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Junior Cycle · Junior Cycle Maths

Junior Cycle Maths: Sets

How often Sets comes up on the Maths papers, every year it was asked, and questions to try.

HL Asked on 5 of the last 5 Higher Level papers, most recently in 2026. banker

OL Asked on 5 of the last 5 Ordinary Level papers, most recently in 2026. banker

Sets, Higher Level(7 marks)

Quick ones on Sets.

(a)In a class of 30, 18 play soccer, 15 play hurling and 4 play neither. How many play both?
  1. 3
  2. 7
  3. 11
(b)In a Venn diagram, which region is A′ ∩ B?
  1. In neither A nor B
  2. In A but not in B
  3. In B but not in A
(c)Which set operation is NOT commutative?
  1. Set difference (\)
  2. Intersection (∩)
  3. Union (∪)
Show the answers

(a) 7

(b) In B but not in A

(c) Set difference (\)

Your turn: Higher Level questions on Sets.

Higher Level

Asked on 5 of the last 5 Higher Level papers, most recently in 2026. banker

Every paper, year by year

YearWhere it came up
2026Q7
2025Q10
2024Q5
2023Q6
2022Q6

Links open the State Examinations Commission’s paper for that year.

More Sets questions

Sets, 3 marks

Venn diagram: A only = 2x, A ∩ B = 7, B only = x, outside = 4. There are 29 in total. Find x.

  1. 8
  2. 9
  3. 6
Show the answer

6

Add all four regions: 2x + 7 + x + 4 = 29, so 3x + 11 = 29, 3x = 18 and x = 6. Check: 12 + 7 + 6 + 4 = 29.

Ordinary Level

Asked on 5 of the last 5 Ordinary Level papers, most recently in 2026. banker

Every paper, year by year

YearWhere it came up
2026Q10
2025Q5
2024Q3
2023Q3
2022Q5

Links open the State Examinations Commission’s paper for that year.

More Sets questions

Sets, 2 marks

A = {2, 4, 6, 8} and B = {4, 5, 6}. Find A ∩ B.

  1. {2, 4, 5, 6, 8}
  2. {2, 8}
  3. {4, 6}
Show the answer

{4, 6}

∩ means intersection: the elements that are in BOTH sets. Only 4 and 6 are in A and also in B.

Sets, 2 marks

What is #{3, 6, 9, 12}?

  1. 30
  2. 4
  3. 12
Show the answer

4

# means the cardinal number: how many elements are in the set. There are 4 elements. It is not the biggest element or their total.

Sets, 2 marks

A = {1, 2, 3} and B = {3, 4}. Find A ∪ B.

  1. {1, 2, 3, 4}
  2. {3}
  3. {1, 2, 4}
Show the answer

{1, 2, 3, 4}

∪ means union: every element that is in A or in B (or both). List 3 once only: {1, 2, 3, 4}. {3} is the intersection.

Other Maths topics

All of Junior Cycle Maths