Completing the Square

Tutorial Videos

Completing the Square – Corbettmaths

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
  • Completing the Square Loop: Set 1 · Set 2
• Andy Lutwyche
  • Codebreaker
  • Explosions
  • Completing The Square
• Math = Love (Sarah Carter)
  • Completing the Square Foldable
  • Completing the Square Organiser
• Don Steward
  • (Something.5) Squared
• Go Teach Maths
  • Completing the Square
• Nuffield Foundation
  • Completing the square activity✦ (notes✦, teacher notes✦, slides✦)
• Ticktock Maths
  • Completing the Square lesson (slides)

Worksheets

• Dr Austin Maths
  • Practice Strips (Word | PDF | Answers)
  • Fill In The Blanks (Word | PDF | Answers)
  • Practice Grid (Word | PDF | Answers)
• Corbettmaths
  • Completing the Square Practice Questions (Q1-3 & 5-6) & Solutions
  • Completing the Square Worksheet (Q1 Only) & Solutions
• Maths 4 Everyone (Ignore Final Row)
  • Completing the Square First Steps
  • Completing the Square Strengthen
• Access Maths
  • Completing the Square: Fluency & Reasoning Sheet 1 | Fluency & Reasoning Sheet 2
• MME
  • Completing the Square a=1 (exam style): Questions | Answers  •  Completing the Square (drill): Questions | Answers
• @taylorda01
  • Completing the square questions✦ (answers✦)
• 1st Class Maths
  • Completing the square exam-style questions✦ (answers✦)
• MadAsMaths (T. Madas)
  • Basic Skills Q39–42 · questions only
• Starting Points Maths
  • Completing the Square · PDF
• 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 Video

Key Skill – Complete the square for quadratics of the form x^2 + bx + c.

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

Tutorial Videos

Completing the Square 2 – Corbettmaths

Corbett Maths Completing the Square 2

Online Platforms (with Videos & Exercises)

• Khan Academy
  • More on completing the square: Videos & practice

Activities & Resources

• Andy Lutwyche
  • (coefficient of x^2 is not 1) Codebreaker
• Acute Learning Problem Pairs
  • Level 2 FM: Completing the Square as PowerPoint or PDF
• Ticktock Maths
  • Completing the Square (a more than 1) lesson (slides)

Worksheets

• Dr Austin Maths
  • Harder Fill In The Blanks (Word | PDF | Answers)
  • Harder Practice Grid (Word | PDF | Answers)
• 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)
  • Completing the Square First Steps
  • Completing the Square Strengthen
• MME
  • Completing the Square a>1 (exam style): Questions | Answers  •  Completing the Square Hard (drill): Questions | Answers
• 1st Class Maths
  • Tricky completing the square exam-style questions✦ (answers✦)
• MadAsMaths (T. Madas)
  • Basic Skills Q43–46 · questions only

Dr Frost Video

Key Skill – Complete the square for quadratics of the form ax^2 + bx + c.

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

• 414a: Complete the square for quadratic expressions given in the form ax² + bx + c, where a is positive.
• 414b: Complete the square for quadratic expressions given in the form ax² + bx + c, where a is negative.
• 414: Exam Practice: Completing the square to put an expression in the form a(x+b)² + c

Tutorial Videos

Completing the Square – Corbettmaths

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
  • Solving Quadratics by Transformation
  • Babylonian Quadratic Equation Solving
• Go Teach Maths
  • Solving Quadratic Equations by Completing the Square
• BossMaths
  • A18b Solving Quadratics by Completing the Square
• Mr Thompson Maths
  • Solving by Completing the Square – Matching Activity✦
• Ticktock Maths
  • Solving Quadratics by Completing the Square lesson (slides)

Worksheets

• Dr Austin Maths
  • Practice Strips (Word | PDF | Answers)
  • Different Methods Practice Grid (Word | PDF | Answers)
• 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
  • Solving Quadratics by Completing the Square RAG
• CIMT MEP (online self-checking)
  • Quadratic Equations: Completing the Square
• 1st Class Maths
  • Solving quadratics by completing the square exam-style questions✦ (answers✦)
• MadAsMaths (T. Madas)
  • Quadratics (Elementary Topics) Q6–10
  • Quadratics Exam Questions Q2, 16, 38 (difficulty 2–3 of 5)

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

Other Videos & Multimedia

Deriving the Quadratic Formula

Corbett Maths Deriving the Quadratic Formula

Worksheets

• Corbettmaths
  • Quadratic Formula Proof Practice Questions

Tutorial Videos

Finding Turning Points using Completing the Square

Corbett Maths Finding Turning Points Using Completing the Square

Online Platforms (with Videos & Exercises)

Activities & Resources

• Andy Lutwyche
  • Turning Points Codebreaker
  • Their Graphs
• Math = Love (Sarah Carter)
  • Vertex Form Card Sort
• Prime Factorisation
  • Vertex Form Card Sort
• Don Steward
  • Quadratics from Roots, Vertex and Y-intercept✦
  • Quadratic Maximum Value
• Go Teach Maths
  • Finding Turning Points by Completing the Square
• thewessens.net Classroom Apps
  • Parabola Explorer (link standard and vertex (completed square) forms to the graph)
• BossMaths
  • A11b Turning Points by Completing the Square
• 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
  • Turning Points Practice Strips (Word | PDF | Answers)
• MME
  • Turning Points of Quadratic Graphs (exam style): Questions | Answers  •  Turning Points of Quadratic Graphs (drill): Questions | Answers
• 1st Class Maths
  • Finding turning points by completing the square exam-style questions✦ (answers✦)

Dr Frost Video

Key Skill – Find the minimum point of a quadratic graph.

K582: Find the Minimum Point of a Quadratic Graph.

Key Skill – Find the maximum point of a quadratic graph.

K583: Find the Maximum Point of a Quadratic Graph.

Key Skill – Find the line of symmetry 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

Tutorial Videos

Algebraic Proof – GCSE Higher Maths

Algebraic Proof – GCSE Higher Maths by 1st Class Maths

Finding a Turning Point Using Completed Square Form – GCSE Higher 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 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)

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
  • Completing the Square GCSE Questions and Solutions
• Mathshelper (Jon Stone)
  • Completing The Square Worksheet
• 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
  • Completing the Square (H): Notes · Worksheet · Solutions
• crashMATHS
  • Completing the square worksheet✦

Activities

• Transum
  • Completing the Square
• 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)