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CAIE IGCSE Mathematics Core C1.2 Sets Questions

Practise using two-set Venn diagrams and set notation to place elements, count complements and describe shaded or excluded regions.

Syllabus
2028–2030
Course
Mathematics 0580
Level
Core

Exam points

  • complete a two-set Venn diagram from counts, listed elements or survey information
  • find n(A), n(A') or a contextual total by reading the correct Venn region
  • describe shaded or contextual regions using union, intersection or complement notation

Covered syllabus points

C1.2.1 Understand and use set language, notation and Venn diagrams to describe

Question 1

[Maximum number: 4]

21E={a,b,d,e,f,h,i,m,p,t,u}21 \quad \mathscr{E}=\{\mathrm{a}, \mathrm{b}, \mathrm{d}, \mathrm{e}, \mathrm{f}, \mathrm{h}, \mathrm{i}, \mathrm{m}, \mathrm{p}, \mathrm{t}, \mathrm{u}\}X={a,e,i,u}X=\{\mathrm{a}, \mathrm{e}, \mathrm{i}, \mathrm{u}\}Y={d,e,m,p,t,u}Y=\{\mathrm{d}, \mathrm{e}, \mathrm{m}, \mathrm{p}, \mathrm{t}, \mathrm{u}\}

Question (a)

(a)

Use this information to complete the Venn diagram.

Figure for Question (a) — CAIE IGCSE Mathematics Core
[ 2 ]

Question (b)

(b)

List the elements of X∩YX \cap Y.

[ 1 ]

Question (c)

(c)

Find n(X′)\mathrm{n}\left(X^{\prime}\right).

[ 1 ]

Question 2

[Maximum number: 4]

Question (a)

(a)

Use set notation to describe the shaded region.

Figure for Question (a) — CAIE IGCSE Mathematics Core
[ 1 ]

Question (b)

(b)

E={people in a club}\mathcal{E}=\{\text{people in a club}\}T={people who play tennis}T=\{\text{people who play tennis}\}S={people who go swimming}S=\{\text{people who go swimming}\}
There are 60 people in the club.
36 people go swimming.

Figure for Question (b) — CAIE IGCSE Mathematics Core
[ 3 ]

Question (i)

(i)

Complete the Venn diagram.

[ 2 ]

Question (ii)

(ii)

Find n(T').

[ 1 ]

Question 3

[Maximum number: 3]
Figure for Question 3 — CAIE IGCSE Mathematics Core

E={students in a year group}E=\{\text{students in a year group}\}H={students who study History}H=\{\text{students who study History}\}G={students who study Geography}G=\{\text{students who study Geography}\}
80 students are in the year group.
40 students study History.

Question (a)

(a)

Complete the Venn diagram.

[ 2 ]

Question (b)

(b)

Find n(G).

[ 1 ]
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