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Rearrange Formulae

In this worksheet, students will rearrange simple formulae in which subject appears once only.

'Rearrange Formulae' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Algebra

Curriculum subtopic:   Notation, Vocabulary and Manipulation, Algebraic Formulae

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

If you rearrange a formula, you change the variable which is its subject. In A = b × h (formula for area of a rectangle), A is the subject, because it's own its own on one side of the equal sign.

 

You can change the subject of the formula by using inverse operations. Have a look at an example below.

 

Example

v = u + at (formula for final velocity). Make a the subject of the formula.

We need to inverse the operations. Let's first move u to the other side by subtracting:

v - u = at

at means a × t. So reverse this, we need to divide by t.

(v - u) ÷ t = a

Now a is the subject of the formula. It is on its own on one side of the equation.

See how (v - u) are in brackets? This is because we want to divide the entire left-hand side by t, not just v or u.

Make x the subject of each formula. Match the questions to the answers.

Column A

Column B

5x - y = 7
(7 - y) ÷ 5
5x + y = 7
x = 7 - 5y
x + 5y = 7
(7 - 5y) ÷ 2
2x + 5y = 7
(7 + y) ÷ 5

Below some formulae were rearranged to make m the subject, but not all of these are correct.

Can you spot which answers are incorrect?

 CorrectIncorrect
Q: P = 3m - 5 A: m = (P + 5) ÷ 3
Q: P = m + 5t A: m = (P - 5t) ÷ 5
Q: P= 5m + 1 A: m = P - 6
Q: P = 5m + 3t A: m = (P - t) ÷ 15

Make t the subject of the formula

v = u + at

v - u ÷ a

(v - a) ÷ u

(v - u) ÷ a

(v + a) ÷ u

Make s the subject of the formula: t = sx - r.

s = t + r - x

s = (t + r) ÷ x

s = (t - x) ÷ r

s = t + r ÷ x

Make p the subject of the formula T = (6p - 7) ÷ 2

p = (2T + 7) & divide; 6

p = 2T + 7 & divide; 6

p = 2(T + 7 & divide; 6)

p = T + 7 × 2 ÷ 6

Make x the subject of the formula.

Column A

Column B

a( x - b) = 2
x = 4a ÷ 3
(x + 2) ÷ 3 = y
x = 3(y - b)
(x ÷ 3) + b = y
x = (2 ÷ a) + b
3x ÷ 4 = a
x = 3y - 2

Make a the subject of the formula 3(2a - 5) = b.

a = (b ÷ 3) + 5 ÷ 2

a = 3b + 5 ÷ 2

a = (b ÷ 3 + 5) ÷ 2

a = 3b - 5 × 2

Match each formula with the correct rearrangement.

Column A

Column B

y = x - 4
x = 2y - 4
y = x + 4
x = y + 4
y = 2x - 4
x = y -4
y = (x + 4) ÷ 2
x = (y + 4) ÷ 2

What is the correct first step to make m the subject of the formula y = mx + c?

+ c

× x

- c

÷ c

What is the correct second step to make t the subject of the formula s = (2t + 3) ÷ r?

times; r

÷ 2

× 2

− 3

  • Question 1

Make x the subject of each formula. Match the questions to the answers.

CORRECT ANSWER

Column A

Column B

5x - y = 7
(7 + y) ÷ 5
5x + y = 7
(7 - y) ÷ 5
x + 5y = 7
x = 7 - 5y
2x + 5y = 7
(7 - 5y) ÷ 2
EDDIE SAYS
Remember to use inverse operations. In 5x - y = 7, you need to move y, so add it to 7 (adding is the inverse of subtracting). This gives you 5x = 7 + y. Now divide by 5. This gives you (7 + y) ÷ 5. The bracket is needed because you need to divide the entire expression on the right-hand side by 5.
  • Question 2

Below some formulae were rearranged to make m the subject, but not all of these are correct.

Can you spot which answers are incorrect?

