Systematic listing Quiz (Grade 2)

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Topic:

Score: 0 / 10

Systematic listing — Notes & Worked Examples Show / Hide

Explanation:

To list all possible outcomes without missing or repeating any, use a systematic order: fix the first item and work through every partner in order, then move to the second item and repeat. Use clear single-letter abbreviations to save time.

You can check how many combinations there should be in total by multiplying the number of choices in each group (e.g. 2 starters × 3 mains = 6 combinations). Read carefully whether items can be repeated or if order matters.

Example 1: A café offers 2 starters: Soup (S) or Melon (M), and 3 mains: Chicken (C), Fish (F), or Pasta (P). List all possible 2-course meals.

Solution:

Fix the starter first, then pair with each main:

• With Soup (S): SC, SF, SP

• With Melon (M): MC, MF, MP

Check: 2 × 3 = 6 combinations in total.

Example 2: Write down all possible 3-digit numbers that can be made using each of the digits 2, 5, and 8 once.

Solution:

Fix the hundreds digit in ascending order:

• Starting with 2: 258, 285

• Starting with 5: 528, 582

• Starting with 8: 825, 852 (Total = 6 numbers)

One Page Guide (PDF) Systematic listing Worksheets

Question 1

[1 mark]

A restaurant offers 2 starters: Soup (S) or Melon (M).
It offers 3 main courses: Beef (B), Fish (F), or Pasta (P).
List all the possible combinations of 1 starter and 1 main course.

Worked Solution & Answer

List systematically starting with each item in turn, or multiply the number of choices for each stage together.
SB, SF, SP, MB, MF, MP

Answer: SB, SF, SP, MB, MF, MP

Question 2

[1 mark]

Use the digits 4, 1, 3.
List all the possible 2-digit numbers you can make without repeating any digits.

Worked Solution & Answer

List systematically starting with each item in turn, or multiply the number of choices for each stage together.
41, 43, 14, 13, 34, 31

Answer: 41, 43, 14, 13, 34, 31

Question 3

[1 mark]

Work out
A fair coin is flipped and a fair 6-sided dice is rolled.
List all the possible outcomes.
(Use H for Heads and T for Tails)

Worked Solution & Answer

List systematically starting with each item in turn, or multiply the number of choices for each stage together.
H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6

Answer: H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6

Question 4

[1 mark]

Use the digits 3, 2, 4.
List all the possible 2-digit numbers you can make without repeating any digits.

Worked Solution & Answer

List systematically starting with each item in turn, or multiply the number of choices for each stage together.
32, 34, 23, 24, 43, 42

Answer: 32, 34, 23, 24, 43, 42

Question 5

[1 mark]

Use the digits 3, 4, 2.
List all the possible 2-digit numbers you can make without repeating any digits.

Worked Solution & Answer

List systematically starting with each item in turn, or multiply the number of choices for each stage together.
34, 32, 43, 42, 23, 24

Answer: 34, 32, 43, 42, 23, 24

Question 6

[1 mark]

Use the digits 3, 4, 1.
List all the possible 2-digit numbers you can make without repeating any digits.

Worked Solution & Answer

List systematically starting with each item in turn, or multiply the number of choices for each stage together.
34, 31, 43, 41, 13, 14

Answer: 34, 31, 43, 41, 13, 14

Question 7

[1 mark]

Use the digits 4, 1, 2.
List all the possible 2-digit numbers you can make without repeating any digits.

Worked Solution & Answer

List systematically starting with each item in turn, or multiply the number of choices for each stage together.
41, 42, 14, 12, 24, 21

Answer: 41, 42, 14, 12, 24, 21

Question 8

[1 mark]

Use the digits 3, 1, 4.
List all the possible 2-digit numbers you can make without repeating any digits.

Worked Solution & Answer

List systematically starting with each item in turn, or multiply the number of choices for each stage together.
31, 34, 13, 14, 43, 41

Answer: 31, 34, 13, 14, 43, 41

Question 9

[1 mark]

Use the digits 1, 3, 2.
List all the possible 2-digit numbers you can make without repeating any digits.

Worked Solution & Answer

List systematically starting with each item in turn, or multiply the number of choices for each stage together.
13, 12, 31, 32, 21, 23

Answer: 13, 12, 31, 32, 21, 23

Question 10

[1 mark]

Use the digits 4, 3, 2.
List all the possible 2-digit numbers you can make without repeating any digits.

Worked Solution & Answer

List systematically starting with each item in turn, or multiply the number of choices for each stage together.
43, 42, 34, 32, 24, 23

Answer: 43, 42, 34, 32, 24, 23

Score: 0 / 10 (0 / 10 marks)

Systematic listing Worksheets Next: Fraction of an amount →

Grade 2 Quizzes

19 Topics

2A - Calculation problems	2B - Using a calculator
2C - Systematic listing	2D - Fraction of an amount
2E - FDP	2F - Simplifying algebra
2G - Writing an expression	2H - Function machines
2J - Solving one step equations	2K - Angles
2L - Area and perimeter	2M - Reading scales
2N - Probability & Probability Scale	2P - Frequency polygons
2Q - Unitary method	2R - Bar charts
2S - Pie charts	2T - Averages
2U - Stem and leaf diagrams