AQA · GCSE

Your journey to excellence inFurther Mathematics

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Fractions, Decimals, Percentages

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Ratio and Proportion

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Order of Operations

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Product Rule for Counting

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Manipulating Surds

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Rationalising the Denominator

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Basic Algebraic Processes

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Functions and Notation

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Domain and Range of Functions

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Composite Functions

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Inverse Functions

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Expanding Brackets

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Binomial Expansion

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Factorising Expressions

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Algebraic Fractions

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Manipulating Formulae

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Factor Theorem

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Completing the Square

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Sketching Functions

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Solving Quadratic Equations

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Simultaneous Equations

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Linear Equations in Three Unknowns

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Quadratic Inequalities

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Index Laws

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Algebraic Proof

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Linear Sequences

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Quadratic Sequences

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Gradient of a Line

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Parallel and Perpendicular Lines

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Distance Between Two Points

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Midpoint and Ratio

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Equation of a Straight Line

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Circle Equation: Centre at Origin

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Circle Equation: General Form

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Tangents to Circles

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Gradient Function

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Differentiation of Polynomials

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Tangent and Normal Equations

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Increasing and Decreasing Functions

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Second Derivative

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Maxima and Minima Points

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Applications of Calculus

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Sketching Curves Using Calculus

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Matrix Multiplication

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Identity Matrix

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Transformations of Unit Square

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Combination of Transformations

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Perimeter and Area

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Surface Area and Volume

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Circle Theorems

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Geometric Proofs

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Sine and Cosine Rules

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Pythagoras' Theorem

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2D and 3D Trigonometry

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Trigonometric Graphs

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Special Triangles

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Trigonometric Identities

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Solving Trigonometric Equations

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