Where can I download free venn diagrams PDF worksheets with answers?

On this MathsLinks page you can download free printable venn diagrams PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, IGCSE MT, Maths Genie, Maths4Everyone, Corbett Practice, plus a printable one-page venn diagrams revision guide.

What GCSE grade is venn diagrams (5Y)?

Venn diagrams (topic code 5Y) is a Grade 5 probability topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Venn diagrams Worksheets (PDF) with Answers — GCSE Maths

Free Venn diagrams PDF Worksheets & Answers

Grade 5 • Topic 5Y

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
IGCSE MT IGCSE (9–1) past paper booklet	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Maths4Everyone GCSE 9–1 practice booklet & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
nrich interactive resource Interactive online resource	Open
Cognito Interactive online lesson & practice	Page
esheets Self-marking online worksheet	Page

Grade 5 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

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

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Venn diagrams Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 IGCSE Jun 2025 1F Q16 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

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 & Mark Scheme (3 marks)

Part (a) Solution:

9 + 8 = 17 B1

Answer (a): 17

Part (b) Solution:

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

Answer (b): 625

Past Paper Example 2 AQA Nov 2020 1F Q12 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

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]

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

(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]

Worked Solution & Mark Scheme (3 marks)

Part (a) Solution:

Total guitar players = 8 + 21 = 29 B1

Answer (a): Answer 29

Part (b) Solution:

People in S only = 4 B1

Answer (b): Answer 4

Part (c) Solution:

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

Answer (c): Answer 17/50

Past Paper Example 3 IGCSE Specimen 1F Q6 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

\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 & Mark Scheme (5 marks)

Part (a) Solution:

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

Part (b) Solution:

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

← 5X Vectors

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5Z Density →

Venn diagrams

Free Venn diagrams PDF Worksheets & Answers

Guide to Venn diagrams: Explanation, Diagrams & Worked Examples

GCSE Past Paper Venn diagrams Questions & Answers