Direct & Inverse Proportion

Tutorial Videos

GCSE Maths – What Does Directly Proportional Mean? (2026/27 exams)

GCSE Maths – What Does Directly Proportional Mean? by Cognito

GCSE Maths – What Does Inversely Proportional Mean? (2026/27 exams)

GCSE Maths – What Does Inversely Proportional Mean? by Cognito

Direct and Inverse Proportion Explained for IGCSE and GCSE Maths

Direct and Inverse Proportion Explained for IGCSE and GCSE Maths by Save My Exams

Proportionality Graphs – Corbettmaths

Corbett Maths Proportionality Graphs

Online Platforms (with Videos & Exercises)

Activities & Resources

• Pixi Maths
  • Graphical Proportion ppt
  • Direct and Inverse Proportion ppt (Slides 1-4)
  • Proportion Matching Statements
• Go Teach Maths
  • Forming Proportional Relationships
  • Identifying Proportional Graphs

Worksheets

• Pixi Maths
  • Graphical Proportion RAG
• AQA (All About Maths)
  • Bridging the Gap Pocket 7: Direct and Inverse Proportion · Word (AQA KS3-4 Bridging the Gap)

Dr Frost Video

Dr Frost Slides & Activities

Dr Frost Slides (1-4 & 10)

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 176g: Determine if a linear relationship is a proportional relationship.
• 176p: Determine if two variables are in direct or inverse proportion from a given table of values.
• 386k: Decide on the proportional relationship between two variables given two pairs of values.
• 176: Exam Practice: Multiplicative scaling and numerical proportion relationships
• 386: Exam Practice: Algebraic direct and inverse proportion

Tutorial Videos

Direct Proportion – Corbettmaths

Corbett Maths Direct Proportion (Up to 2:51)

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Writing & solving proportions: Videos & practice

Activities

• Andy Lutwyche
  • Codebreaker
  • Clumsy Clive
  • Spider
  • Spot The Mistakes
  • Explosions
  • Problems Codebreaker
  • Codebreaker (2)
• Goal Free Problems
  • Foundation Algebra set Q12 (original questions)
• Go Teach Maths
  • Direct Proportion
• Desmos
  • Standards Unit N6 – Developing Proportional Reasoning (UK) (by Ben Sparks: digital version of Standards Unit N6)
• MathsbyFintan
  • Direct Proportion Graphs✦
• BossMaths
  • Solving problems involving direct proportion✦

Worksheets

• Dr Austin Maths
  • Practice Grid (Word | PDF✦ | Answers✦)
  • Fill in the Blanks (Word | PDF✦ | Answers✦)
  • Worded Problems Practice Strips (Word | PDF | Answers)
  • Practice Strips (Word | PDF | Answers)
  • Crack the Code (Word | PDF | Answers)
• Access Maths
  • Direct Proportion Fluency & Reasoning Sheet
• MME
  • Direct & Inverse Proportion, foundation (exam style): Questions | Answers
• Pret Homework (@MrDraperMaths)
  • Direct Proportion (@MrDraperMaths, docx)

Dr Frost Video

Key Skill – Establish the constant of proportionality for variables which are directly proportional.

K472: Establish the Constant of Proportionality for Variables Which are Directly Proportional.

Dr Frost Slides & Activities

Dr Frost Slides (5)

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 386a: Determine the formula connecting two variables which are directly proportional.
• 386g: Determine and then use the formula connecting two variables in context which are directly proportional. (not yet active)
• 386i: Complete a table of values for a directly proportional relationship.
• 386: Exam Practice: Algebraic direct and inverse proportion

Tutorial Videos

GCSE Maths – How to Write Algebraic Expressions for Directly Proportional Relationships

GCSE Maths – How to Write Algebraic Expressions for Directly Proportional Relationships by Cognito

Direct and Inverse Proportion | Grade 7-9 Series | GCSE Maths Tutor

Direct and Inverse Proportion | Grade 7-9 Series | GCSE Maths Tutor by The GCSE Maths Tutor

