Unit 2
Mathematical Methods (Western Australia)
Topic 1: Functions and Graphs
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Index Law 1 – multiplication of indices
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Index Law 2 – dividing indices
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Index Law 3 – raising to the power of zero
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Index Law 4 – Raising a power to another power
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Index Law 5 – worked examples using the fifth index law
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Index Law 6 – expanding brackets around a fraction raised to a power
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Index law 7 Negative Indices – converting Negative indices into positive indices using fractions
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Index Laws Fractional indices
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Index Laws Negative bases
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Index Laws simplifying by decomposing
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Scientific notation Converting to scientific notation
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Scientific Notation Convert scientific notation to decimal
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Scientific notation Multiplying and dividing
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Exponential Functions Basic shape and Translations
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Exponential Functions Dilations
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Exponential functions 2 Sketching
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Exponential functions sketching part 2
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Exponential functions 3 Finding equation from a sketch
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Exponential Model and Applications
Topic 2: Arithmetic and Geometric Sequences and Series
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Sequence Notation
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Recurrence Relations
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Using a recurrence relation
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Defining a sequence in terms of n
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Applications of recurrence relations
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Applications of recurrence relations non arithmetic
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Using a calculator with recurrence relations
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Arithmetic sequence formula
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Rearranging the arithmetic sequence formula
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Arithmetic sequences using simultaneous equations
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Arithmetic sequences and series
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Simultaneous equations using arithmetic series and sequences
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Application of the arithmetic sequence
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Simple Interest using arithmetic sequences
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The Middle Term as the arithmetic mean in an arithmetic sequence
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Introduction to the Sum of an arithmetic series
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Finding the number of terms in an arithmetic sequence
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Arithmetic series Finding the number of terms that sum to a given number
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Application of arithmetic series
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Geometric sequences and the recursive definition
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Geometric Sequence formula
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Geometric sequences finding the common ratio
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Geometric Sequences finding the value of n
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Geometric Sequences and simultaneous equations
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Geometric Sequences Geometric mean
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Compound interest as a geometric sequence
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Geometric series formula proof and example
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Geometric series find the value of n
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Regular deposits as a geometric series
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Geometric Series Sum to Infinity and Zeno’s Paradox
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Geometric series sum to infinity application
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Geometric Series Sum to infinity writing recurring decimals as fractions
Topic 3: Introduction to Differential Calculus
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Variable and constant rates of change
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Average rates of change
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Intro to instantaneous rates of change
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The Gradient function
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Differentiation from first principles
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Differentiating polynomials by rule
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Finding Stationary points
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Nature of Stationary points
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Optimisation when the function is unknown
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Introduction to Kinematics
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Finding the equation of a tangent
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Finding the equation of a normal