What is N5: Listing strategies?

A systematic listing strategy fixes one choice and cycles through every permitted second choice before moving on. Use a clear order, such as increasing digits or alphabetical letters, so you can see that no result is missing or repeated.

How many marks are N5 questions worth?

In verified past-paper appearances, N5 questions on Edexcel GCSE Maths 1MA1 have been worth 1–4 marks.

Which past exam papers has N5 appeared in?

N5 has appeared in 14 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Apply systematic listing strategies, including use of the product rule for counting (m ways of doing one task and n ways of doing another gives m × n ways in total)

Listing strategies

Worked answers, methods and verified real exam appearances for N5 on Edexcel GCSE Maths 1MA1.

Explanation

A systematic listing strategy fixes one choice and cycles through every permitted second choice before moving on. Use a clear order, such as increasing digits or alphabetical letters, so you can see that no result is missing or repeated.
When order matters, AB and BA are different outcomes; when order does not matter, list each pair only once.
A table or tree can organise several stages.
Higher tier: if one task can be completed in $m$ ways and a following independent choice in $n$ ways, the product rule gives $m\times n$ combined outcomes.
Examiners award completeness only when the structure of the list is evident.

Worked example

Higher tier: Three different digits are chosen from $2$ , $4$ , $5$ and $7$ to make an even three-digit number. How many numbers are possible?

1.Fix the final digit as $2$ : choose and order two of the remaining three digits, giving $3\times2=6$ numbers.
2.Fix the final digit as $4$ : again there are $3\times2=6$ numbers.
3.Add the two disjoint cases: $6+6=12$ .

Answer: $12$ even numbers.

Common mistakes

Don't change two positions at once and omit a valid outcome.
Don't count AB and BA twice when the question says order does not matter.
Don't use the product rule even though later choices depend on earlier restrictions.

Exam tip

Group a list by one fixed position or case; an unstructured collection may not earn the method mark for systematic listing.

Worked practice

Tier 1 · Easy

A badge uses one of the letters A, B or C and one of the numbers

1

2

3

. List every possible badge code in a systematic order.

(2)

(Total for Question 1 is 2 marks)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	A₁, A₂, A₃, B₁, B₂, B₃, C₁, C₂, C₃	2	Hold the letter fixed while cycling through the numbers: A₁, A₂, A₃; then B₁, B₂, B₃; then C₁, C₂, C₃. This gives all $9$ codes once each.

Tier 2 · Standard

A three-digit number is made using three different digits from

2

4

5

and

7

. List all the possible even numbers.

(3)

(Total for Question 2 is 3 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$452$ , $472$ , $542$ , $572$ , $742$ , $752$ , $254$ , $274$ , $524$ , $574$ , $724$ , $754$	3	List by the final digit. Ending in $2$ gives $452$ , $472$ , $542$ , $572$ , $742$ , $752$ . Ending in $4$ gives $254$ , $274$ , $524$ , $574$ , $724$ , $754$ . The fixed final digit makes the list systematic and complete.

Tier 3 · Hard

Two different numbers are selected from

1

2

3

4

and

5

. The order of selection does not matter. List every pair whose product is even and whose sum is greater than

5

(3)

(Total for Question 3 is 3 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$(2,4)$ , $(2,5)$ , $(3,4)$ , $(4,5)$	3	List unordered pairs in rows beginning with $1$ , then $2$ , then $3$ , then $4$ . Reject pairs with an odd product or sum at most $5$ . The pairs left are $(2,4)$ , $(2,5)$ , $(3,4)$ and $(4,5)$ .

Tier 1 · Easy

Use two different digits from

1

2

and

3

to make a two-digit number. List all the possible numbers.

(2)

(Total for Question 4 is 2 marks)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$12,13,21,23,31,32$	2	Fix the tens digit in turn. Starting with $1$ gives $12,13$ ; starting with $2$ gives $21,23$ ; starting with $3$ gives $31,32$ .

Tier 2 · Standard

A route uses gate A or gate B, followed by lane

1

2

3

. Lane

3

is closed after gate B. List all the possible routes.

