🎯 By the End of This Lesson...
You should be able to:
- select the correct set concept without being prompted;
- use notation, operations and Venn diagrams accurately;
- explain your reasoning clearly;
- identify the lessons that need more revision.
🌍 Why This Matters
Mixed practice tests whether you can recognise the correct idea independently—the skill required in an examination.
Mixed Review: Choose the Idea Yourself
These questions mix notation, subsets, operations and Venn-diagram counting. Decide which idea is needed before calculating.
💡 Exam Tip
Underline key words such as both, only, at least one and neither. Translate them into regions or symbols before doing any arithmetic.
Part A: Set Language
- Write the prime numbers below 15 in roster form.
- Write the integers from −4 to 4 in set-builder notation.
- State whether {1,3} ⊂ {1,2,3}.
- How many subsets does a 7-element set have?
- Explain the difference between ∈ and ⊆.
Part B: Operations
- U={1,...,12}, A={2,4,6,8,10,12}, B={3,6,9,12}. Find A∩B, A∪B and A′.
- Find A\B and B\A using the sets in Question 6.
- n(A)=32, n(B)=27 and n(A∩B)=14. Find n(A∪B).
Part C: Word Problems
- Of 70 students, 42 study History, 36 study Geography and 18 study both. Find the number studying neither.
- In a three-set survey, n(A)=35, n(B)=30, n(C)=28, n(A∩B)=12, n(A∩C)=11, n(B∩C)=10 and n(A∩B∩C)=5. Find the union.
✅ Check Your Work
Show mixed review answers
- {2,3,5,7,11,13}
- {x∈ℤ: −4≤x≤4}
- Yes.
- 2⁷=128.
- ∈ links an element to a set; ⊆ links one set to another.
- A∩B={6,12}; A∪B={2,3,4,6,8,9,10,12}; A′={1,3,5,7,9,11}.
- A\B={2,4,8,10}; B\A={3,9}.
- 32+27−14=45.
- At least one=42+36−18=60; neither=10.
- 35+30+28−12−11−10+5=65.
Reflection
- Can you translate words into set notation?
- Can you distinguish membership from subset relationships?
- Can you select union, intersection, complement or difference?
- Can you solve two-set and three-set counting problems?
➡️ What’s Next?
Revision Guidance and Readiness
- Attempt the questions without notes first.
- Use the answers or worked solutions to identify the exact step that needs attention.
- Return to the relevant lesson, then retry missed questions.
- You are ready to move on when you can explain your method and check your result independently.