Quadratics

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AS Maths – Pure – Solving Quadratic Equations

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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2A/B Slides (Courtesy of Owen134866)

Dr Frost Video

• Whole Topic Video
• 372 Solve quadratics of the form x²+bx+c=0, solvable by factorisation. Key Skill Video (GCSE)

Bicen Maths Live Lesson

Quadratics 1 • Solving Quadratics • P1 Ex2A/B • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 1-9

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

• 367b: Solve quadratic equations given in the form x² ± bx ± c = 0, solvable by factorisation.
• 367c: Solve quadratic equations requiring rearrangement to the form x² ± bx ± c = 0 by factorising.
• 367d: Solve quadratic equations given in the form ax² ± bx ± c = 0, requiring factorising.
• 367e: Solve quadratic equations requiring rearrangement to the form ax² ± bx ± c = 0 by factorising.
• 367g: Solve a quadratic equation of the form ax²-b²=0 or ax²=b² by factorisation.
• 367h: Determine the original quadratic equation given its integer solutions.
• 367i: Determine the original quadratic equation given its non-integer solutions.
• 417a: Solve a quadratic equation using the quadratic formula to get exact solutions.
• 417b: Solve a quadratic equation using the quadratic formula to get numeric solutions.
• 417c: Solve quadratic equations using the quadratic formula, requiring rearrangement.
• 417d: Determine the original quadratic equation given use of the quadratic formula.
• 462a: Solve an equation of the form ax + b/x + c = 0
• 462b: Solve an equation with a single algebraic fraction on one side of the equation, leading to a quadratic equation.
• 462c: Solve an equation of the form ax+b/cx+d = ex+f/gx+h
• 462d: Solve an equation of the form a/bx+c ± d/ex+f = g
• 462e: Solve an equation with fractions requiring prior factorisation of one of the fractions.
• 367: Exam Practice: Solving quadratic equations by factorisation
• 417: Exam Practice: Quadratic formula to solve quadratic equations
• 462: Exam Practice: Solving equations involving fractions that lead to a quadratic equation

Practice Questions

• Practise Questions

Other Videos

Solving Quadratic Equations by Factorising

The Quadratic Formula

The Quadratic Formula

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Solving Quadratics by Factoring
  • The Quadratic Formula
  • Strategizing to Solve Quadratic Equations

Activities

• Berwick Maths Diagnostic Questions
• SRWhitehouse
  • Quadratic formula activity✦
• Underground Mathematics
  • Quadratic solving sorter✦

Worksheets

• Jethwa Maths Starter Activity (p7-8)
• The Chalk Face Solving Quadratics by Factorising
• The Chalk Face Quadratic Powers Problem
• kutasoftware Worksheets
  • by Taking Square Roots
  • by Factoring
  • with the Quadratic Formula
  • by Completing the Square
• MathedUp
  • Quadratic equations: Questions · Challenge · Answers
• Dr Oliver Mathematics
  • Quadratic equations questions✦ (solutions✦)
• MadAsMaths (T. Madas)
  • Quadratics (Elementary Topics) Q1–5
  • Equations Exam Questions I Q18, 32, 36, 38 (difficulty 3 of 5)
  • Polynomials Exam Questions (Intro) Q16 (difficulty 3 of 5)
  • Quadratics Exam Questions Q1, 3, 12, 15, 23, 30, 32, 54, 61–62, 84, 87, 92, 99, 101 (difficulty 2–5 of 5)
  • Surd Exam Questions✦ Q85 (difficulty 5 of 5)
  • Discriminant Exam Questions Standard Q6 (difficulty 3 of 5)

AS Maths – Pure – Completing the Square

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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2C/D Slides (Courtesy of Owen134866)

Dr Frost Video

• 376 Complete the square for quadratics of the form x²+bx+c. Key Skill Video (GCSE)
• 377 Complete the square for quadratics of the form ax²+bx+c. Key Skill Video (GCSE)

Bicen Maths Live Lesson

Quadratics 3 • Completing the Square • P1 Ex2C • 🤖

Quadratics 4 • Solving by Completing the Square • P1 Ex2D • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 10-16

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.
• 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.
• 415a: Solve a quadratic equation when given in completed square form.
• 415b: Solve a quadratic equation by completing the square.
• 413: Exam Practice: Completing the square to put an expression in the form (x+a)² + b
• 414: Exam Practice: Completing the square to put an expression in the form a(x+b)² + c
• 415: Exam Practice: Solving quadratic equations by completing the square

Other Videos

Completing The Square

Completing the Square

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Completing the Square Intro
  • More on Completing the Square

Activities

• Berwick Maths Diagnostic Questions
• Underground Mathematics Quadratic Formula Proof Activity✦
• Goal Free Problems
  • A-Level Algebra & Coordinate Geometry set Q6

