Equations & Inequalities

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AS Maths – Pure – Linear Simultaneous Equations

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Dr Frost Video

• 283 Solve simultaneous equations where one unknown has equal positive coefficients. Key Skill Video (GCSE)
• 284 Solve simultaneous equations where one unknown has equal coefficients with different signs. Key Skill Video (GCSE)
• 285 Solve simultaneous equations with unequal coefficients where the unknowns have the same signs. Key Skill Video (GCSE)
• 286 Solve simultaneous equations with unequal coefficients where the second unknowns have different signs. Key Skill Video (GCSE)

Bicen Maths Live Lesson

Equations & Inequalities 1 • Simultaneous Linear and Non-Linear Equations • P1 Ex3A/B • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (Up to 10:11)

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• Dr Frost Slides 1-8

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Key Skills

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

• 276a: Solve linear simultaneous equations/systems of equations where one unknown has equal positive coefficients.
• 276b: Solve linear simultaneous equations/systems of equations where one unknown has equal negative coefficients.
• 276c: Solve linear simultaneous equations/systems of equations where one unknown has equal coefficients with different signs.
• 276d: Solve linear simultaneous equations/systems of equations where one equation needs to be scaled.
• 276e: Solve linear simultaneous equations/systems of equations where both equations need to be scaled.
• 276f: Solve linear simultaneous equations/systems of equations requiring rearrangement by elimination.
• 276g: Solve linear simultaneous equations/systems of equations by substitution.
• 276i: Form and solve linear simultaneous equations/systems of equations for a given non-geometric context.
• 276j: Form and solve linear simultaneous equations/systems of equations for a given geometric context.
• 276: Exam Practice: Solving linear simultaneous equations/systems of equations using elimination or substitution

Other Videos

Solving Simultaneous Equations

Solving Simultaneous Equations

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Systems of Equations

Activities

• Berwick Maths Diagnostic Questions
• The Chalk Face Simultaneous Equations Problem

Worksheets

• Jethwa Maths Starter Activities (p1-2)
• SRWhitehouse Simultaneous Equations✦ (TES Account Required)
• kutasoftware Worksheets
  • Solving Systems of Equations by Graphing
  • Solving Systems of Equations by Elimination
  • Solving Systems of Equations by Substitution
  • Systems of Equations Word Problems
  • Systems of Two Equations
  • Systems of Two Equations, Word Problems
• StudyWell
  • Simultaneous Equations exam questions with solutions✦
• Dr Oliver Mathematics
  • Simultaneous equations questions✦ (solutions✦)
• MadAsMaths (T. Madas)
  • Equations Exam Questions I Q34 (difficulty 3 of 5)
  • Equations Basic Techniques Linear Simultaneous Equations Q1–7

AS Maths – Pure – Quadratic Simultaneous Equations

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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Dr Frost Video

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Bicen Maths Live Lesson

Equations & Inequalities 1 • Simultaneous Linear and Non-Linear Equations • P1 Ex3A/B • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (From 10:11)

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• Dr Frost Slides 1-8

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

• 419b: Solve non-linear simultaneous equations/systems of equations where y is the subject of both equations, to give a quadratic equation to be solved.
• 419c: Solve non-linear simultaneous equations where x or y is the subject of the linear equation.
• 419d: Solve non-linear simultaneous equations where x or y is not the subject of the linear equation.
• 419e: Solve simultaneous equations/systems of equations given in the form ax + by = c and x² + y² = d
• 419f: Solve simultaneous equations/systems of equations with variables in denominator of fractions e.g. x/y+2y/x=4 and y=x-2
• 419g: Form and solve non-linear simultaneous equations/systems of equations for a given context.
• 419h: Find the points of intersection of a line and a quadratic curve. (not yet active)
• 276h: Solve non-linear simultaneous equations/systems of equations where y is the subject of both equations, to give a linear equation to be solved.
• 419: Exam Practice: Solving non-linear simultaneous equations/systems of equations by substitution
• 276: Exam Practice: Solving linear simultaneous equations/systems of equations using elimination or substitution

