Algebra

    AQA
    GCSE

    Algebra serves as the fundamental language of mathematics, utilizing symbols to represent numbers, variables, and relationships. It encompasses the manipulation of expressions, the solution of linear and quadratic equations, inequalities, and the analysis of sequences and functions. This topic bridges arithmetic computation with abstract reasoning, enabling the modeling of real-world scenarios and the generalization of numerical patterns.

    19
    Objectives
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    Exam Tips
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    Pitfalls
    5
    Key Terms
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    Mark Points

    Learning Objectives

    What you need to know and understand

    • Use and interpret algebraic notation
    • Substitute numerical values into formulae and expressions, including scientific formulae
    • Understand and use the concepts and vocabulary of expressions, equations, formulae, inequalities, terms and factors
    • Simplify and manipulate algebraic expressions by collecting like terms, multiplying a single term over a bracket, taking out common factors, and using laws of indices
    • Expand products of two or more binomials
    • Factorising quadratic expressions of the form x^2 + bx + c
    • Factorising quadratic expressions of the form ax^2 + bx + c
    • Simplify and manipulate algebraic expressions involving surds and algebraic fractions
    • Rearrange formulae to change the subject
    • Know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent
    • Interpret simple expressions as functions with inputs and outputs; interpret inverse and composite functions
    • Work with coordinates in all four quadrants
    • Plot graphs of equations that correspond to straight-line graphs; use y = mx + c to identify parallel and perpendicular lines
    • Identify and interpret gradients and intercepts of linear functions graphically and algebraically
    • Identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square
    • Recognise, sketch and interpret graphs of linear, quadratic, cubic, reciprocal, exponential and trigonometric functions
    • Sketch translations and reflections of a given function
    • Plot and interpret graphs in real contexts, to find approximate solutions to problems such as simple kinematic problems
    • Calculate or estimate gradients of graphs and areas under graphs, and interpret results

    Key Terminology

    Essential terms to know

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