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	A₁, A₂, A₃, B₁, B₂	2	Hold the gate fixed. Gate A gives A₁, A₂ and A₃. Gate B would give B₁, B₂ and B₃, but B₃ is unavailable, leaving B₁ and B₂.

Tier 3 · Hard

One spinner is labelled

1

2

4

and another is labelled

1

3

. Both spinners are spun once. List all the possible totals. Write each total once. You must show all your working.

(2)

(Total for Question 6 is 2 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$2,\ 3,\ 4,\ 5,\ 7$	2	Fix the result on the first spinner. With $1$ , the totals are $2,4$ ; with $2$ , they are $3,5$ ; with $4$ , they are $5,7$ . This records all six outcomes, so the possible totals are $2, 3, 4, 5, 7$ .

Tier 2 · Standard

An appointment can start at

10{:}00

10{:}30

11{:}00

and can last

30

minutes or

60

minutes. It must finish by

11{:}30

. List all the possible start-time and duration pairs.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$10{:}00$ and $30$ minutes; $10{:}00$ and $60$ minutes; $10{:}30$ and $30$ minutes; $10{:}30$ and $60$ minutes; $11{:}00$ and $30$ minutes	3	List both durations for $10{:}00$ and both for $10{:}30$ . At $11{:}00$ , only the $30$ -minute appointment finishes by $11{:}30$ ; a $60$ -minute appointment finishes too late. This gives five pairs.

Tier 3 · Hard

An outfit has one jacket, one pair of trousers and one pair of shoes. The jackets are black and grey. The trousers are navy, cream and khaki. The shoes are boots and trainers. The grey jacket is never worn with the khaki trousers, and the navy trousers are never worn with the trainers. List all the possible outfits.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	black-navy-boots; black-cream-boots; black-cream-trainers; black-khaki-boots; black-khaki-trainers; grey-navy-boots; grey-cream-boots; grey-cream-trainers	4	Hold the jacket and trousers fixed, then test both pairs of shoes. The black jacket gives five outfits: navy-boots, both cream outfits and both khaki outfits. The grey jacket gives three outfits: navy-boots and both cream outfits. The restrictions remove every grey-khaki outfit and each navy-trainers outfit.

Tier 3 · Hard

Higher only: A light signal uses one of four colours, one of three patterns and one of two durations. A red signal can use only the steady pattern. The other colours can use any pattern. Work out the total number of different signals.

(4)

(Total for Question 9 is 4 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$20$ signals	4	For each of the three non-red colours there are $3\times2=6$ pattern-duration choices, giving $3\times6=18$ signals. Red has one pattern and two durations, giving $2$ more. The total is $18+2=20$ .

Q10

Tier 3 · Hard

A robot reaches its target by making exactly three moves east and two moves north. It can make the five moves in any order. Work out the number of different routes. You must show a systematic method.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$10$ routes	4	List routes by the positions of the two north moves: NNEEE, NENEE, NEENE, NEEEN, ENNEE, ENENE, ENEEN, EENNE, EENEN and EEENN. This systematic list has $10$ different routes.

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2024-11	2H	Q14	2	Allowed	Higher	QP MS
2023-11	2F	Q9	2	Allowed	Foundation	QP MS
2022-11	2F	Q5	1	Allowed	Foundation	QP MS
2021-11	3F	Q7	2	Allowed	Foundation	QP MS
2019-11	2H	Q14	2	Allowed	Higher	QP MS
2024-06	3H	Q13	2	Allowed	Higher	QP MS
2019-06	1H	Q16	4	Non-calculator	Higher	QP MS
2024-06	2F	Q10	2	Allowed	Foundation	QP MS
2021-11	2H	Q13	2	Allowed	Higher	QP MS
2022-06	3H	Q11	2	Allowed	Higher	QP MS
2022-11	3H	Q15	2	Allowed	Higher	QP MS
2023-11	3H	Q16	3	Allowed	Higher	QP MS
2023-06	1H	Q19	2	Non-calculator	Higher	QP MS
2019-11	1F	Q11	2	Non-calculator	Foundation	QP MS

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