Question 1 Easy
Make x the subject of y=2x-5.
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Answer: (y+5)/2
- Add 5: y + 5 = 2x.
- Divide by 2: x = (y+5)/2.
- Method (1): Add 5: y + 5 = 2x.
- Accuracy (1): Divide by 2: x = (y+5)/2.
Harder rearranging formulae practice questions with answers
A second set of harder rearranging formulae questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.
More questions
Question 2 Easy
Make x the subject of y=x/4.
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Answer: 4y
- Multiply by 4.
- x = 4y.
- Method (1): Multiply by 4.
- Accuracy (1): x = 4y.
Question 3 Medium
Make x the subject of y=x²+1.
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Answer: √(y-1)
- Subtract 1: x² = y - 1.
- Square root: x = √(y-1).
- Method (1): Subtract 1: x² = y - 1.
- Accuracy (1): Square root: x = √(y-1).
Question 4 Medium
Make x the subject of y=x²+4.
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Answer: √(y-4)
- Subtract 4: x² = y - 4.
- Square root: x = √(y-4).
- Method (1): Subtract 4: x² = y - 4.
- Accuracy (1): Square root: x = √(y-4).
Question 5 Hard
Make x the subject of y(x-2)=3.
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Answer: 2 + 3/y
- Divide by y: x - 2 = 3/y.
- Add 2: x = 2 + 3/y.
- Method (1): Divide by y: x - 2 = 3/y.
- Accuracy (1): Add 2: x = 2 + 3/y.
Question 6 Hard
Make x the subject of y(x-5)=4.
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Answer: 5 + 4/y
- Divide by y: x - 5 = 4/y.
- Add 5: x = 5 + 4/y.
- Method (1): Divide by y: x - 5 = 4/y.
- Accuracy (1): Add 5: x = 5 + 4/y.
Exam-style question
A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.
Exam-style question 12 marks
Make x the subject of y=√(x+16).
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Answer: y²-16
- Square both sides: y² = x + 16.
- Subtract 16 from both sides.
- Isolate x: x = y² - 16.
- State subject formula: y²-16.
- Method (1): Square both sides to get y² = x + 16
- Accuracy (1): x = y² - 16
Quick checks
Short one-step questions. Pick an option before you open the answer.
Check 1
How do you undo y = 2x+6?
- y²-4
- (y-7)/3
- (y-6)/2
Show answer
(y-6)/2 Subtract 6 and divide by 2, giving (y-6)/2.
Check 2
What is x if y = 3x+7?
- (y-7)/3
- √(y-1)
- (y-6)/2
Show answer
(y-7)/3 (y-7)/3.
Check 3
What is x if y = √(x+1)?
- (y+5)/2
- √(y-1)
- y²-1
Show answer
y²-1 Square and subtract 1: y²-1.
Check 4
What is x if y = √(x+4)?
- y²-1
- 4y
- y²-4
Show answer
y²-4 Square and subtract 4: y²-4.
Check 5
What is x if y = x²+1?
- 4y
- √(y-1)
- (y-6)/2
Show answer
√(y-1) √(y-1), taking the positive root.
Check 6
From 5x+2 = yx+8, what factor multiplies x?
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Collect x terms: x(5-y). Collect x terms: x(5-y).
Check 7
Why is the numerator 6 in that equation?
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8 - 2 = 6. 8 - 2 = 6.
Check 8
Write x from y(x-2) = 3.
- 2 + 3/y
- 5 + 4/y
- x appears on both sides
Show answer
2 + 3/y Divide by y, then add 2: 2 + 3/y.
Check 9
Write x from y(x-5) = 4.
- 2 + 3/y
- 5 + 4/y
- x appears on both sides
Show answer
5 + 4/y Divide by y, then add 5: 5 + 4/y.
Check 10
What is x if y = x/4?
- (y-7)/3
- 4y
- (y-6)/2
Show answer
4y Multiply both sides by 4: 4y.
Check 11
What is x if y = 2x-5?
- y²-1
- y²-4
- (y+5)/2
Show answer
(y+5)/2 Add 5 and divide by 2: (y+5)/2.
Check 12
Why is a root question different from y = mx+c?
Show answer
You square y, you do not just divide. You square y, you do not just divide.
Check 13
Why is 5x+2 = yx+8 harder than y = 2x+6?
- 2 + 3/y
- 5 + 4/y
- x appears on both sides
Show answer
x appears on both sides x appears on both sides, so it has to be factorised.
Check 14
From 4x+1 = yx+9, what is x?
Show answer
8/(4-y). 8/(4-y).
Check 15
Make x the subject of y = x²+4, taking the positive root.
Show answer
Subtract 4 to get x² = y - 4, then take the positive square root: √(y-4). √(y-4).
Keep going with Harder rearranging formulae
Practise free
AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.