All About Maths

Algebra: quadratics, rearranging formulae and identities (8300 - Foundation - Algebra)

Topic:Algebra: quadratics, rearranging formulae and identities

Route Map

Specification references (in recommended teaching order)

Specification content Specification notes
A4
  • Simplify and manipulate algebraic expressions (including those involving surds) by:
    • expanding products of two binomials
    • factorising quadratic expressions of the form `x^2 + bx + c` including the difference of two squares
    • simplifying expressions involving sums, products and powers, including the laws of indices

    A5
    • Understand and use standard mathematical formulae
    • Rearrange formulae to change the subject
    • including use of formulae from other subjects in words and using symbols
    A6
    • Know the difference between an equation and an identity
    • Argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments

      A7
      • Where appropriate, interpret simple expressions as functions with inputs and outputs


        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

        Algebra: quadratics, rearranging formulae and identities - all resources for 3 year route map - zip folder
        Downloadable resource in zip format. 07/10/2014
        15.6 MB
        Related resources:
        Topic overview and lesson plans
        Downloadable resource in doc format. 07/10/2014
        799 KB
        Related resources:

        Lesson 1 Activity 1
        Downloadable resource in doc format. 02/10/2014
        195 KB
        Related resources:
        Lesson 1 Activity 2
        Downloadable resource in doc format. 02/10/2014
        540 KB
        Related resources:
        Lesson 1 Activity 3
        Downloadable resource in doc format. 02/10/2014
        569 KB
        Related resources:
        Lesson 2 Activity 1
        Downloadable resource in ppt format. 02/10/2014
        2.3 MB
        Related resources:
        Lesson 2 Activity 2
        Downloadable resource in doc format. 02/10/2014
        665 KB
        Related resources:
        Lesson 3 Activity 1
        Downloadable resource in ppt format. 02/10/2014
        1.6 MB
        Related resources:
        Lesson 3 Activity 2
        Downloadable resource in doc format. 02/10/2014
        1.6 MB
        Related resources:
        Lesson 4 Activity 1
        Downloadable resource in ppt format. 02/10/2014
        1.3 MB
        Related resources:
        Lesson 5 Activity 1
        Downloadable resource in ppt format. 02/10/2014
        1.4 MB
        Related resources:
        Lesson 5 Activity 2
        Downloadable resource in doc format. 02/10/2014
        2.5 MB
        Related resources:
        Lesson 6 Activity 1
        Downloadable resource in ppt format. 02/10/2014
        1.9 MB
        Related resources:
        Lesson 6 Activity 2
        Downloadable resource in ppt format. 02/10/2014
        196 KB
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        Lesson 7 Activity 1
        Downloadable resource in ppt format. 02/10/2014
        1.3 MB
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        Lesson 8 Activity 1
        Downloadable resource in doc format. 02/10/2014
        928 KB
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        Lesson 8 Activity 2
        Downloadable resource in doc format. 02/10/2014
        205 KB
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        Lesson 8 Activity 3
        Downloadable resource in ppt format. 02/10/2014
        1.7 MB
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        Lesson 8 Activity 4
        Downloadable resource in doc format. 02/10/2014
        481 KB
        Related resources:

        Lesson 6 Worksheet 1
        Downloadable resource in doc format. 02/10/2014
        5.1 MB
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        Lesson 6 Worksheet 2
        Downloadable resource in doc format. 02/10/2014
        587 KB
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        Lesson 7 Worksheet 1
        Downloadable resource in doc format. 02/10/2014
        7.5 MB
        Related resources:
        Lesson 8 Worksheet 1
        Downloadable resource in doc format. 02/10/2014
        1.4 MB
        Related resources:
        Lesson1 Worksheet 1
        Downloadable resource in doc format. 02/10/2014
        3.7 MB
        Related resources:

        Lesson 1 Homework sheet 1
        Downloadable resource in doc format. 02/10/2014
        3.7 MB
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        Lesson 1 Homework sheet 2
        Downloadable resource in doc format. 02/10/2014
        1.6 MB
        Related resources:
        Lesson 2 Homework sheet 1
        Downloadable resource in doc format. 02/10/2014
        3.9 MB
        Related resources:
        Lesson 3 Homework sheet 1
        Downloadable resource in doc format. 02/10/2014
        1.5 MB
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        Lesson 4 Homework sheet 1
        Downloadable resource in doc format. 02/10/2014
        372 KB
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        Lesson 5 Homework sheet 1
        Downloadable resource in doc format. 02/10/2014
        480 KB
        Related resources:
        Lesson 6 Homework sheet 1
        Downloadable resource in doc format. 02/10/2014
        633 KB
        Related resources:
        Lesson 7 Homework sheet 1
        Downloadable resource in doc format. 02/10/2014
        3.2 MB
        Related resources:

