What is N3: Inverse operations and priority of operations?

Inverse operations undo one another: addition pairs with subtraction, multiplication with division, and squaring with square root when the required value is non-negative. Use these relationships to check calculations or reverse a sequence of operations.

How many marks are N3 questions worth?

In verified past-paper appearances, N3 questions on Edexcel GCSE Maths 1MA1 have been worth 1–3 marks.

Which past exam papers has N3 appeared in?

N3 has appeared in 13 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Recognise and use relationships between operations, including inverse operations; use conventional notation for priority of operations, including brackets, powers, roots and reciprocals

Inverse operations and priority of operations

Worked answers, methods and verified real exam appearances for N3 on Edexcel GCSE Maths 1MA1.

Explanation

Inverse operations undo one another: addition pairs with subtraction, multiplication with division, and squaring with square root when the required value is non-negative. Use these relationships to check calculations or reverse a sequence of operations.
For a written calculation, follow conventional priority: brackets first; then powers and roots; then multiplication and division; then addition and subtraction.
Operations at the same priority are completed from left to right.
A reciprocal is also an inverse operation for multiplication: the reciprocal of $\dfrac{a}{b}$ is $\dfrac{b}{a}$ .
Examiners expect each priority stage to be visible when the question carries more than one mark.

Worked example

A positive number is squared, $11$ is subtracted, and the reciprocal of the result is $\dfrac{1}{14}$ . Find the number.

1.Reverse the reciprocal: the value before taking it was $14$ .
2.Undo subtracting $11$ : $14+11=25$ .
3.Undo the square using the positive square root: $\sqrt{25}=5$ .

Answer: $5$ .

Common mistakes

Don't add before multiplying in $18-3^2\times2$ .
Don't say the reciprocal of $\dfrac{a}{b}$ is $-\dfrac{a}{b}$ .
Don't forget that a square root symbol denotes the non-negative square root.

Exam tip

In a reverse-process question, undo the operations in the opposite order and write one inverse operation per line.

Worked practice

Tier 1 · Easy

Work out

18-3^2\times2

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$0$	1	Evaluate the power first: $3^2=9$ . Then multiply, $9\times2=18$ , and subtract: $18-18=0$ .

Tier 2 · Standard

Work out

\left(\sqrt{81}-5\right)^2\div2

(2)

(Total for Question 2 is 2 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$8$	2	Inside the brackets, $\sqrt{81}-5=9-5=4$ . Then $4^2=16$ and $16\div2=8$ .

Tier 3 · Hard

A positive number is squared,

11

is subtracted, and the reciprocal of the result is

\dfrac{1}{14}

. Find the original number.

(3)

(Total for Question 3 is 3 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$5$	3	Undo the reciprocal first: the result before taking the reciprocal was $14$ . Add $11$ to undo the subtraction, giving $25$ . The positive square root of $25$ is $5$ .

Tier 1 · Easy

Write down the reciprocal of

8

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$\dfrac{1}{8}$ (or $0.125$ )	1	The reciprocal multiplies by the original number to make $1$ . Since $8\times\dfrac{1}{8}=1$ , the reciprocal is $\dfrac{1}{8}$ .

Tier 2 · Standard

Insert one pair of brackets into

18-4\times2+3

to make the value

31

(1)

(Total for Question 5 is 1 mark)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$(18-4)\times2+3=31$	1	Place the brackets around $18-4$ . Then $(18-4)\times2+3=14\times2+3=31$ .

Tier 3 · Hard

Work out

2^3+36\div\sqrt{9}

, then subtract the reciprocal of

\dfrac{1}{4}

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$16$	3	$2^3=8$ and $\sqrt9=3$ , so $36\div\sqrt9=12$ . The reciprocal of $\dfrac14$ is $4$ , giving $8+12-4=16$ .

Tier 2 · Standard

Luca says that

728\div14=54

. Use an inverse operation to show that Luca is wrong. Work out the correct answer.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$54\times14=756\ne728$ , so Luca is wrong; $728\div14=52$	3	$14\times54=756$ , not $728$ , so the inverse operation shows Luca's answer is wrong. Since $14\times52=728$ , the correct answer is $52$ .

Tier 3 · Hard

Ravi works out

60\div5\times3

by first calculating

5\times3

and gets

4

. Explain Ravi's error and work out the correct value.

(3)

(Total for Question 8 is 3 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	Ravi should calculate from left to right; the correct value is $36$ .	3	Multiplication and division have equal priority, so they are completed from left to right. First $60\div5=12$ , then $12\times3=36$ . Ravi incorrectly treated the expression as $60\div(5\times3)$ .

Tier 3 · Hard

Work out

96\div\left[2\left(3^2-1\right)\right]+\sqrt{49}

(3)

(Total for Question 9 is 3 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$13$	3	Complete the inner operations first: $3^2-1=8$ , so $2\left(3^2-1\right)=16$ . Then $96\div16=6$ and $\sqrt{49}=7$ , giving $6+7=13$ .

Q10

Tier 3 · Hard

A number machine multiplies its input by

5

and then subtracts

8

. The output is

47

. Ben says to reverse the machine by adding

8

and then dividing by

5

. Layla says to divide by

5

and then add

8

. Who is correct? Work out the input.

(3)

(Total for Question 10 is 3 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	Ben is correct; the input is $11$ .	3	Inverse operations must be applied in reverse order. Add $8$ to the output, giving $55$ , and then divide by $5$ , giving $11$ . Checking: $11\times5-8=47$ , so Ben is correct.

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2024-11	2F	Q20	2	Allowed	Foundation	QP MS
2023-06	2H	Q1	3	Allowed	Higher	QP MS
2021-11	2F	Q9	1	Allowed	Foundation	QP MS
2024-11	1F	Q12	1	Non-calculator	Foundation	QP MS
2024-06	1F	Q11	3	Non-calculator	Foundation	QP MS
2023-06	2F	Q20	3	Allowed	Foundation	QP MS
2022-06	3F	Q15	2	Allowed	Foundation	QP MS
2022-11	2F	Q25	3	Allowed	Foundation	QP MS
2022-11	1F	Q3	1	Non-calculator	Foundation	QP MS
2019-06	1F	Q3	1	Non-calculator	Foundation	QP MS
2022-11	3F	Q17	3	Allowed	Foundation	QP MS
2019-06	3F	Q14	2	Allowed	Foundation	QP MS
2024-06	2F	Q19	3	Allowed	Foundation	QP MS

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