What is A2: Substitution?

Substitution replaces every occurrence of a variable with its given value while preserving the original operations. Put negative and fractional values in brackets so that powers and signs act on the whole value.

How many marks are A2 questions worth?

In verified past-paper appearances, A2 questions on Edexcel GCSE Maths 1MA1 have been worth 2–6 marks.

Which past exam papers has A2 appeared in?

A2 has appeared in 22 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Substitute numerical values into formulae and expressions, including scientific formulae

Substitution

Worked answers, methods and verified real exam appearances for A2 on Edexcel GCSE Maths 1MA1.

Explanation

Substitution replaces every occurrence of a variable with its given value while preserving the original operations. Put negative and fractional values in brackets so that powers and signs act on the whole value.
Follow the order of operations: evaluate powers before multiplication, division, addition and subtraction.
In a scientific formula, include the stated units and convert them first if necessary.
Keep full calculator precision until the requested rounding.
Examiners award method for a correct substituted expression, so write that line before evaluating rather than giving only a calculator answer.

Worked example

The kinetic energy formula is $E=\dfrac12mv^2$ . Find $E$ when $m=3.2\,\text{kg}$ and $v=5\,\text{m s}^{-1}$ .

1.Substitute both values: $E=\dfrac12\times3.2\times5^2$ .
2.Evaluate the power first: $5^2=25$ .
3. $E=0.5\times3.2\times25=40\,\text{J}$ .

Answer: $40\,\text{J}$ .

Common mistakes

Don't substitute $v=5$ into $v^2$ as $2\times5$ .
Don't write $(-3)^2$ as $-9$ after omitting the brackets.
Don't round an intermediate value and lose accuracy in the final answer.

Exam tip

Show the formula with every value substituted before entering it into the calculator.

Worked practice

Tier 1 · Easy

Work out

2x^2-5

when

x=-3

(2)

(Total for Question 1 is 2 marks)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$13$	2	Substitute using brackets: $2(-3)^2-5=2\times9-5=18-5=13$ .

Tier 2 · Standard

The kinetic energy of an object is given by

E=\frac12mv^2

. Work out

E

when

m=3.2\,\text{kg}

and

v=5\,\text{m s}^{-1}

(3)

(Total for Question 2 is 3 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$40\,\text{J}$	3	Substitute both values: $E=\frac12\times3.2\times5^2$ . Since $5^2=25$ , $E=0.5\times3.2\times25=40\,\text{J}$ .

Tier 3 · Hard

Use

E=mc^2

to calculate

E

when

m=4.2\times10^{-8}\,\text{kg}

and

c=3\times10^8\,\text{m s}^{-1}

. Give your answer in standard form.

(3)

(Total for Question 3 is 3 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$3.78\times10^9\,\text{J}$	3	Substitute before evaluating: $E=(4.2\times10^{-8})(3\times10^8)^2$ . Squaring gives $9\times10^{16}$ , so $E=4.2\times9\times10^8=37.8\times10^8=3.78\times10^9\,\text{J}$ .

Tier 1 · Easy

Work out

5a-b

when

a=4

and

b=-3

(2)

(Total for Question 4 is 2 marks)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$23$	2	Substitute both values, keeping the negative value in brackets: $5(4)-(-3)=20+3=23$ .

Tier 2 · Standard

The distance

d

metres travelled at speed

v

metres per second for

t

seconds is given by

d=vt

. Work out the value of

d

when

v=7.5

and

t=12

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$90\,\text{m}$	2	Substitute $v=7.5$ and $t=12$ : $d=7.5\times12=90$ . The distance is $90\,\text{m}$ .

Tier 3 · Hard

Work out

H=3d^2-2de

when

d=-2

and

e=5

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$32$	3	Substitute using brackets: $H=3(-2)^2-2(-2)(5)$ . Evaluate the power and products to get $H=12-(-20)=32$ .

Tier 2 · Standard

Work out

Q=\dfrac{a+b^2}{2c}

when

a=-5

b=3

and

c=2

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$Q=1$	3	Substitute using brackets: $Q=\dfrac{-5+3^2}{2(2)}$ . The numerator is $-5+9=4$ and the denominator is $4$ , so $Q=1$ .

Tier 3 · Hard

The value of

S

is given by

S=\dfrac{(u-v)^2}{w}

. Work out

S

when

u=5.4

v=1.8

and

w=0.6

(3)

(Total for Question 8 is 3 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$S=21.6$	3	Substitute the values before evaluating: $S=\dfrac{(5.4-1.8)^2}{0.6}$ . This is $\dfrac{3.6^2}{0.6}=\dfrac{12.96}{0.6}=21.6$ .

Tier 3 · Hard

The value of

R

is given by

R=\dfrac{a^2-bc}{a+c}

. Work out

R

when

a=-2

b=3

and

c=\dfrac12

. Write the result as a fully simplified fraction.

(3)

(Total for Question 9 is 3 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$R=-\dfrac53$	3	Substitute using brackets: $R=\dfrac{(-2)^2-3(\tfrac12)}{-2+\tfrac12}$ . The numerator is $4-\tfrac32=\tfrac52$ and the denominator is $-\tfrac32$ . Therefore $R=\tfrac52\div(-\tfrac32)=-\tfrac53$ .

Q10

Tier 3 · Hard

The value of

r

is given by

r=3p-2q

. The value of

S

is then given by

S=\dfrac{r^2-pq}{p-q}

. Work out

S

when

p=-1

and

q=4

. Show the value of

r

that you use.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$r=-11$ $S=-25$	4	First substitute into the relation for $r$ : $r=3(-1)-2(4)=-3-8=-11$ . Then $S=\dfrac{(-11)^2-(-1)(4)}{-1-4}=\dfrac{121+4}{-5}=\dfrac{125}{-5}=-25$ .

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2024-11	1H	Q8	3	Non-calculator	Higher	QP MS
2021-11	2F	Q24	6	Allowed	Foundation	QP MS
2022-06	1F	Q14	2	Non-calculator	Foundation	QP MS
2019-11	3F	Q7	2	Allowed	Foundation	QP MS
2019-11	2F	Q20	4	Allowed	Foundation	QP MS
2023-11	1F	Q12	6	Non-calculator	Foundation	QP MS
2022-11	1H	Q9	4	Non-calculator	Higher	QP MS
2019-06	2F	Q11	2	Allowed	Foundation	QP MS
2024-06	2H	Q3	2	Allowed	Higher	QP MS
2024-06	3F	Q29	4	Allowed	Foundation	QP MS
2022-06	3F	Q23	4	Allowed	Foundation	QP MS
2021-11	1F	Q26	4	Non-calculator	Foundation	QP MS
2022-06	3H	Q2	4	Allowed	Higher	QP MS
2019-11	1F	Q17	3	Non-calculator	Foundation	QP MS
2019-11	2F	Q28	3	Allowed	Foundation	QP MS
2024-11	2F	Q24	4	Allowed	Foundation	QP MS
2022-11	1F	Q25	2	Non-calculator	Foundation	QP MS
2022-11	2F	Q8	2	Allowed	Foundation	QP MS
2023-11	2F	Q20	4	Allowed	Foundation	QP MS
2024-06	2F	Q13	3	Allowed	Foundation	QP MS
2019-06	3F	Q15	4	Allowed	Foundation	QP MS
2024-06	2F	Q22	2	Allowed	Foundation	QP MS

Other points in A Algebra · notation and manipulation

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