Prior Content: Solving Simple Equations, Solving Quadratics, Factorising, Drawing & Using Graphs, Graphical Transformations
Possible Next Steps: Algebraic Proof, Functions, Manipulating Formulae/ Changing the Subject
Contents
- 1.1 Completing the Square when ‘a’ Equals 1
- 1.2 Completing the Square when ‘a’ Does not Equal 1
- 2.1 Solving Quadratics by Completing the Square
- 3.1 Completing the Square to Draw Quadratics
- 4.1 Completing the Square in Proofs
- Whole Topic Summary Resources (Including Past Paper Questions)
1.1 Completing the Square when ‘a’ Equals 1
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Completing the Square (Up to 4:36)
Online Platforms (with Videos & Exercises)
- Khan Academy
- Completing the square: Videos & practice
Activities & Resources
- Maths 4 Everyone
- Andy Lutwyche
- Math = Love (Sarah Carter)
- Don Steward
- Go Teach Maths
- Nuffield Foundation
- Ticktock Maths
- Completing the Square lesson (slides)
Worksheets
- Dr Austin Maths
- Corbettmaths
- Completing the Square Practice Questions (Q1-3 & 5-6) & Solutions
- Completing the Square Worksheet (Q1 Only) & Solutions
- Maths 4 Everyone (Ignore Final Row)
- Access Maths
- Completing the Square: Fluency & Reasoning Sheet 1 | Fluency & Reasoning Sheet 2
- MME
- @taylorda01
- 1st Class Maths
- MadAsMaths (T. Madas)
- Basic Skills Q39–42 · questions only
- Starting Points Maths
- Mr Morley Maths
- Completing the Square: Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme
- Pret Homework (@DancingScotty)
- Completing the Square (@DancingScotty, docx)
Dr Frost Resources
Dr Frost Video
K580: Complete the Square for Quadratics of the Form x2+bx+c.
Dr Frost Slides & Activities
- All in one summary sheet
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
- 413a: Complete the square for quadratic expressions given in the form x2 + bx + c where b is even.
- 413b: Complete the square for quadratic expressions given in the form x2 + bx + c where b is odd.
- 413c: Complete the square for quadratic expressions given in the form x2 + bx + c where b is algebraic.
- 413d: Complete the square for quadratic expressions given in the form x2 + bx + c where b is a surd.
- 413: Exam Practice: Completing the square to put an expression in the form (x+a)2 + b
Extension Materials
1.2 Completing the Square when ‘a’ Does not Equal 1
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Completing the Square 2
Online Platforms (with Videos & Exercises)
- Khan Academy
- More on completing the square: Videos & practice
Activities & Resources
- Andy Lutwyche
- Acute Learning Problem Pairs
- Level 2 FM: Completing the Square as PowerPoint or PDF
- Ticktock Maths
Worksheets
- Dr Austin Maths
- Corbettmaths
- Completing the Square Practice Questions (Q7) & Solutions
- Completing the Square Worksheet (Q3 Only) & Solutions
- Completing the Square (AQA Level 2) Practice Questions & Solutions
- Maths 4 Everyone (Final Row)
- MME
- 1st Class Maths
- MadAsMaths (T. Madas)
- Basic Skills Q43–46 · questions only
Dr Frost Resources
Dr Frost Video
K581: Complete the Square for Quadratics of the Form ax2+bx+c.
Dr Frost Slides & Activities
- Dr Frost Slides (4)
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
Extension Materials
2.1 Solving Quadratics by Completing the Square
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Completing the Square (From 4:36)
Online Platforms (with Videos & Exercises)
Activities & Resources
- Pixi Maths
- Solving Quadratic Equations ppt (Slides 34 Onwards)
- Don Steward
- Go Teach Maths
- BossMaths
- Mr Thompson Maths
- Ticktock Maths
Worksheets
- Dr Austin Maths
- Corbettmaths
- Completing the Square Practice Questions (Q4) & Solutions
- Completing the Square Worksheet (Q2 & 4) & Solutions
- Solving Quadratics Using Completing the Square (AQA Level 2 Practice Questions & Solutions
- Pixi Maths
- CIMT MEP (online self-checking)
- 1st Class Maths
- MadAsMaths (T. Madas)
- Quadratics (Elementary Topics) Q6–10
- Quadratics Exam Questions Q2, 16, 38 (difficulty 2–3 of 5)
Dr Frost resources
Dr Frost Videos
Dr Frost Slides & Activities
- All in one summary sheet
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
- 415a: Solve a quadratic equation when given in completed square form.
- 415b: Solve a quadratic equation by completing the square.
