Where can I download free function machines PDF worksheets with answers?

On this MathsLinks page you can download free printable function machines 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 function machines revision guide.

What GCSE grade is function machines (2H)?

Function machines (topic code 2H) is a Grade 2 algebra topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Function machines Worksheets (PDF) with Answers — GCSE Maths

Free Function machines PDF Worksheets & Answers

Grade 2 • Topic 2H

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
Dr Austin Practice grid / worksheet & answers	Qs	Ans
Maths4EveryOne KS2 SATs questions & 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
MathsBot interactive resource Interactive online resource	Open
esheets Self-marking online worksheet	Page

Grade 2 topics
2A - Calculation problems	2B - Using a calculator
2C - Systematic listing	2D - Fraction of an amount
2E - FDP	2F - Simplifying algebra
2G - Writing an expression	2H - Function machines
2J - Solving one step equations	2K - Angles
2L - Area and perimeter	2M - Reading scales
2N - Probability & Probability Scale	2P - Frequency polygons
2Q - Unitary method	2R - Bar charts
2S - Pie charts	2T - Averages
2U - Stem and leaf diagrams

Explanation:

To find the output of a function machine, start with the input and apply each operation in order from left to right. To find the input when given the output, work backwards from right to left using the inverse (opposite) operations (+ becomes −, × becomes ÷).

When the input is a letter x, write the algebraic result after each box to form an expression or equation.

Example 1: Using the machine above:
(a) Find the output when the input is 6.
(b) Find the input when the output is 29.

(a) Forward: 6 × 4 = 24, then 24 − 7 = 17

(b) Reverse with inverse operations (+ 7, then ÷ 4):

• 29 + 7 = 36, then 36 ÷ 4 = 9

Example 2: Using the machine above:
(a) Write the output when the input is x.
(b) Find x when the output is equal to x + 20.

(a) x → 4x → 4x − 7

(b) Solve 4x − 7 = x + 20 → 3x = 27 → x = 9

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Function machines Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 GCSE May 2025 1F Q13 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here is a number machine.

(a) Find the output when the input is 6 [1 mark]

(b) Find the input when the output is –11 [2 marks]

Worked Solution & Mark Scheme (3 marks)

Part (a) Solution:

6 × 3 – 8 = 18 – 8 = 10 B1

Answer (a): 10

Part (b) Solution:

(–11 + 8) ÷ 3 = –3 ÷ 3 = –1 M1 A1

Answer (b): –1

Past Paper Example 2 AQA Jun 2025 3F Q4 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here is a number machine.

(a) Work out the output when the input is 4 [1 mark]

(b) Work out the input when the output is 19 [2 marks]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

4 × 3 – 5 = 12 – 5 = 7 B1

Answer (a): Answer 7

Part (b) Solution:

Reverse machine: (19 + 5) ÷ 3 = 24 ÷ 3 = 8 M1 A1

Answer (b): Answer 8

Part (c) Solution:

16 + 2 = 18
To get 3 from 18: 18 ÷ 6 = 3 (or 18 – 15 = 3) B1

Answer (c): ÷ 6 (or – 15)

Past Paper Example 3 GCSE Nov 2024 1F Q13 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here is a number machine.

(a) Find the output when the input is 11 [2 marks]

(b) When the input is 10, the output is 28
Complete this number machine. [2 marks]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

(11 + 5) ÷ 2 = 8 M1 A1

Answer (a): 8

Part (b) Solution:

28 ÷ 4 = 7 M1
10 – 3 = 7 A1

Answer (b): – 3 (or × 0.7)

← 2G Writing an expression

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Function machines

Free Function machines PDF Worksheets & Answers

Guide to Function machines: Explanation, Diagrams & Worked Examples

GCSE Past Paper Function machines Questions & Answers