Practice Questions

• Practise Questions

Other Videos

Quadratic Simultaneous Equations

Solving Quadratic Simultaneous Equations

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Underground Mathematics
  • Two-way algebra✦

Worksheets

• Jethwa Maths Starter Activities (p7-8)
• SRWhitehouse Simultaneous Equations✦ (TES Account Required)
• Don Steward Quadratic Meets Linear✦
• MadAsMaths (T. Madas)
  • Equations Exam Questions I Q2–3, 5–6, 9, 12, 17, 19, 22–27, 35, 37, 39, 41, 47, 49–52, 57, 59, 64–66 (difficulty 2–5 of 5)
  • Quadratics Exam Questions Q5, 35, 41 (difficulty 2–3 of 5)
  • Surd Exam Questions✦ Q55 (difficulty 4 of 5)
  • Line Coordinate Geometry Exam Questions Basic Q28; Standard Q29 (difficulty 3–4 of 5)
  • Equations Basic Techniques Non-Linear Simultaneous Equations Q1–12
  • Equations: Advanced Skills Q39 (difficulty 4 of 5)

AS Maths – Pure – Simultaneous Equations on Graphs

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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Bicen Maths Live Lesson

Equations & Inequalities 2 • Simultaneous Equations and the Discriminant • P1 Ex3C • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 9-13

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

• 275a: Solve linear simultaneous equations/systems of equations using an existing plot of each line.
• 275b: Solve linear simultaneous equations/systems of equations by first plotting each line.
• 419a: Use a given value of x or y to verify a point of intersection of two graphs with given equations. (not yet active)
• 421e: Solve simultaneous equations/systems of equations using graphical methods, where one is linear and the other is quadratic or a given curved graph.
• 492i: Use the discriminant to determine when a straight line is tangent to a quadratic graph.
• 275: Exam Practice: Solving linear simultaneous equations/systems of equations using graphical methods
• 419: Exam Practice: Solving non-linear simultaneous equations/systems of equations by substitution
• 421: Exam Practice: Using graphs to count solutions and find approximate solutions to equations
• 492: Exam Practice: Discriminant of a quadratic function

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• The Chalk Face Simultaneous Equations: Line & Curve
• Goal Free Problems
  • A-Level Algebra & Coordinate Geometry set Q18, Q27

Worksheet

• Jethwa Maths Starter Activities (p3-4) Q2

AS Maths – Pure – Linear Inequalities

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3D Slides (Courtesy of Owen134866)

Dr Frost Video

• Whole Topic Video (Up to 1:33)

Bicen Maths Live Lesson

Equations & Inequalities 3 • Set Notation • P1 Ex3D • 🤖

Equations & Inequalities 4 • Linear Inequalities • P1 Ex3D • 🤖

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 14-17

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

• 339c: Solve a linear inequality in one variable involving simple fractions.
• 339d: Solve a linear inequality in one variable involving brackets.
• 339e: Solve a linear inequality in one variable involving brackets and fractions.
• 339f: Solve a linear inequality in one variable where the coefficient of x is negative.
• 340a: Solve a linear inequality with the unknown on both sides.
• 340b: Solve a linear inequality with brackets and the unknown on both sides.
• 340c: Solve a linear inequality involving a single fraction and the unknown on both sides.
• 340d: Solve a linear inequality involving multiple fractions and the unknown on both sides.
• 341b: Solve a two-ended linear inequality in one variable with two steps.
• 341c: Solve a two-ended linear inequality in one variable involving fractions.
• 341e: Solve a two-ended linear inequality in one variable which has a negative coefficient.
• 341h: Combine two inequalities with an overlapping range.
• 341i: Combine two more complex inequalities involving an ‘or’/disjunction.
• 341j: Solve a pair of linear inequalities in one variable and state the integer values that satisfy both.
• 341k: Solve a more complex two-ended linear inequality where the variable appears in the outer expressions.
• 339: Exam Practice: Solving linear inequalities in one variable
• 340: Exam Practice: Solving linear inequalities with one variable on both sides
• 341: Exam Practice: Solving two-ended linear inequalities and combining inequalities

Other Videos

Solving Inequalities

Solving Linear Inequalities

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Multi-Step Inequalities: Solving Equations & Inequalities
  • Compound Inequalities Follow with Quiz 3