Worksheets

• Jethwa Maths Starter Activity (p1-2)
• The Chalk Face Examples & Questions
• PMT OCR Set 1 Completing the Square PPQs & Solutions (Old Spec)
• SRWhitehouse Completing the square✦ (TES Account Required)
• kutasoftware Worksheets
  • Completing the Square
• Mathshelper (Jon Stone)
  • Completing The Square
• Maths Genie
  • Completing the Square: Questions · Solutions · Lesson · Topic page
• MadAsMaths (T. Madas)
  • Quadratics (Elementary Topics) Q6–10
  • Identities Q5 (difficulty 2 of 5)
  • Quadratics Exam Questions Q2, 4, 6–10, 13, 16–18, 21, 25, 27, 29, 33–34, 36–38, 40, 42–44, 46–48, 50, 56, 58–59, 63, 65, 69, 71, 74, 76, 79, 81–82, 90, 93–94, 98 (difficulty 2–5 of 5)
  • Basic Skills Q39–46 · questions only
  • Curve Sketching Exam Questions Q1 (difficulty 2 of 5)
• Starting Points Maths
  • Completing the Square: Backwards Fading

AS Maths – Pure – Functions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (Up to 8:06)

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2E Part 1 Slides (Courtesy of Owen134866)

Dr Frost Video

• Whole Topic Video (From 6:38 to 8:35)

Bicen Maths Live Lesson

Quadratics 5 • Function Notation, Roots • P1 Ex2E • 🤖

Quadratics 6 • Maxima/Minima • P1 Ex2E • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 17-23

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

• 432a: Calculate the output of a function, given the input.
• 432e: Determine the input of a non-linear function, given the output.
• 432i: Solve equations given in the form f(…) = k for more general algebraic inputs.
• 432l: Solve equations where the output of two functions is equated, leading to a quadratic equation.
• 433b: Determine the roots of a function using a graph. (not yet active)
• 416a: Determine the minimum point of a quadratic graph when given in completed square form.
• 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.
• 437c: Determine the range of a quadratic function in completed square form. (not yet active)
• 437d: Determine the range of a quadratic function with a given domain. (not yet active)
• 432: Exam Practice: Function notation and calculating outputs or inputs or a function
• 433: Exam Practice: Graph representation of functions
• 416: Exam Practice: Minimum or maximum point of a quadratic graph by completing the square
• 437: Exam Practice: Domain and range of simple functions

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Underground Mathematics Pick a Card✦ 

Worksheets

• Jethwa Maths Starter Activity (p3-4)
• MadAsMaths (T. Madas)
  • Quadratics Exam Questions Q26, 31 (difficulty 3 of 5)

AS Maths – Pure – Functions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (From 8:06)

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2E Part 2 Slides (Courtesy of Owen134866)

Textbook Exercise

Q7-8

Dr Frost Video

• Whole Topic Video (Q5, 7 & 8)

Bicen Maths Live Lesson

Quadratics 2 • ‘Pseudo’ Quadratics • P1 Ex2A/B • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 22

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

• 485a: Solve a hidden quadratic equation given in the form xⁿ by substitution.
• 485b: Solve a hidden quadratic equation containing roots by substitution
• 485c: Solve a hidden quadratic equation given in the form xⁿ by substitution, that requires multiplying through by a power of x.
• 485d: Solve an equation where indices can be equated, leading to a quadratic equation.
• 485e: Solve a quadratic equation in terms of an exponential term of the form a^x (no logarithms).
• 485: Exam Practice: Solving hidden quadratic equations (no logs or trigonometric functions)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• PMT OCR Set 1 Hidden Quadratics PPQs & Solutions (Old Spec)
• Mathshelper (Jon Stone)
  • Quadratics In Disguise✦
• MadAsMaths (T. Madas)
  • Equations Exam Questions I Q20, 68 (difficulty 3–5 of 5)
  • Indices Exam Questions✦ Q14, 17, 24, 35, 38, 41–42, 46 (difficulty 3–4 of 5)
  • Quadratics Exam Questions Q14, 19, 53 (difficulty 2–3 of 5)
  • Indices Practice Indicial Equations Q10–12 · questions only
  • Equations: Advanced Skills Q1–12, 14–19, 21–23, 26, 29–32, 35–38, 40–43, 49, 53, 57, 61 (difficulty 2–5 of 5)

AS Maths – Pure – Quadratic Graphs

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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2F Slides (Courtesy of Owen134866)

Dr Frost Video

• Whole Topic Video (Up to 6:35)
• 202 Plot a quadratic graph. Key Skill Video (GCSE)

Bicen Maths Live Lesson

Quadratics 7 • Sketching Quadratics • P1 Ex2F • 🤖

Quadratics 8 • Finding Equations from Graphs • P1 Ex2F • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 24-31

