All About Maths

Further equations and graphs (8300 - Higher - Algebra)

Topic:Further equations and graphs

Route Map

Specification references (in recommended teaching order)

Specification content Specification notes
A17
  • Solve linear equations in one unknown algebraically including those with the unknown on both sides of the equation
  • Find approximate solutions using a graph
  • including use of brackets
A18
  • Solve quadratic equations (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula
  • Find approximate solutions using a graph

    A12
    • Recognise, sketch and interpret graphs of linear and quadratic functions

      A11
      • Identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square
      • including the symmetrical property of a quadratic
      A21
      • Translate simple situations or procedures into algebraic expressions or formulae
      • derive an equation, solve the equation and interpret the solution
      • including solution of geometrical problems and problems set in context


      The subject content (above) matches that set out in the Department for Education’s Mathematics GCSE subject content and assessment objectives document.

      The expectation is that:

      • All students will develop confidence and competence with the content identified by standard type
      • All students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content
      • Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.

      Teaching resources

      Teaching resources - see below
      Downloadable resource in format. 29/08/2014

      GCSE Bitesize - Solving and using quadratic equations
      Pages 1-3 of this website introduce the methods for solving quadratic equations using factorisation, completing the square and using the quadratic formula.19/08/2015
      E-library
      Type(s): Overview (e-library)
      Sketching Quadratics
      A powerpoint and associated worksheet in which students must factorise a quadratic and/or complete the square to sketch the curve and identify the turning point. You will need to register for a TES account to access this resource, this is free of charge. 19/08/2015
      E-library
      Type(s): Overview (e-library) | Worksheets (e-library)

      CIMT Quadratic Functions
      Online overview of solving quadratics using graphs, factorisation and the quadratic formula with associated computer-marked exercises.19/08/2015
      E-library
      Type(s): Activities (e-library)
      Completing the square powerpoint
      A full lesson of activities including a starter and a quiz to complete the lesson - students learn to complete the square and use it to solve quadratic equations. You will need to register for a TES account to access this resource, this is free of charge. 19/08/2015
      E-library
      Type(s): Activities (e-library)
      Maths is Fun - Completing the Square
      An introduction to completing the square, including the method for solving the equation for completed square form. Includes ten increasingly demanding online questions.19/08/2015
      E-library
      Type(s): Activities (e-library)
      Nrich: A cartesian puzzle
      Students are given eight sets of three points and asked to identify the fourth point that would form a parallelogram in each case. 02/09/2015
      E-library
      Type(s): Activities (e-library)
      Quadratics Graph Excel
      An Excel file in which students can explore the sketching of quadratics in factorised and completed square form. You will need to register for a TES account to access this resource, this is free of charge. 19/08/2015
      E-library
      Type(s): Activities (e-library)
      Teachit Maths - Completing the square dominoes
      Students cut out the dominoes and complete the square to match the expressions and make a continuous loop of dominoes.19/08/2015
      E-library
      Type(s): Activities (e-library)

      Sketching Quadratics
      A powerpoint and associated worksheet in which students must factorise a quadratic and/or complete the square to sketch the curve and identify the turning point. You will need to register for a TES account to access this resource, this is free of charge. 19/08/2015
      E-library
      Type(s): Overview (e-library) | Worksheets (e-library)
      Step by step quadratic formula
      A helpful worksheet which sets out the stages of solving a quadratic equation using the formula in a grid - useful for the first lesson on this topic. You will need to register for a TES account to access this resource, this is free of charge. 19/08/2015
      E-library
      Type(s): Worksheets (e-library)

      Coordinates and graphs - Homework Sheet and Mark Scheme
      Downloadable resource in doc format. 09/04/2010
      140 KB108 KB
      Related resources: Higher | Unit 3 | Coordinates and Graphs | Further equations and graphs | Further sketching graphs | Homework Sheets
      Quadratic equations - Homework Sheet and Mark Scheme
      Downloadable resource in doc format. 08/04/2010
      105 KB196 KB
      Related resources: Higher | Unit 2 | Quadratic Equations | Algebra: quadratics, rearranging formulae and identities | Further equations and graphs | Homework Sheets
      Quadratic Equations - Worksheet and Answers
      Downloadable resource in doc format. 22/05/2010
      176 KB174 KB
      Related resources: Higher | Unit 2 | Quadratic Equations | Algebra: quadratics, rearranging formulae and identities | Further equations and graphs | Supplementary Resources

      Topic Tests

      8300 GCSE Higher Solving Equations Using Graphs Mark Scheme
      Downloadable resource in pdf format. 04/11/2022
      267 KB
      Related resources: Further equations and graphs
      8300 GCSE Higher Solving Equations Using Graphs Topic Test
      Downloadable resource in pdf format. 04/11/2022
      382 KB
      Related resources: Further equations and graphs
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