4024/12 Oct/Nov 2024, Question 23: Three-Set Venn Diagrams
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Complete a three-set Venn diagram for 40 people taking singing, dancing and acting lessons, using given counts and a relationship involving the all-three region.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 3 marks
Fill in the missing Venn diagram regions using the given totals and the condition linking singing-only to all three lessons.
- 1S ∩ A only = 3, D only = 7
- 2Let all three = t, so S only = 4t
- 3S total: 4t + 6 + 3 + t = 19, so 5t = 10, t = 2
- 4All three = 2, S only = 4 × 2 = 8
- 5D ∩ A only = 40 − (8 + 6 + 7 + 3 + 2 + 10) = 4, outside all circles = 0
AnswerS only: 8 S ∩ D only: 6 D only: 7 S ∩ A only: 3 S ∩ D ∩ A: 2 D ∩ A only: 4 A only: 10 Outside all circles: 0
Part (b) · 1 mark
Express the region containing 10 people, acting only, using set notation.
- 1The 10 people take acting only: A ∩ S′ ∩ D′
AnswerA ∩ S′ ∩ D′
Stuck on a step? Read the free lesson: Three-Set Venn Diagrams
Practise more three-set venn diagrams questions
Real 4024 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on three-set venn diagrams
Also searched as: 4024/12/O/N/24 · 4024_w24_qp_12 · 4024 w24 12 · question 23.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.