Exam Practice

• Exam Practice: All Sections up to this Point · Quadratic Functions and their Graphs

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

• 368g: Determine the x- and y-intercepts of a quadratic graph with equation given in the form y=ax²+bx+c
• 368h: Determine the x- and y-intercepts of a quadratic graph with equation given in the form y=(ax+b)(cx+d)
• 368j: Sketch a quadratic graph given in the form y=(ax+b)(cx+d), including its intercepts only.
• 368l: Sketch a quadratic graph of the form y=ax²+bx+c, including its intercepts only.
• 368m: Sketch a quadratic graph of the form y=-x²+bx+c, including its intercepts only.
• 368n: Sketch a quadratic graph of the form y=-ax²+bx+c, including its intercepts only.
• 368p: Identify a sketch of a quadratic graph given its equation.
• 368q: Determine the equation of the line of symmetry of a sketched quadratic graph.
• 368r: Determine the line of symmetry of a quadratic graph from its equation.
• 368s: Determine a root of a sketched graph given the turning point and another root.
• 368t: Determine the coordinate of the turning point of a quadratic using symmetry and a sketch of the graph.
• 368u: Determine the equation of a quadratic function from its graph.
• 368v: Determine an unknown constant in a quadratic function given a point on the curve and a sketch.
• 416b: Determine the original quadratic function given the maximum or minimum point.
• 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.
• 368: Exam Practice: Quadratic graphs and their features
• 416: Exam Practice: Minimum or maximum point of a quadratic graph by completing the square

Practice Questions

• Practise Questions

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• PhET Drawing Quadratics Interactive Resource
• Math = Love (Sarah Carter)
  • Forms of a Quadratic Foldable
  • Quadratic Forms Flyswatter Game
• Underground Mathematics
  • Which parabola?✦
  • Parabella✦

• Berwick Maths Diagnostic Questions
• The Chalk Face Graphing Quadratics ppt
• Underground Mathematics Which quadratic✦
• Important Points on Quadratic Graphs Table Apologies I could not find the Author of this

Worksheets

• Jethwa Maths Starter Activity (p5-6) Some Discriminant Elements
• The Chalk Face Sketching Quadratics from Factorising Worksheet
• Don Steward Quadratic Points✦
• Susan Wall Quadratic Functions✦
• MEI Quadratics Two-Way Table✦
• Standards Unit Quadratics Card Sort✦
• PMT OCR MEI C1 Factorising & Sketching Quadratics 1 PPQs & MS
• PMT OCR MEI C1 Factorising & Sketching Quadratics 2 PPQs & MS
• PMT OCR MEI C1 Factorising & Sketching Quadratics 3 PPQs & MS
• kutasoftware Worksheets
  • Graphing Quadratic Functions
• MadAsMaths (T. Madas)
  • Quadratics Exam Questions Q11, 49, 51, 55, 57, 66, 70 (difficulty 2–4 of 5)
  • Quadratic Sketching Q1–18

AS Maths – Pure – Discriminant

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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2G Slides (Courtesy of Owen134866)

Dr Frost Video

KS5 – The Discriminant

Whole Topic Video

Bicen Maths Live Lesson

Quadratics 9 • The Discriminant • P1 Ex2G • 🤖

Quadratics 10 • Problems involving the Discriminant • P1 Ex2G • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 32-39

Exam Practice

• Exam Practice

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

• 492a: Calculate the discriminant of a quadratic function with numeric coefficients.
• 492b: Use the discriminant of a simple quadratic function to determine the number of solutions to an equation.
• 492c: Understand the relationship between the discriminant of a quadratic function and its sketch.
• 492d: Determine the discriminant of a quadratic function with algebraic coefficients.
• 492e: Use the discriminant to reason about the number of solutions of a factorised cubic.
• 492f: Use the discriminant to determine the values for algebraic coefficients in a quadratic function, where there are equal roots.
• 492g: Use the discriminant to determine the values for algebraic coefficients in a quadratic function, where there are no roots or distinct roots.
• 492h: Use the discriminant to determine the values for algebraic coefficients in a quadratic function, requiring rearrangement.
• 492i: Use the discriminant to determine when a straight line is tangent to a quadratic graph.
• 492j: Prove that a quadratic with algebraic coefficients always has either distinct or no solutions.
• 492: Exam Practice: Discriminant of a quadratic function

Practice Questions

• Practise Questions

Other Videos

The Discriminant

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Underground Mathematics Discriminating✦ (& Teacher Notes✦)
• Goal Free Problems
  • A-Level Algebra & Coordinate Geometry set Q22