Activities

• Berwick Maths Diagnostic Questions

Worksheets

• The Chalk Face Multiple Linear Inequalities
• kutasoftware Worksheets
  • Graphing One-Variable Inequalities
  • One-Step Inequalities
  • Two-Step Inequalities
  • Multi-Step Inequalities
  • Compound Inequalities
• MadAsMaths (T. Madas)
  • Inequalities Basic Practice Linear Inequalities Q1–3
  • Inequalities Various Inequalities Q1, 3 (difficulty 2 of 5)

AS Maths – Pure – Quadratic Inequalities

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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Dr Frost Video

• Whole Topic Video (From 1:33 to 12:40)

Bicen Maths Live Lesson

Equations & Inequalities 5 • Quadratic Inequalities • P1 Ex3E • 🤖

Equations & Inequalities 6 • Inequalities involving Division by x • P1 Ex3E • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 18-23

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

• 458a: Solve quadratic inequalities given in the form x² + bx + c > 0 or x² + bx + c < 0
• 458b: Solve quadratic inequalities given in the form x² + bx> 0 or x² +bx < 0
• 458c: Solve quadratic inequalities given in the form x² – a²> 0 or x² – a² < 0
• 458d: Solve inequalities requiring rearrangement to the form x² + bx + c > 0 or x² + bx + c < 0
• 458e: Solve inequalities requiring expanding brackets and rearrangement to the form x² + bx + c > 0 or x² + bx + c < 0
• 458f: Solve quadratic inequalities given in the form ax² + bx + c > 0 or ax² + bx + c < 0
• 458g: Solve quadratic inequalities requiring rearrangement to the form ax² + bx + c > 0 or ax² + bx + c < 0
• 458h: Solve quadratic inequalities requiring expanding brackets and rearrangement to the form ax² + bx + c > 0 or ax² + bx + c < 0
• 458i: Solve quadratic inequalities given in the form ax² > bx or ax² < bx
• 458j: Solve quadratic inequalities given in the form ax² > b or ax² < b
• 458k: Solve quadratic inequalities given in the form -x² + bx + c > 0 or -x² + bx + c < 0
• 458m: Solve quadratic inequalities involving a division by a positive algebraic expression.
• 458n: Express the solution of a quadratic inequality using set notation.
• 458o: Combine a linear and a quadratic inequality.
• 458p: Form and solve a quadratic inequality to find the terms in a quadratic sequence that fulfil certain criteria.
• 458q: Form and solve a quadratic inequality for a given context.
• 458: Exam Practice: Solving quadratic inequalities

Practice Questions

• Practise Questions

Other Videos

Solving Quadratic Inequalities

Solving Quadratic Inequalities

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• MEI
  • Categorising quadratic inequalities✦

Worksheets

• Jethwa Maths Starter Activities (p3-4) Q1
• mssteelmaths.com Quadratic inequalities✦
• Jo Morgan Quadratic Inequalities – Spot the Mistake✦ (TES Account Required)
• Underground Mathematics Inequalities for Some Occasions✦
• Mathshelper (Jon Stone)
  • Quadratic Inequalities
• Maths Genie
  • Quadratic Inequalities: Questions · Solutions · Lesson · Topic page
• MadAsMaths (T. Madas)
  • Inequalities Exam Questions Q1–3, 5–9, 11–23, 26 (difficulty 2–4 of 5)
  • Inequalities Basic Practice Quadratic Inequalities Q1–13
  • Inequalities Various Inequalities Q2 (difficulty 2 of 5)

AS Maths – Pure – Inequalities on Graphs

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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Dr Frost Video

• Whole Topic Video (From 12:40)

Bicen Maths Live Lesson

Equations & Inequalities 7 • Inequalities and Regions on Graphs • P1 Ex3F/G • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (Up to 3:56)

