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Changing the subject of a formula practice questions with answers

Foundation and Higher · Grade 5 · Non-calculator

A second set of changing the subject of a formula 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 1 Easy

Make x the subject of y=5x+10.

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Answer: (y-10)/5

  1. Subtract 10 from both sides: y - 10 = 5x.
  2. Divide by 5: x = (y-10)/5.
  • Method (1): Subtract 10 from both sides: y - 10 = 5x.
  • Accuracy (1): Divide by 5: x = (y-10)/5.

Question 2 Easy

Make x the subject of y=6x+3.

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Answer: (y-3)/6

  1. Subtract 3 from both sides: y - 3 = 6x.
  2. Divide by 6: x = (y-3)/6.
  • Method (1): Subtract 3 from both sides: y - 3 = 6x.
  • Accuracy (1): Divide by 6: x = (y-3)/6.

Question 3 Medium

Make x the subject of y=x/4.

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Answer: 4y

  1. Identify inverse of dividing by 4: multiply by 4.
  2. Multiply both sides: x = 4y.
  • Method (1): Identify inverse of dividing by 4: multiply by 4.
  • Accuracy (1): Multiply both sides: x = 4y.

Question 4 Medium

Make x the subject of y=x/5.

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Answer: 5y

  1. Identify inverse of dividing by 5: multiply by 5.
  2. Multiply both sides: x = 5y.
  • Method (1): Identify inverse of dividing by 5: multiply by 5.
  • Accuracy (1): Multiply both sides: x = 5y.

Question 5 Hard

Make x the subject of y=9-x.

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Answer: 9-y

  1. Add x to both sides: y + x = 9.
  2. Subtract y: x = 9 - y.
  • Method (1): Add x to both sides: y + x = 9.
  • Accuracy (1): Subtract y: x = 9 - y.

Question 6 Hard

Make x the subject of y=x/7.

Show answer

Answer: 7y

  1. Identify inverse of dividing by 7: multiply by 7.
  2. Multiply both sides: x = 7y.
  • Method (1): Identify inverse of dividing by 7: multiply by 7.
  • Accuracy (1): Multiply both sides: x = 7y.

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 = 15 - x.

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Answer: 15-y

  1. Add x to both sides: y + x = 15.
  2. Subtract y from both sides: x = 15 - y.
  • Method (1): y + x = 15, or one correct rearranging step
  • Accuracy (1): 15 - y

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

To make x the subject of y = mx + c, which operation is undone first?

  1. The added constant +c
  2. The multiplier m
  3. Neither
Show answer

The added constant +c Subtract the constant c first, then divide by m.

Check 2

From y = 3x + 7, what is x?

  1. (y-7)/3
  2. 3y+7
  3. (y+7)/3
Show answer

(y-7)/3 Subtract 7 then divide by 3.

Check 3

From y = 2x + 6, what is x?

  1. (y-6)/2
  2. 2y+6
  3. (y+6)/2
Show answer

(y-6)/2 Subtract 6 then divide by 2.

Check 4

From y = 2x - 5, what is x?

  1. (y+5)/2
  2. (y-5)/2
  3. 2y-5
Show answer

(y+5)/2 Add 5 then divide by 2.

Check 5

From y = 3x - 6, what is x?

  1. (y+6)/3
  2. (y-6)/3
  3. 3y-6
Show answer

(y+6)/3 Add 6 then divide by 3.

Check 6

From y = x/4, what is x?

  1. 4y
  2. y/4
  3. y-4
Show answer

4y Multiply both sides by 4.

Check 7

From y = x/5, what is x?

  1. 5y
  2. y/5
  3. y-5
Show answer

5y Multiply both sides by 5.

Check 8

From y = 5 - x, what is x?

  1. 5-y
  2. y-5
  3. 5+y
Show answer

5-y Add x to both sides, then subtract y from both sides: x = 5 - y.

Check 9

From y = 8 - x, what is x?

  1. 8-y
  2. y-8
  3. 8+y
Show answer

8-y Add x to both sides, then subtract y from both sides: x = 8 - y.

Check 10

How do you undo a subtracted constant in a formula?

  1. Add it to the other side
  2. Subtract it again
  3. Divide by it
Show answer

Add it to the other side Addition is the inverse operation of subtraction.

Check 11

How do you undo division by 4 in y = x/4?

  1. Multiply by 4
  2. Divide by 4
  3. Add 4
Show answer

Multiply by 4 Multiplication is the inverse operation of division.

Check 12

If y = 5 - x, what do x and y always sum to?

  1. 5
  2. 0
  3. 10
Show answer

5 x + y = 5.

Check 13

From y = 4x + 1, what is x?

  1. (y-1)/4
  2. (y+1)/4
  3. 4y+1
Show answer

(y-1)/4 Subtract 1 then divide by 4.

Check 14

From y = 4x - 8, what is x?

  1. (y+8)/4
  2. (y-8)/4
  3. 4y-8
Show answer

(y+8)/4 Add 8 then divide by 4.

Check 15

What does it mean to make x the subject of a formula?

  1. Isolate x on one side with coefficient 1
  2. Substitute numbers for x
  3. Find the gradient of x
Show answer

Isolate x on one side with coefficient 1 The subject stands alone on one side of the equals sign.

Keep going with Changing the subject of a formula

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