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Linear and quadratic equations and their graphs (8300 - Higher - Algebra)

Topic:Linear and quadratic equations and their 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 algebraically by factorising
  • Find approximate solutions using a graph

    A21
    • Translate simple situations or procedures into algebraic expressions or formulae; derive an equation and the 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

    Diagnostic Questions - quadratic graphs 1
    AQA have teamed up with Craig Barton's Diagnostic Questions website to share free diagnostic questions assessment for our new 2017 GCSE Maths specification.21/07/2017
    E-library
    Type(s): Diagnostic Questions (e-library)
    Diagnostic Questions - quadratic graphs 2
    AQA have teamed up with Craig Barton's Diagnostic Questions website to share free diagnostic questions assessment for our new 2017 GCSE Maths specification.21/07/2017
    E-library
    Type(s): Diagnostic Questions (e-library)
    Diagnostic Questions - quadratic graphs 3
    AQA have teamed up with Craig Barton's Diagnostic Questions website to share free diagnostic questions assessment for our new 2017 GCSE Maths specification.21/07/2017
    E-library
    Type(s): Diagnostic Questions (e-library)

    CIMT Equations in Context
    An online exercise in which students form and solve equations in a range of real life and mathematical contexts.07/08/2015
    E-library
    Type(s): Activities (e-library)
    Finding the roots from a quadratic graph
    A powerpoint involving reading the roots from quadratic graphs, including cases where there are equal roots or no real roots. You will need to register for a TES account to access this resource, this is free of charge. 02/09/2015
    E-library
    Type(s): Activities (e-library)
    Line graph matching cards
    A matching activity which reinforces the use of m and c for the gradient and y-intercept of straight line. You will need to register for a TES account to access this resource, this is free of charge. 02/09/2015
    E-library
    Type(s): Activities (e-library)
    National STEM Centre: Graphical Solution of Equations
    An Excel file in which students can produce the graphs of given functions and use these to solve equations. You will need to register for an account to access this resource, this is free of charge. 07/08/2015
    E-library
    Type(s): Activities (e-library)
    Quadatic Sketch Treasure Hunt
    A treasure hunt activity in which students must match quadratic expressions with their graphs by identifying roots in the factorised form of the quadratics. You will need to register for a TES account to access this resource, this is free of charge. 07/08/2015
    E-library
    Type(s): Activities (e-library)
    Starter / Plenary for straight line graphs
    A nice starter or plenary activity - a multiple choice ten question quiz in which students must identify the gradient, intercept and other properties of given lines. You will need to register for a TES account to access this resource, this is free of charge. 02/09/2015
    E-library
    Type(s): Activities (e-library) | Plenaries (e-library) | Starters (e-library)
    Transum Algebra in Action
    Four levels of online questions in which students form and solve equations in a range of contexts.07/08/2015
    E-library
    Type(s): Activities (e-library)
    Using one graph to solve another
    Two lessons of powerpoints and worksheets in which students use graphs to solve equations such as x2+x = 3x+6. You will need to register for a TES account to access this resource, this is free of charge. 07/08/2015
    E-library
    Type(s): Activities (e-library)
    Which graph?
    Students must pair up the quadratic equation with the corresponding graph, by identifying the roots.02/09/2015
    E-library
    Type(s): Activities (e-library)

    Starter / Plenary for straight line graphs
    A nice starter or plenary activity - a multiple choice ten question quiz in which students must identify the gradient, intercept and other properties of given lines. You will need to register for a TES account to access this resource, this is free of charge. 02/09/2015
    E-library
    Type(s): Activities (e-library) | Plenaries (e-library) | Starters (e-library)

    Starter / Plenary for straight line graphs
    A nice starter or plenary activity - a multiple choice ten question quiz in which students must identify the gradient, intercept and other properties of given lines. You will need to register for a TES account to access this resource, this is free of charge. 02/09/2015
    E-library
    Type(s): Activities (e-library) | Plenaries (e-library) | Starters (e-library)

    Forming and solving equations
    A complete lesson with powerpoint examples of how to form and solve equations in a range of real life and mathematical contexts with an associated worksheet. You will need to register for a TES account to access this resource, this is free of charge. 07/08/2015
    E-library
    Type(s): Worksheets (e-library)
    Intro to graphically solving equations
    An introductory activity in which students must match the equations to the given linear and quadratic graphs and use these to solve a range of given equations. You will need to register for a TES account to access this resource, this is free of charge. 07/08/2015
    E-library
    Type(s): Worksheets (e-library)
    Solving quadratic equations graphically
    A worksheet involving solving quadratic equations using the graphs provided. You will need to register for a TES account to access this resource, this is free of charge. 02/09/2015
    E-library
    Type(s): Worksheets (e-library)

    Sketch for presents game
    A game in which students draw a line on a given diagram in a way that collects the most presents. However, they can only win the presents if they can state the equation of the line they have drawn! You will need to register for a TES account to access this resource, this is free of charge. 02/09/2015
    E-library
    Type(s): Game (e-library)

    Maths is Fun: Quadratic Equation Solver
    An interactive demonstration in which a quadratic equation is inputted and a the solutions can be seen on the graph which is sketched automatically on screen (NB The section on the quadratic formula is higher tier only).02/09/2015
    E-library
    Type(s): Miscellaneous (e-library)

    Topic Tests

    8300 GCSE Higher Drawing quadratic graphs Mark Scheme
    Downloadable resource in pdf format. 22/06/2023
    226 KB
    Related resources: Linear and quadratic equations and their graphs
    8300 GCSE Higher Drawing quadratic graphs Topic Test
    Downloadable resource in pdf format. 23/06/2023
    379 KB
    Related resources: Linear and quadratic equations and their graphs
    8300 GCSE Higher Solving simultaneous equations graphically Mark Scheme
    Downloadable resource in pdf format. 23/06/2023
    226 KB
    Related resources: Linear and quadratic equations and their graphs
    8300 GCSE Higher Solving simultaneous equations graphically Topic Test
    Downloadable resource in pdf format. 23/06/2023
    338 KB
    Related resources: Linear and quadratic equations and their graphs
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