be ready to do this without a calculator. Paper 1 is the non-calculator paper.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write one operation per line, showing both sides — each correct step is usually a method mark.
A five-second check with a test number catches almost every rearranging error.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.