🎯 By the End of This Lesson...
You should be able to:
- demonstrate secure knowledge of set language and notation;
- solve two-set and three-set examination problems;
- check answers using totals and counting formulas;
- judge whether you are ready to move to the next topic.
🌍 Why This Matters
The checkpoint combines notation, operations and Venn-diagram reasoning so you can measure genuine exam readiness rather than simple recall.
🎉 Sets Final Checkpoint
This assessment brings together the complete Sets topic. Work without opening earlier notes first, then use the answers to diagnose gaps.
Confidence Checklist
- I can describe sets in several forms.
- I can use membership and subset symbols.
- I can classify sets.
- I can calculate union, intersection, complement and difference.
- I can interpret two-set and three-set Venn diagrams.
- I can solve counting problems and check totals.
💡 Exam Tip
Show your working in structured questions. Correct region values and a clear counting equation can earn marks even if the final answer is wrong.
Section A: Core Knowledge
- Define a well-defined set.
- Write the factors of 24 in roster notation.
- Write {4,8,12,16,20} in set-builder notation.
- State n({a,b,b,c,d}).
- How many subsets does a 4-element set have?
Section B: Operations
- U={1,2,...,15}, A=multiples of 3 and B=factors of 12. Find A, B, A∩B, A∪B and A′.
- Find A\B and B\A.
- n(A)=41, n(B)=36 and n(A∪B)=58. Find n(A∩B).
Section C: Exam-Style Problems
- In a school of 120 learners, 68 play football, 54 play volleyball and 27 play both. Find football only, volleyball only and neither.
-
In a three-set survey of 90 people:
n(A)=42, n(B)=38, n(C)=35, n(A∩B)=16, n(A∩C)=14,
n(B∩C)=13 and n(A∩B∩C)=6. Find:
- the number in A∩B only;
- the number in A only;
- the number in at least one set;
- the number in none.
Section D: Extension Thinking
- A set has 256 subsets. Find its number of elements.
- Explain why n(A∪B) is not always equal to n(A)+n(B).
- Describe in words the region (A∪B)′ and the region A\B.
✅ Check Your Work
Show checkpoint answers
- A collection with a clear rule for deciding membership.
- {1,2,3,4,6,8,12,24}
- {x∈ℕ: x is a multiple of 4 and 4≤x≤20}
- 4
- 16
-
A={3,6,9,12,15}; B={1,2,3,4,6,12};
A∩B={3,6,12};
A∪B={1,2,3,4,6,9,12,15};
A′={1,2,4,5,7,8,10,11,13,14}. - A\B={9,15}; B\A={1,2,4}.
- 41+36−58=19.
- Football only=41; volleyball only=27; at least one=95; neither=25.
-
- 16−6=10
- 42−10−8−6=18, where A∩C only=14−6=8
- 42+38+35−16−14−13+6=78
- 90−78=12
- 8 elements, because 2⁸=256.
- Elements in the intersection would be counted twice.
- (A∪B)′ means neither A nor B; A\B means A only.
Celebration Message
You can now use sets as a language for organising information,
comparing groups and solving counting problems. These ideas will return
in probability, statistics and data handling.