Venn diagrams Quiz (Grade 5)

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Topic:

Score: 0 / 10

Venn diagrams — Notes & Worked Examples Show / Hide

Explanation:

When completing a Venn diagram, always fill in the central overlap (intersection A ∩ B) first. Subtract the overlap from the total for circle A to find the "A only" region, do the same for "B only", and check that all regions (including outside the circles) add up to the universal set ξ.

Set notation: A ∩ B means in both A and B; A ∪ B means in A or B (or both); A′ means not in A.

Example 1: In a class of 30 students (ξ), 18 study French (F), 14 study Spanish (S), and 5 study neither. How many study both?

Solution:

In F ∪ S = 30 − 5 = 25

18 + 14 = 32

Both = 32 − 25 = 7

Answer: 7 students

Example 2: Using Example 1, a student is chosen at random. Find (a) P(F ∪ S) and (b) P(F given S).

Solution:

(a) 25 out of 30 are in F ∪ S → 2530 = 56

(b) Given the student studies Spanish (14 students),

7 of those also study French → 714 = 12

Answer: (a) 56, (b) 12

One Page Guide (PDF) Venn diagrams Worksheets

Question 1

[2 marks]

ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {even numbers}
B = {multiples of 3}
Complete the Venn diagram.

Worked Solution & Answer

Even integers are multiples of 2 (form 2n); odd integers leave a remainder of 1 when divided by 2 (form 2n + 1).
A only: 2, 4, 8, 10; A ∩ B: 6; B only: 3, 9; Outside: 1, 5, 7

Answer: A only: 2, 4, 8, 10; A ∩ B: 6; B only: 3, 9; Outside: 1, 5, 7

Question 2

[2 marks]

The Venn diagram shows the number of people in sets A and B.
A person is chosen at random.
Find P(A ∪ B).

Worked Solution & Answer

Intersection (∩) = in **both** sets (overlap); Union (∪) = in **either** set or both; Complement (') = **not** in that set; n(X) = number of elements in X.
4553

Answer: 4553

Question 3 IGCSE Jun 2019 1HR Q13

[2 marks]

(a) On the Venn diagram, shade the set (A ∪ B)' ∩ C. (1) (b) Use set notation to describe the shaded region in the Venn diagram (D, E, F). (1)

(a) On the Venn diagram, shade the set (A ∪ B)' ∩ C [1 mark]

(b) Use set notation to describe the shaded region in the Venn diagram below. [1 mark]

Worked Solution & Answer

(a)

Outside A ∪ B intersected with C B1

Answer (a): Region inside C and outside A ∪ B shaded

(b)

Inside F and inside D or E: (D ∪ E) ∩ F B1

Answer (b): (D ∪ E) ∩ F

Question Paper (PDF) • Mark Scheme (PDF)

Question 4 IGCSE Jun 2025 1F Q16

[3 marks]

Some students were asked if they study French (F) or Spanish (S)
The Venn diagram gives information about the results.
The values shown represent numbers of students.

(a) How many of these students study only French or only Spanish? [1 mark]

(b) Find the probability that this student studies both French and Spanish. [2 marks]

Worked Solution & Answer

(a)

9 + 8 = 17 B1

Answer (a): 17

(b)

Total students = 9 + 6 + 8 + 2 = 25 M1
⇒ P(both) = 6/25 A1

Answer (b): 625

Question Paper (PDF) • Mark Scheme (PDF)

Question 5

[3 marks]

Here is a Venn diagram.

(a) Write down the numbers that are in set P' [1 mark]

(b) Find the probability that this number is in the set P ∪ Q [2 marks]

Worked Solution & Answer

(a)

Numbers not in P: 10, 11, 13, 14, 16, 17 B1

Answer (a): 10, 11, 13, 14, 16, 17

(b)

5 numbers in P ∪ Q out of 9 total M1
⇒ 5/9 A1

Answer (b): 59

Question Paper (PDF) • Mark Scheme (PDF)

Question 6 AQA Nov 2020 1F Q12

[3 marks]

The Venn diagram shows information about 50 people who are in bands.
S = singers
G = guitar players

(a) How many of the people are guitar players? [1 mark]

Answer

(b) How many of the people are singers but not guitar players? [1 mark]

Answer

(c) One of the people is chosen at random.
Write down the probability that the person is not a singer and not a guitar player. [1 mark]

Answer

Worked Solution & Answer

(a)

Total guitar players = 8 + 21 = 29 B1

Answer (a): Answer 29

(b)

People in S only = 4 B1

Answer (b): Answer 4

(c)

People outside both circles = 17
Total people = 50
Probability = 1750 B1

Answer (c): Answer 17/50

Question Paper (PDF) • Mark Scheme (PDF)

Question 7 IGCSE Nov 2023 1F Q15 / 1H Q1

[3 marks]

Here is a Venn diagram.

