Where can I download free frequency trees PDF worksheets with answers?

On this MathsLinks page you can download free printable frequency trees PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Maths Genie, Corbett Practice, Corbett Textbook, Maths Made Easy, plus a printable one-page frequency trees revision guide.

What GCSE grade is frequency trees (3Y)?

Frequency trees (topic code 3Y) is a Grade 3 probability topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Frequency trees Worksheets (PDF) with Answers — GCSE Maths

Free Frequency trees PDF Worksheets & Answers

Grade 3 • Topic 3Y

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
Transum interactive resource Interactive online resource	Open
esheets Self-marking online worksheet	Page

Grade 3 topics
3A - Error intervals	3B - Operations with fractions
3C - Estimation	3D - Writing and simplifying ratio
3E - Ratio	3F - Proportion recipes
3G - Percentages	3H - Percentage change
3J - Exchange rates	3K - Conversions and units
3L - Scale drawings	3M - Best buy questions
3N - Substitution	3P - Solving linear equations
3Q - Straight line graphs	3R - Area and circumference
3S - Rotations	3T - Reflections
3U - Enlargements	3V - Translations
3W - Mixed transformations	3X - Area of compound shapes
3Y - Frequency trees	3Z - Two way tables

Explanation:

A frequency tree organises data by splitting a total group into two categories, and then splitting each branch further. The two branches coming out of any circle must always add up to the number inside that circle.

Work through the clues step by step, filling in any numbers given directly and subtracting from the parent circle to find the partner branch. When asked for a probability at the end, check carefully whether it is out of the whole group or a specific subgroup.

Example 1: 60 students sat a test. 35 are girls. 28 girls passed. In total, 47 students passed. Complete the frequency tree.

Boys = 60 − 35 = 25; Girls Fail = 35 − 28 = 7

Boys Pass = 47 − 28 = 19; Boys Fail = 25 − 19 = 6

Example 2: Using the frequency tree from Example 1:
(a) One student is chosen at random. Find P(Boy who failed).
(b) A boy is chosen at random. Find P(Passed).

Solution:

(a) Out of all 60 students, 6 are boys who failed:

P(Boy who failed) = 660 = 110

(b) Out of the 25 boys, 19 passed:

Answer: (a) 660 (or 110) (b) 1925

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Frequency trees Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 GCSE Nov 2023 3F Q15 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

A travel agent sold 100 holidays in April.
Each of these holidays was in the UK or was abroad.
64 of the 100 holidays were sold to families.
The rest of the holidays were sold to couples.
11 of the 18 holidays abroad were sold to couples.

(a) Use this information to complete the frequency tree. [3 marks]

(b) Find the probability that this holiday was **not** abroad. [2 marks]

Worked Solution & Mark Scheme (5 marks)

Part (a) Solution:

Couples = 36, Couples UK = 36 – 11 = 25 M2
Families abroad = 18 – 11 = 7, Families UK = 64 – 7 = 57 A1

Answer (a): families = 64 (UK = 57, abroad = 7); couples = 36 (UK = 25, abroad = 11)

Part (b) Solution:

57/64 M1 A1

Answer (b): 5764

Past Paper Example 2 AQA Jun 2022 3F Q9 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

Some students were asked about their daily exercise.

(a) 12 more students answered Yes than answered No.
Complete the frequency tree. [3 marks]

(b) One of the 35 students who answered Yes is chosen at random.
What is the probability that they exercise for at least 1 hour? [1 mark]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

Yes = 35 M1
Since Yes is 12 more than No: No = 35 - 12 = 23 M1
Total students = 35 + 23 = 58
From 35 Yes students, 27 exercise at least 1 hour, so 35 - 27 = 8 exercise less than 1 hour. A1

Answer (a): Answer Total = 58, No = 23, Less than 1 hour = 8

Part (b) Solution:

Out of the 35 students who answered Yes, 27 exercise for at least 1 hour, so probability = 2735. B1

Answer (b): Answer 2735

Past Paper Example 3 GCSE Nov 2019 1F Q15 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

120 people were at a hockey match.
Each person was asked if they wanted to stand or to sit to watch the match.
[INDENT]75 of the people were female
[INDENT]29 of the males wanted to stand
[INDENT]30 of the people wanted to sit

(a) Use this information to complete the frequency tree. [3 marks]

(b) Write down the probability that this person is a male who wanted to stand. [1 mark]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

Males = 120 – 75 = 45 M1
Male sit = 45 – 29 = 16 M1
Female sit = 30 – 16 = 14
Female stand = 75 – 14 = 61 A1

Answer (a): male=45 (sit=16, stand=29); female=75 (sit=14, stand=61)

Part (b) Solution:

29/120 B1

Answer (b): 29120

← 3X Area of compound shapes

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Frequency trees

Free Frequency trees PDF Worksheets & Answers

Guide to Frequency trees: Explanation, Diagrams & Worked Examples

GCSE Past Paper Frequency trees Questions & Answers