Worksheets

• Jethwa Maths Starter Activity (p9-10)
• PMT OCR Set 1 Discriminant PPQs & Solutions (Old Spec)
• kutasoftware Worksheets
  • The Discriminant
• Mathshelper (Jon Stone)
  • Discriminant
• Maths Genie
  • The Discriminant: Questions · Solutions · Lesson · Topic page
• Dr Oliver Mathematics
  • Discriminant questions✦ (solutions✦)
• MadAsMaths (T. Madas)
  • Quadratics Exam Questions Q20, 28, 80, 86, 89, 91, 100 (difficulty 3–5 of 5)
  • Discriminant Exam Questions Basic Q1–4, 6–7; Standard Q1–2, 7, 9–12, 18, 20–21, 27; Hard Q2–4, 6–9; Enrichment Q1, 7 (difficulty 2–5 of 5)
  • Discriminant Practice Basic Q1–26; Standard Q1–25; Hard Q1–2 (difficulty 2–4 of 5)

AS Maths – Pure – Modelling with Quadratics

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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2H Slides (Courtesy of Owen134866)

Dr Frost Video

• Whole Topic Video (From 8:35)

Bicen Maths Live Lesson

Quadratics 11 • Modelling • P1 Ex2H • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 40-42

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

• 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.
• 418a: Form (and solve) a quadratic equation or expression from the area of a rectangle.
• 418c: Form (and solve) a quadratic equation or expression from the area of a more complex rectilinear shape.
• 418g: Form (and solve) a quadratic equation or expression using the sides of a right-angled triangle using Pythagoras’ Theorem.
• 416: Exam Practice: Minimum or maximum point of a quadratic graph by completing the square
• 418: Exam Practice: Forming and solving quadratic or non-linear expressions or equations from a given context (excluding probability problems)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Desmos
  • Penny Circle (gather data and build a quadratic model)

Worksheets

• Mathsaurus Mixed Exam Board PPQs
• MadAsMaths (T. Madas)
  • Quadratics Exam Questions Q22, 60, 67–68, 73, 75, 77–78, 83, 95–96 (difficulty 3–5 of 5)

Whole Topic Videos

Quadratics 12 • Modelling – Exam Qs • P1 Ex2H • 🤖

Bicen Maths Exam Questions

External Whole Topic Past Paper Style Questions

• Jethwa Maths Worksheet (p4-9 First 5 Qs Only)
• Dr Frost Topic Test (Teacher Log in Required)
• Mathsaurus Mixed Exam Board PPQs
• Naiker Maths Exam Qs (2005-2011)✦ & MS✦
• Naiker Maths Exam Qs (2012-2017) & MS
• PMT
  • Summary Quadratics PPQs
  • AQA Selected Quadratics PPQs (Old Spec)
  • Edexcel Set 1 Quadratics PPQs (Old Spec)
  • Edexcel Set 2 Quadratics PPQs (Old Spec)
  • Summary Cheat Sheet
• crashMATHS
  • End of topic test: Algebra I (GCSE review & quadratics): Test✦

Worksheets

• Mathshelper (Jon Stone)
  • Quadratics Test
  • Quadratic Formula, Completing Square & Discriminant
• Maths Genie
  • Quadratics: Questions · Solutions · Lesson · Topic page
• Physics & Maths Tutor
  • Quadratics: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• Jethwa Maths
  • Quadratics: 10 minute tests✦
• SRWhitehouse
  • Quadratics revision✦
  • Mixed quadratics questions✦
• MadAsMaths (T. Madas)
  • Quadratics Exam Questions Q97 (difficulty 5 of 5)
  • Discriminant Exam Questions Enrichment Q3 (difficulty 5 of 5)
• Dr Austin Maths
  • Revision Practice Grid (Word | PDF | Answers)
  • Expressions and Equations Fill in the Blanks (Word | PDF✦ | Answers✦)
  • More Expressions and Equations Fill in the Blanks (Word | PDF✦ | Answers✦)
  • Solving by Rearranging Practice Grid (Word | PDF✦ | Answers✦)
  • Sketching Graphs Fill in the Blanks (Word | PDF✦ | Answers✦)
  • Finding Equations from Graphs Practice Grid (Word | PDF✦ | Answers✦)
  • The Discriminant Fill in the Blanks (Word | PDF✦ | Answers✦)
  • Using the Discriminant Crack the Code (Word | PDF✦ | Answers✦)
  • Hidden Fill in the Blanks (Word | PDF✦ | Answers✦)

Activities

• MEI
  • MEI teaching notes, misconceptions & prompts: Quadratic functions✦
• Interwoven Maths
  • Quadratics: always, sometimes, never✦
• Swinton Maths
  • Hidden quadratics fill in the blanks✦
• NRICH (student problems)
  • Powerful quadratics✦
  • Discriminating (always, sometimes, never cards)✦
• Andy Lutwyche
  • Erica’s Errors
  • Different Guises