The 5 Hardest Direct & Inverse Proportion Exam Style Questions | GCSE Maths Tutor

The 5 Hardest Direct & Inverse Proportion Exam Style Questions by The GCSE Maths Tutor

Direct Proportion – Corbettmaths

Corbett Maths Direct Proportion (From 2:51)

Online Platforms (with Videos & Exercises)

Activities & Resources

• Pixi Maths
  • Direct and Inverse Proportion ppt (Slides 5-9)
• Andy Lutwyche
  • Codebreakers (Algebraic)
  • Superman
• BossMaths
  • R13a Equations for Direct & Inverse Proportion✦
• Ticktock Maths
  • Higher Direct Proportion lesson (slides)

Worksheets

• Dr Austin Maths
  • Practice Grid (Word | PDF✦ | Answers✦)
  • Fill in the Blanks (Word | PDF✦ | Answers✦)
  • Worded Problems Practice Strips (Word | PDF | Answers)
• Pixi Maths
  • Direct Proportion RAG
• Miss Konstantine (MathsHKO)
  • Proportion with Squares and Cubes
• Mathshelper (Jon Stone)
  • Direct Proportion✦
• Access Maths
  • Direct Proportion Problems
• MME
  • Direct & Inverse Proportion using algebra (exam style): Questions | Answers
• Mr Morley Maths
  • Direct and Inverse Proportion: Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme

Dr Frost Video

Dr Frost Slides & Activities

Dr Frost Slides (7-12)

Topic Tests

• Standard Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 386b: Determine the formula connecting two variables which are directly proportional involving powers/roots.
• 386e: Determine and then use the formula connecting two variables which are directly proportional, possibly involving powers/roots.
• 386m: Use the constant of proportionality for direct or inverse proportion involving a percentage change.
• 386: Exam Practice: Algebraic direct and inverse proportion

Tutorial Videos

Inverse Proportion – Corbettmaths

Corbett Maths Inverse Proportion (Up to 2:15)

Activities

• Andy Lutwyche
  • Codebreakers
• Math = Love (Sarah Carter)
  • Paragraph Function Modelling Task
• EEPS
  • Paragraphs with Rulers Activity
• Don Steward
  • Faster Film Rates
  • Cake Slices
• Go Teach Maths
  • Work-Hours
  • Inverse Proportion
• BossMaths
  • R10b Inverse Proportion
• martin8baker (Heron Maths)
  • Inverse proportion slides and activities✦
• Nyima Dorjee (via Steven Wragg)
  • Breakfast shift✦

Worksheets

• Dr Austin Maths
  • Practice Grid (Editable Word | PDF✦ | Answers✦)
  • Fill in the Blanks (Word | PDF✦ | Answers✦)
  • Worded Practice Strips (Word | PDF✦ | Answers✦)
  • Practice Strips (Word | PDF | Answers)
• Access Maths
  • Inverse Proportion Fluency & Reasoning Sheet
• Pret Homework (@MrKMorrison)
  • Direct & Inverse Proportion (@MrKMorrison, pptx)

Dr Frost Video

Key Skill – Establish the constant of proportionality for variables which are inversely proportional

K474: Establish the Constant of Proportionality for Variables Which are Inversely Proportional.

Dr Frost Slides & Activities

Dr Frost Slides (13)

Topic Test

• Advanced Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 386c: Determine the formula connecting two variables which are inversely proportional.
• 386h: Determine and then use the formula connecting two variables in context which are inversely proportional. (not yet active)
• 386j: Complete a table of values for an inversely proportional relationship.
• 386: Exam Practice: Algebraic direct and inverse proportion

Further Practice

• Practise Questions

Tutorial Videos

GCSE Maths Revision – Direct and Inverse proportion

GCSE Maths Revision – Direct and Inverse proportion by HEGARTYMATHS

Direct/Inverse Proportion – GCSE Higher Maths

Direct/Inverse Proportion – GCSE Higher Maths by 1st Class Maths

Inverse proportion : y is inversely proportional to the square of x

Inverse proportion : y is inversely proportional to the square of x by Oxford Mathematics Education – Yarm