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• Dr Frost Slides 24-26

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

• 458l: Form and solve a quadratic inequality involving functions.
• 421a: Determine the number of solutions to f(x)=g(x) given graphs of y=f(x) and y=g(x)
• 421b: Determine the number of solutions to an equation that can be rearranged to f(x)=g(x) given graphs of y=f(x) and y=g(x)
• 421c: Determine the range of values for k in f(x)=k given the graph of y=f(x) and the number of solutions.
• 458: Exam Practice: Solving quadratic inequalities
• 421: Exam Practice: Using graphs to count solutions and find approximate solutions to equations

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• amwgauss Inequalities on Graphs (TES Account Required)
• Underground Mathematics Inequality Sets✦
• MadAsMaths (T. Madas)
  • Inequalities Exam Questions Q4, 10 (difficulty 2–3 of 5)

AS Maths – Pure – Inequality Regions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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Bicen Maths Live Lesson

Equations & Inequalities 7 • Inequalities and Regions on Graphs • P1 Ex3F/G • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (From 3:56)

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 24-26

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

• 456b: Identify a region in 2D indicated by a linear inequality in two variables.
• 456d: Identify regions in 2D indicated by two linear inequalities where at least one is in two variables.
• 456e: Identify regions in 2D indicated by three or more linear inequalities where at least one is in two variables.
• 456f: Determine a fixed number of integer solutions which satisfy a given set of linear inequalities in two variables.
• 456g: Determine the linear inequalities represented by a region on a graph.
• 456h: Consider the validity of related linear inequalities in two variables, given others known to be true.
• 456i: Identify regions in 2D indicated by a mixture of linear and quadratic inequalities.
• 456j: Determine the linear and quadratic inequalities represented by a region on a graph.
• 456: Exam Practice: Linear inequalities on a 2D plane

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Underground Mathematics
  • Linear inequalities graphically✦

Worksheets

• kutasoftware Worksheets
  • Graphing Quadratic Inequalities
• Dr Austin Maths
  • Describing Graphical Inequalities Practice Grid✦ (answers✦)
• MadAsMaths (T. Madas)
  • Inequalities Exam Questions Q24–25 (difficulty 4 of 5)

External Whole Topic Past Paper Style Questions

• Jethwa Maths Quadratics Worksheet (p4-9 After Q5 for Quadratic Inequalities), Topic Test (p4-8)
• Dr Frost Topic Test (Teacher Log in Required)
• Mathsaurus Mixed Exam Board PPQs
• Naiker Maths Exam Qs (2005-2011) & MS
• StudyWell
• PMT
  • Summary Inequalities PPQs
  • Summary Simultaneous Equations PPQs
  • Edexcel Set 1 Simultaneous Equations PPQs (Old Spec)
  • Edexcel Set 2 Simultaneous Equations PPQs (Old Spec)
  • Edexcel Set 2 Inequalities PPQs (Old Spec)
  • OCR Set 1 Inequalities PPQs & Solutions (Old Spec)
  • OCR Set 1 Simultaneous Equations PPQs & Solutions (Old Spec)
  • OCR MEI Inequalities PPQs & Solutions (Old Spec)
  • Summary Cheat Sheet

Worksheets

• Maths Genie
  • Equations and Inequalities: Questions · Solutions · Lesson · Topic page
• Physics & Maths Tutor
  • Inequalities: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MME
  • C1 Algebra: Questions | Answers
• Jethwa Maths
  • Simultaneous Equations and Inequalities: 10 minute tests✦
• MadAsMaths (T. Madas)
  • Inequalities Exam Questions Q27 (difficulty 5 of 5)
• Dr Austin Maths
  • Solving Systems Fill in the Blanks (Word | PDF✦ | Answers✦)
  • Set Notation Fill in the Blanks (Word | PDF✦ | Answers✦)
  • Shading Regions with Quadratic Practice Grid (Word | PDF | Answers)
  • Graphical Fill in the Blanks (Word | PDF✦ | Answers✦)
  • Solving Graphically Practice Grid (Word | PDF | Answers)
  • Mixed Simultaneous Crack the Code (Word | PDF✦ | Answers✦)

Activities

• MEI
  • MEI teaching notes, misconceptions & prompts: Equations and inequalities✦
• SRWhitehouse
  • Introduction to algebra matching activity✦
• Andy Lutwyche
  • Erica’s Errors On Simultaneous