Algebra

    AQA
    GCSE

    Algebra in Further Mathematics extends the boundaries of the real number system and standard algebraic manipulation encountered in A-Level Mathematics. It introduces abstract structures such as Complex Numbers and Matrices, providing powerful tools for solving polynomial equations and analyzing linear transformations. This topic also formalizes mathematical logic through Proof by Induction and explores the relationships between roots and coefficients, serving as the foundational language for advanced pure mathematics and engineering applications.

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    Objectives
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    Exam Tips
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    Pitfalls
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    Key Terms
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    Mark Points

    Learning Objectives

    What you need to know and understand

    • The basic processes of algebra including use of the associative, commutative and distributive laws
    • Definition of a function; Domain and range of a function; Composite functions; Inverse functions
    • Use of the factor theorem for rational values of the variable for polynomials
    • Prove (n + 5)^2 - (n + 3)^2 is divisible by 4 for any integer value of n

    Key Terminology

    Essential terms to know

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