CORRECT ANSWER
 CorrectIncorrect
Q: P = 3m - 5 A: m = (P + 5) ÷ 3
Q: P = m + 5t A: m = (P - 5t) ÷ 5
Q: P= 5m + 1 A: m = P - 6
Q: P = 5m + 3t A: m = (P - t) ÷ 15
EDDIE SAYS
Only the first question has been answered correctly. In the remaining three the inverse operations were not done properly. Have a look at these again. Can you spot where the mistakes are?
  • Question 3

Make t the subject of the formula

v = u + at

CORRECT ANSWER
(v - u) ÷ a
EDDIE SAYS
(v - u) ÷ a is the correct option. a. looks very similar, but is missing brackets. This is a common mistake. Always use brackets if you want to divide the entire expression.
  • Question 4

Make s the subject of the formula: t = sx - r.

CORRECT ANSWER
s = (t + r) ÷ x
EDDIE SAYS
Did you use inverse operations to change the subject of t = sx - r? Add r first: t + r = sx Divide by x: (t + r) ÷ x = s Now s is the subject of the formula.
  • Question 5

Make p the subject of the formula T = (6p - 7) ÷ 2

CORRECT ANSWER
p = (2T + 7) & divide; 6
EDDIE SAYS
This is a little trickier! Firstly, let's deal with ÷ 2: do the inverse, which is × 2 2T = 6p - 7 Now add the 7. 2T + 7 = 6p Finally, divide by 6. Don't forget about using brackets: (2T + 7) ÷ 6 = p.
  • Question 6

Make x the subject of the formula.

CORRECT ANSWER

Column A

Column B

a( x - b) = 2
x = (2 ÷ a) + b
(x + 2) ÷ 3 = y
x = 3y - 2
(x ÷ 3) + b = y
x = 3(y - b)
3x ÷ 4 = a
x = 4a ÷ 3
EDDIE SAYS
Remember that multiplication is the inverse of division. If the formula to be rearranged has brackets, first deal with everything outside of the brackets and then move into the brackets. In (x + 2) ÷ 3 = y, first do the inverse of dividing by 3. You get (x + 2) = 3y. Now you can move into the brackets, and do the inverse of adding two: x = 3y - 2. Done!
  • Question 7

Make a the subject of the formula 3(2a - 5) = b.

CORRECT ANSWER
a = (b ÷ 3 + 5) ÷ 2
EDDIE SAYS
This is quite a complex formula to work with, so be careful! First, divide by 3. (2a - 5) = b ÷ 3 Now add 5. 2a = b ÷ 3 + 5 Finally, divide by 2. You will need brackets here to catch the whole expression a = (b ÷ 3 + 5) ÷ 2
  • Question 8

Match each formula with the correct rearrangement.

CORRECT ANSWER

Column A

Column B

y = x - 4
x = y + 4
y = x + 4
x = y -4
y = 2x - 4
x = (y + 4) ÷ 2
y = (x + 4) ÷ 2
x = 2y - 4
EDDIE SAYS
To change the subject of a formula, you need to use inverse operations. The last two formulae are the hardest. Let's have a look at y = 2x - 4. First +4, this will give you y + 4 = 2x Now ÷ 2. The answer will be x = (y + 4) ÷ 2
  • Question 9

What is the correct first step to make m the subject of the formula y = mx + c?

CORRECT ANSWER
- c
EDDIE SAYS
To make m the subject of y=mx + c, first you need to move c, and that means subtracting it. So the correct answer is -c.
  • Question 10

What is the correct second step to make t the subject of the formula s = (2t + 3) ÷ r?

CORRECT ANSWER
− 3
EDDIE SAYS
Let\'s have a look at the formula s = (2t + 3) ÷ r The first step is to × r, so you get s × r = 2t + 3 Now the second step will be to move + 3, but subtracting it! − 3 is the correct second step. Can you guess the final step? Well done if you thought it was ÷ 2!
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