What is A5: Formulae?

The subject of a formula is the variable isolated on one side. Changing the subject must preserve an equivalent relationship, so perform the same operation on both sides and undo operations in reverse order.

How many marks are A5 questions worth?

In verified past-paper appearances, A5 questions on Edexcel GCSE Maths 1MA1 have been worth 1–6 marks.

Which past exam papers has A5 appeared in?

A5 has appeared in 19 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Understand and use standard mathematical formulae; rearrange formulae to change the subject

Formulae

Worked answers, methods and verified real exam appearances for A5 on Edexcel GCSE Maths 1MA1.

Explanation

The subject of a formula is the variable isolated on one side. Changing the subject must preserve an equivalent relationship, so perform the same operation on both sides and undo operations in reverse order.
Clear fractions or brackets when this makes the structure easier to see.
Foundation questions usually isolate a subject that appears once.
Higher tier: the subject may appear more than once or inside a fraction, requiring expansion and collection of its terms.
Examiners expect each inverse operation to be visible and the final subject to appear alone.

Worked example

Make $t$ the subject of $v=u+at$ .

1.Subtract $u$ from both sides: $v-u=at$ .
2.Divide both sides by $a$ : $\dfrac{v-u}{a}=t$ .
3.Write the subject first: $t=\dfrac{v-u}{a}$ .

Answer: $t=\dfrac{v-u}{a}$ .

Common mistakes

Don't change a sign while moving a term without applying an operation to both sides.
Don't divide only one term of a sum instead of the entire side.
Don't stop with the requested subject still multiplied by another quantity.

Exam tip

State one balancing operation per line until the requested subject is alone.

Worked practice

Tier 1 · Easy

Make

w

the subject of

A=lw

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$w=\frac{A}{l}$	1	Divide both sides by $l$ to isolate $w$ : $A/l=w$ , so $w=A/l$ .

Tier 2 · Standard

The area of a trapezium is given by

A=\dfrac12(a+b)h

, where

A

is measured in

\text{cm}^2

and

a

b

and

h

are measured in cm. (a) Make

h

the subject of the formula. (b) Hence work out

h

when

A=45\,\text{cm}^2

a=7\,\text{cm}

and

b=11\,\text{cm}

(3)

(Total for Question 2 is 3 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	(a) $h=\dfrac{2A}{a+b}$ (b) $h=5\,\text{cm}$	3	(a) Multiply both sides by $2$ : $2A=(a+b)h$ . Divide by $(a+b)$ : $h=\dfrac{2A}{a+b}$ . (b) Substituting, $h=\dfrac{2\times45}{7+11}=\dfrac{90}{18}=5\,\text{cm}$ .

Tier 3 · Hard

Make

a

the subject of

P=\frac{a+b}{a-b}

(4)

(Total for Question 3 is 4 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$a=\frac{b(P+1)}{P-1}$	4	Multiply by $a-b$ : $P(a-b)=a+b$ . Expanding gives $Pa-Pb=a+b$ . Collect the $a$ -terms: $Pa-a=Pb+b$ , so $a(P-1)=b(P+1)$ . Dividing by $P-1$ gives $a=b(P+1)/(P-1)$ .

Tier 1 · Easy

Make

x

the subject of

y=x+7

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$x=y-7$	1	Subtract $7$ from both sides to isolate $x$ : $y-7=x$ , so $x=y-7$ .

Tier 2 · Standard

Make

l

the subject of

P=2l+2w

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$l=\dfrac{P-2w}{2}$ (or $l=\dfrac{P}{2}-w$ )	2	Subtract $2w$ from both sides: $P-2w=2l$ . Divide by $2$ to get $l=\dfrac{P-2w}{2}$ , which is equivalent to $l=\dfrac{P}{2}-w$ .

Tier 3 · Hard

Make

p

the subject of

q=\dfrac{3p-r}{5}

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$p=\dfrac{5q+r}{3}$	3	Multiply both sides by $5$ : $5q=3p-r$ . Add $r$ to both sides to get $5q+r=3p$ . Divide by $3$ , giving $p=\dfrac{5q+r}{3}$ .

Tier 2 · Standard

Make

v

the subject of

K=\dfrac{m(n+v)}{4}

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$v=\dfrac{4K}{m}-n$ (or $v=\dfrac{4K-mn}{m}$ )	3	Multiply both sides by $4$ to get $4K=m(n+v)$ . Divide by $m$ , giving $\dfrac{4K}{m}=n+v$ . Subtract $n$ to obtain $v=\dfrac{4K}{m}-n$ .

Tier 3 · Hard

Make

x

the subject of

A=\dfrac{k(b+cx)}{d}

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$x=\dfrac{Ad-bk}{ck}$ (or $x=\dfrac{Ad/k-b}{c}$ )	4	Multiply by $d$ : $Ad=k(b+cx)$ . Divide by $k$ : $\dfrac{Ad}{k}=b+cx$ . Subtract $b$ and divide by $c$ to get $x=\dfrac{Ad/k-b}{c}=\dfrac{Ad-bk}{ck}$ .

Tier 3 · Hard

Nadia tries to make

x

the subject of

y=\dfrac{x-a}{b}+c

. She writes

x=by-a-c

. Explain Nadia's error and make

x

the subject correctly.

(3)

(Total for Question 9 is 3 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	Nadia must subtract $c$ before multiplying the whole result by $b$ , and she must add $a$ $x=b(y-c)+a$ (or $x=by-bc+a$ )	3	Subtract $c$ first: $y-c=\dfrac{x-a}{b}$ . Multiplying the complete left side by $b$ gives $b(y-c)=x-a$ . Add $a$ to obtain $x=b(y-c)+a=by-bc+a$ .

Q10

Tier 3 · Hard

Higher only: Make

x

the subject of

P=2x+k(x-a)

. State the restriction on

k

needed for your formula.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$x=\dfrac{P+ak}{k+2}$ $k\ne-2$	4	Expand and collect the $x$ -terms: $P=2x+kx-ak=x(k+2)-ak$ . Hence $P+ak=x(k+2)$ , so $x=\dfrac{P+ak}{k+2}$ . Division by $k+2$ requires $k\ne-2$ .

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2019-11	1H	Q12	1	Non-calculator	Higher	QP MS
2023-06	1H	Q17	4	Non-calculator	Higher	QP MS
2023-11	2F	Q22	6	Allowed	Foundation	QP MS
2021-11	1H	Q11	4	Non-calculator	Higher	QP MS
2024-06	3F	Q29	4	Allowed	Foundation	QP MS
2022-06	3F	Q23	4	Allowed	Foundation	QP MS
2022-06	3H	Q2	4	Allowed	Higher	QP MS
2022-11	1H	Q24	6	Non-calculator	Higher	QP MS
2023-11	2H	Q1	6	Allowed	Higher	QP MS
2024-11	1F	Q25	2	Non-calculator	Foundation	QP MS
2019-06	2H	Q15	3	Allowed	Higher	QP MS
2022-06	2H	Q17	5	Allowed	Higher	QP MS
2022-11	3H	Q1	2	Allowed	Higher	QP MS
2024-11	3H	Q15	4	Allowed	Higher	QP MS
2019-06	3F	Q19	2	Allowed	Foundation	QP MS
2019-11	2H	Q10	2	Allowed	Higher	QP MS
2023-11	3H	Q10	3	Allowed	Higher	QP MS
2021-11	2H	Q21	4	Allowed	Higher	QP MS
2022-11	3F	Q21	2	Allowed	Foundation	QP MS

Other points in A Algebra · notation and manipulation

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