(a) A [1 mark]

(b) A ∩ B [1 mark]

Worked Solution & Answer

(a)

All elements inside circle A B1

Answer (a): 5, 7, 9, 11, 13, 15

(b)

Elements in intersection of A and B B1

Answer (b): 5, 15

(c)

Elements outside both circles B1

Answer (c): 6, 8, 12, 14, 16

Question Paper (PDF) • Mark Scheme (PDF)

Question 8 AQA Nov 2024 3F Q14

[4 marks]

The Venn diagram shows information about people who work in a gym.
• T = people who can work as a trainer.
• R = people who can work in reception.

(a) How many people can work as a trainer **and** in reception? [1 mark]

Answer

(b) How many people can work in reception but **not** as a trainer? [1 mark]

Answer

Worked Solution & Answer

(a)

Intersection T ∩ R = 3 B1

Answer (a): Answer 3

(b)

In R only = 12 B1

Answer (b): Answer 12

(c)

Total trainers = 17 + 3 = 20 M1
Total people = 17 + 3 + 12 + 5 = 37
Fraction = 2037 A1

Answer (c): Answer 2037

Question Paper (PDF) • Mark Scheme (PDF)

Question 9 IGCSE Specimen 1F Q6

[5 marks]

\mathscr{E} = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {1, 2, 3, 4, 6, 12}
B = {2, 3, 5, 7, 11}

(a) Complete the Venn diagram to show this information. [3 marks]

(b) (i) A ∩ B
(ii) B' [2 marks]

Worked Solution & Answer

(a)

Intersection = {2, 3} M1
A only = {1, 4, 6, 12} M1
B only = {5, 7, 11}
Outside = {8, 9, 10} A1

Answer (a): A only: 1, 4, 6, 12; A ∩ B: 2, 3; B only: 5, 7, 11; Outside: 8, 9, 10

(b)

2, 3. (ii) Complement of B = 1, 4, 6, 8, 9, 10, 12 M1 A1

Answer (b): (i) 2, 3 (ii) 1, 4, 6, 8, 9, 10, 12

Question Paper (PDF) • Mark Scheme (PDF)

Question 10

[5 marks]

\mathscr{E} = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 5, 6, 8, 9}
B = {2, 6, 9}

(a) Complete the Venn diagram to represent this information. [3 marks]

(b) Find the probability that the number is in the set A ∩ B [2 marks]

Worked Solution & Answer

(a)

A only: 1, 5, 8 M1
Intersection: 6, 9 M1
B only: 2
Outside: 3, 4, 7 A1

Answer (a): A only: 1, 5, 8; Intersection: 6, 9; B only: 2; Outside: 3, 4, 7

(b)

Two numbers (6 and 9) out of 9 in A ∩ B M1
⇒ 2/9 A1

Answer (b): 29

Question Paper (PDF) • Mark Scheme (PDF)

Score: 0 / 10 (0 / 32 marks)

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Grade 5 Quizzes

25 Topics

5A - Combining ratios	5B - Direct and inverse proportion
5C - Reverse percentages	5D - Standard form
5E - Speed	5F - Changing the subject
5G - Quadratic expressions	5H - Solving quadratic equations
5J - Drawing quadratic graphs	5K - Cubic/reciprocal graphs
5L - Simultaneous equations	5M - Sector areas and arc lengths
5N - Sim. equ. graphically	5P - Midpoint of a line segment
5Q - Gradient of a line	5R - Equation of a line
5S - Spheres and cones	5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)	5V - Exact trig. values
5W - Probability trees	5X - Vectors
5Y - Venn diagrams	5Z - Density
5AA - Pressure