        Diagnostic Questions - quadratics, rearranging formulae and identities 1
        AQA have teamed up with Craig Barton's Diagnostic Questions website to share free diagnostic question assessment for the 2017 GCSE Maths qualification.27/04/2017
        E-library
        Type(s): Diagnostic Questions (e-library) | Algebra: quadratics, rearranging formulae and identities
        Diagnostic Questions - quadratics, rearranging formulae and identities 2
        AQA have teamed up with Craig Barton's Diagnostic Questions website to share free diagnostic question assessment for the 2017 GCSE Maths qualification. 27/04/2017
        E-library
        Type(s): Diagnostic Questions (e-library) | Algebra: quadratics, rearranging formulae and identities
        Diagnostic Questions - quadratics, rearranging formulae and identities 3
        AQA have teamed up with Craig Barton's Diagnostic Questions website to share free diagnostic question assessment for the 2017 GCSE Maths qualification. 27/04/2017
        E-library
        Type(s): Diagnostic Questions (e-library) | Algebra: quadratics, rearranging formulae and identities

        Sorting Equations and Identities
        Sorting equations and identities lesson plan 21/01/2015
        E-library
        Type(s): Lesson plans (e-library) | Algebra: quadratics, rearranging formulae and identities

        Formula
        Definition of formula03/03/2015
        E-library
        Type(s): Overview (e-library) | Algebra: quadratics, rearranging formulae and identities

        CIMT: Expanding and Factorising Quadratics
        The expanding and factorising section of this website offers an explanation and examples on how to expand and factorise, including the difference of two squares, followed by some online exercises.05/08/2015
        E-library
        Type(s): Activities (e-library) | Algebra: quadratics, rearranging formulae and identities
        Difference of Two Squares
        Explore the difference in the squares of numbers 21/01/2015
        E-library
        Type(s): Activities (e-library) | Algebra: quadratics, rearranging formulae and identities
        Double brackets starter / plenary activity
        Designed for use with an interactive voting system this multiple choice quiz offers practise in factorising expressions into two brackets including a couple of challenging questions suitable only for higher tier students. You will need to register for a TES account to access this resource, this is free of charge. 05/08/2015
        E-library
        Type(s): Activities (e-library) | Plenaries (e-library) | Starters (e-library) | Algebra: quadratics, rearranging formulae and identities
        Quadratic Expression Match Up
        A lesson of activities including a starter and differentiated match up activities, including some of the form ax2+bx+c for extension work for Higher tier students. You will need to register for a TES account to access this resource, this is free of charge. 05/08/2015
        E-library
        Type(s): Activities (e-library) | Algebra: quadratics, rearranging formulae and identities
        Transum: Changing the Subject
        Six increasingly demanding online exercises involving changing the subject of a formula.05/08/2015
        E-library
        Type(s): Activities (e-library) | Algebra: quadratics, rearranging formulae and identities
        Using Formulae
        Using formulae activity 21/01/2015
        E-library
        Type(s): Activities (e-library) | Algebra: quadratics, rearranging formulae and identities
        Using Formulae
        Changing the subject of a formula activity 21/01/2015
        E-library
        Type(s): Activities (e-library) | Algebra: quadratics, rearranging formulae and identities
        Using Formulae
        Changing the subject of a formula activity 21/01/2015
        E-library
        Type(s): Activities (e-library) | Algebra: quadratics, rearranging formulae and identities

        Double brackets starter / plenary activity
        Designed for use with an interactive voting system this multiple choice quiz offers practise in factorising expressions into two brackets including a couple of challenging questions suitable only for higher tier students. You will need to register for a TES account to access this resource, this is free of charge. 05/08/2015
        E-library
        Type(s): Activities (e-library) | Plenaries (e-library) | Starters (e-library) | Algebra: quadratics, rearranging formulae and identities