- 415: Exam Practice: Solving quadratic equations by completing the square
Further Practice
- Practise Questions
EXTENSION MATERIALS
Other Videos & Multimedia
Corbett Maths Deriving the Quadratic Formula
Worksheets
- Corbettmaths
- Quadratic Formula Proof Practice Questions
3.1 Completing the Square to Draw Quadratics
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Finding Turning Points Using Completing the Square
Online Platforms (with Videos & Exercises)
Activities & Resources
- Andy Lutwyche
- Math = Love (Sarah Carter)
- Prime Factorisation
- Don Steward
- Go Teach Maths
- thewessens.net Classroom Apps
- Parabola Explorer (link standard and vertex (completed square) forms to the graph)
- BossMaths
- Desmos
- Match My Parabola (scaffolded challenges writing quadratics (incl. vertex/completed-square form) to match graphs)
Worksheets
- Corbettmaths
- Completing the Square Practice Questions (Q8-9) & Solutions
- Completing the Square Worksheet (Q4 From Apply Section) & Solutions
- Dr Austin Maths
- MME
- 1st Class Maths
Dr Frost resources
Dr Frost Video
K582: Find the Minimum Point of a Quadratic Graph.
K583: Find the Maximum Point of a Quadratic Graph.
K584: Find the Line of Symmetry of a Quadratic Graph.
Dr Frost Slides & Activities
- All in one summary sheet
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
- 416a: Determine the minimum point of a quadratic graph when given in completed square form.
- 416b: Determine the original quadratic function given the maximum or minimum point.
- 416c: Determine the maximum point of a quadratic graph when given in completed square form.
- 416d: Determine the minimum point of a quadratic graph.
- 416e: Determine the maximum point of a quadratic graph.
- 416f: Determine the equation of the line of symmetry for a quadratic graph by completing the square.
- 416g: Sketch a quadratic graph, including its intercepts and turning point by completing the square.
- 416h: Use information from a scenario, modelled as a quadratic curve to find the horizontal or vertical distance to the turning point.
- 416i: Use information from a scenario, modelled as a quadratic curve with a given turning point, to determine the equation of the curve.
- 416j: Use information from a scenario, modelled as a quadratic curve with a given turning point, to determine the width of the curve for a particular height.
- 416: Exam Practice: Minimum or maximum point of a quadratic graph by completing the square
Further Practice
- Practise Questions
EXTENSION MATERIALS
Online Platforms
- Khan Academy
- Vertex form of quadratics: Videos & practice
4.1 Completing the Square in Proofs
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Algebraic Proof – GCSE Higher Maths by 1st Class Maths
Finding a Turning Point Using Completed Square Form – GCSE Higher Maths by 1st Class Maths
Online Platforms (with Videos & Exercises)
Activities & Resources
Worksheets
- Corbettmaths
- Completing the Square (AQA Level 2) Last 2 Qs Practice Questions & Solutions
Dr Frost resources
Dr Frost Videos
- Topic Video
- KS 66 Angles about a point.
Dr Frost Slides & Activities
- All in one summary sheet
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
- 560b: Use proof by deduction to show that a quadratic expression is always positive. (not yet active)
- 560: Exam Practice: Proof by deduction
Further Practice
- Practise Questions (may include angles in a triangle and on a straight line)
EXTENSION MATERIALS
Whole Topic Summary Resources (Including Past Paper Questions)
Download Completing the Square PPQs as WW Powerpoint for Edexcel IGCSE, AQA GCSE, Edexcel GCSE or OCR GCSE (or all GCSE together)
Other Whole Topic Resources
Acute Learning Problem Pairs
- Completing The Square as PowerPoint or PDF
Worksheets
- Corbettmaths
- Completing the Square (AQA Level 2) Practice Questions & Solutions
- Maths 4 Everyone
- Mathshelper (Jon Stone)
- MathedUp
- Completing the Square: Worksheet · Practice · Quiz · Question Gallery
- Completing the Square: Worksheet · Practice · Quiz · Question Gallery
- Maths Genie
- Completing the Square: Booklet · Worksheet · Solutions · Lesson · Topic page
- Naiker Maths
- Completing the Square: Worksheet
- Physics & Maths Tutor
- crashMATHS
Activities
- Transum
- Interactive Maths
- Completing the Square: QQI | 10QQI | Count Down | Relay | Bingo | Bingo 2
- Completing the Square: Worksheets
- Richard Perring (@LearningMaths)
- Completing the square mystery✦ (by Richard Perring (@LearningMaths); copy hosted by Jo Morgan)
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.