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CAIE IGCSE Mathematics Extended E1.2 Sets Questions

Practise completing and shading Venn diagrams and interpreting unions, intersections, complements and set cardinality in notation.

Syllabus
2028–2030
Course
Mathematics 0580
Level
Extended

Exam points

  • translate unions, intersections and complements into the correct region of a Venn diagram
  • complete missing Venn-region counts using the set total and all overlapping regions
  • evaluate n(A), n(A ∩ B) or a complemented set by summing only the required regions

Covered syllabus points

E1.2.1 Understand and use set language, notation and Venn diagrams to describe

Question 1

[Maximum number: 5]

Question (a)

(a)
Figure for Question (a) — CAIE IGCSE Mathematics Extended

Use set notation to describe the shaded region in the Venn diagram.

[ 1 ]

Question (b)

(b)

Shade the correct region in each Venn diagram.

Figure for Question (b) — CAIE IGCSE Mathematics Extended
[ 2 ]

Question (c)

(c)
Figure for Question (c) — CAIE IGCSE Mathematics Extended

50 students are asked if they like English ( E ) and if they like mathematics ( M ). 3 say they do not like English and do not like mathematics.
33 say they like English.
42 say they like mathematics.

[ 2 ]

Question (i)

(i)

Complete the Venn diagram.

[ 2 ]

Question 2

[Maximum number: 5]

This year, 40 students have each travelled by one or more of plane (P), train (T) or boat (B).
7 have travelled only by plane.
11 have travelled only by train.
9 have travelled only by boat.

n(P∩T)=8n(B∩T)=3n(B∩P)=6\begin{aligned} & \mathrm{n}(P \cap T)=8 \\ & \mathrm{n}(B \cap T)=3 \\ & \mathrm{n}(B \cap P)=6 \end{aligned}
Figure for Question 2 — CAIE IGCSE Mathematics Extended

Question (a)

(a)

Complete the Venn diagram.

[ 3 ]

Question (b)

(b)

Find n((P∪B)′)\mathrm{n}\left((P \cup B)^{\prime}\right).

[ 1 ]

Question (c)

(c)

Use set notation to complete the statement.

(P∪T∪B)′=(P \cup T \cup B)^{\prime}=
[ 1 ]

Question 3

[Maximum number: 2]

The Venn diagram shows the number of students in a class of 40 who study physics ( P ), mathematics ( M ) and geography ( G ).

Figure for Question 3 — CAIE IGCSE Mathematics Extended

Question (a)

(a)

Use set notation to describe the shaded region.

[ 1 ]

Question (b)

(b)

Find n((P∩G)∪M′)\mathrm{n}\left((P \cap G) \cup M^{\prime}\right).

[ 1 ]
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