        Double brackets starter / plenary activity
        Designed for use with an interactive voting system this multiple choice quiz offers practise in factorising expressions into two brackets including a couple of challenging questions suitable only for higher tier students. You will need to register for a TES account to access this resource, this is free of charge. 05/08/2015
        E-library
        Type(s): Activities (e-library) | Plenaries (e-library) | Starters (e-library) | Algebra: quadratics, rearranging formulae and identities

        'Show that' - rearranging the formulae
        A differentiated worksheet in which students must rearrange expressions to give the answer provided. You will need to register for a TES account to access this resource, this is free of charge. 05/08/2015
        E-library
        Type(s): Worksheets (e-library) | Algebra: quadratics, rearranging formulae and identities
        Changing the subject of area and volume formulae
        A straightforward worksheet in which students must rearrange various formulae for area and volume - the later questions are more suitable for higher tier students. You will need to register for a TES account to access this resource, this is free of charge. 05/08/2015
        E-library
        Type(s): Worksheets (e-library) | Algebra: quadratics, rearranging formulae and identities
        Factorising into double brackets
        A differentiated worksheet in which students use the letters alongside the answers to answer the clues. The hardest questions include some quadratics of the form ax2+bx+c for an extension challenge for Higher tier students. You will need to register for a TES account to access this resource, this is free of charge. 05/08/2015
        E-library
        Type(s): Worksheets (e-library) | Algebra: quadratics, rearranging formulae and identities
        Factorising quadratics step by step worksheet
        A scaffolded worksheet which supports students in finding the numbers which will go in the brackets of the factorised expression. You will need to register for a TES account to access this resource, this is free of charge. 05/08/2015
        E-library
        Type(s): Worksheets (e-library) | Algebra: quadratics, rearranging formulae and identities
        Multiplying Negatives
        Multiplying negatives interactive worksheet21/01/2015
        E-library
        Type(s): Worksheets (e-library) | Videos (e-library) | Algebra: quadratics, rearranging formulae and identities
        Positive and Negative Numbers
        How to add and subtract positive and negative numbers interactive worksheet 21/01/2015
        E-library
        Type(s): Worksheets (e-library) | Algebra: quadratics, rearranging formulae and identities

        Multiplying Negatives
        Multiplying negatives interactive worksheet21/01/2015
        E-library
        Type(s): Worksheets (e-library) | Videos (e-library) | Algebra: quadratics, rearranging formulae and identities

        Coordinates and graphs - Lesson plan 1
        Downloadable resource in doc format. 08/04/2010
        122 KB
        Related resources: Coordinates and linear graphs | Coordinates and linear graphs (2-year route) | Foundation | Unit 2 | Coordinates and Graphs | Lesson Plans
        Formulae and algebraic argument - Formulae - Lesson plan 2
        Downloadable resource in doc format. 08/04/2010
        135 KB
        Related resources: Basic algebra | Equations | Foundation | Unit 2 | Formulae and Algebraic Argument | Lesson Plans
        Formulae and algebraic argument - Formulae - Plenary activity for lesson 2
        Downloadable resource in doc format. 05/04/2010
        105 KB
        Related resources: Basic algebra | Equations | Foundation | Unit 2 | Formulae and Algebraic Argument | Supplementary Resources
        Formulae and algebraic argument - Formulae - Worksheet 1
        Downloadable resource in doc format. 07/04/2010
        246 KB160 KB
        Related resources: Basic algebra | Equations | Foundation | Unit 2 | Formulae and Algebraic Argument | Supplementary Resources
        Formulae and algebraic argument - Formulae - Worksheet 2
        Downloadable resource in doc format. 04/04/2010
        100 KB97 KB
        Related resources: Basic algebra | Equations | Foundation | Unit 2 | Formulae and Algebraic Argument | Supplementary Resources

        Topic Tests

        8300 GCSE Foundation Expanding and Factorising Quadratics Practice Mark Scheme
        Downloadable resource in pdf format. 22/12/2022
        243 KB
        Related resources: Algebra recap and extension
        8300 GCSE Foundation Expanding and Factorising Quadratics Practice Topic Test
        Downloadable resource in pdf format. 22/12/2022
        220 KB
        Related resources: Algebra recap and extension
        8300 GCSE Foundation Writing and Rearranging Formulae Mark Scheme
        Downloadable resource in pdf format. 22/09/2022
        249 KB
        Related resources:
        8300 GCSE Foundation Writing and Rearranging Formulae Topic Test
        Downloadable resource in pdf format. 22/09/2022
        249 KB
        Related resources:
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