Inverse Proportion – Corbettmaths

Corbett Maths Inverse Proportion (From 2:15)

Online Platforms (with Videos & Exercises)

Activities & Resources

• Pixi Maths
  • Direct and Inverse Proportion ppt (Slides 10 Onwards)
• Ticktock Maths
  • Higher Inverse Proportion lesson (slides)

Worksheets

• Dr Austin Maths
  • Practice Grid (Word | PDF✦ | Answers✦)
  • Fill in the Blanks (Word | PDF✦ | Answers✦)
  • Worded Practice Strips (Word | PDF✦ | Answers✦)
• Pixi Maths
  • Inverse Proportion RAG
• Mathshelper (Jon Stone)
  • Inverse Proportion✦
• MadAsMaths (T. Madas)
  • Practical Arithmetic Problem Solving Q14, 26 (difficulty 4 of 5)

Dr Frost Video

Download slides

Dr Frost Slides (2 Only)

Activity

Why to Avoid FOIL

Topic Test

• Standard Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 386d: Determine the formula connecting two variables which are inversely proportional involving powers/roots.
• 386f: Determine and then use the formula connecting two variables which are inversely proportional, possibly involving powers/roots.
• 386l: Determine a formula to connect two proportional relationships with a common variable.
• 386n: Determine a formula for a directly or inversely proportional relationship where the inputs are algebraic.
• 386: Exam Practice: Algebraic direct and inverse proportion

Worksheets

Acute Learning Problem Pairs

• Proportion as PowerPoint or PDF

Worksheets

• Dr Austin Maths
  • Revision Practice Grid (Word | PDF✦ | Answers✦)
• Corbettmaths
  • Direct & Inverse Proportion Practice Questions & Solutions
  • Direct & Inverse Proportion Worksheet & Solutions
• Maths 4 Everyone
  • Direct and Inverse Proportions GCSE Questions and Solutions
• Andy Lutwyche
  • Two Problems
• Mathshelper (Jon Stone)
  • General Proportion✦
• MathedUp
  • Direct & Inverse Proportion: Worksheet · Practice · Quiz · Question Gallery
• Maths Genie
  • Direct and Inverse Proportion: Booklet · Worksheet · Solutions · Lesson · Topic page
  • Direct and Inverse Proportion: Booklet · Worksheet · Solutions · Lesson · Topic page
• Mathsaurus (Kevin Olding)
  • Direct and inverse proportion 1 (exam questions)
  • Direct and inverse proportion 2 (exam questions)
• Physics & Maths Tutor
  • Direct and Inverse Proportion: Notes · Worksheet · Solutions
• MME
  • Direct & Inverse Proportion (drill): Questions | Answers
• Dr Frost
  • Direct and Inverse Proportion Full Coverage GCSE Questions✦
• 1st Class Maths
  • Proportion exam-style questions✦ (answers✦)

Activities

• NRICH (student problems)
  • Ratio, Proportion & Rates of Change (Age 11-16): Problems
  • Ratio, Proportion & Rates of Change (Age 11-16): Short Problems
• Don Steward
  • Physics in Proportion✦
  • Direct and Inverse Proportion✦
• Transum
  • Direct and Inverse Proportion
• Go Teach Maths
  • Direct & Inverse Proportion
• BossMaths
  • Recognising and interpreting graphs that illustrate direct and inverse proportion✦
• MathsPad
  • Proportion tables slides✦ (worksheet✦)

External Whole Topic Past Paper Style Questions

• Transum
  • Exam-style questions: Proportion
• NCETM
  • NCETM KS4 Mastery PD: 8.1 Working with direct and inverse proportion (PDF) · Solutions
  • NCETM KS4 Mastery PD: 8.2 Graphical representations of proportionality (PDF)