Unit 1
Mathematical Methods (Western Australia)
Topic 1: Functions and Graphs
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Finding Midpoints on a cartesian plane
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Finding a point given a point and a midpoint
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The distance formula
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Parallel lines and their gradients
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Perpendicular lines and their gradients
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Relations Domain and Range
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What’s a function
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Function notation
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Graphing on calculator using restricted domains
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Function Transformations intro
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Function transformation afx
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Function transformation f(x+a)
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Functions Transformation fx+a
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Functions transformations f(ax)
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domain and range notation
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Anatomy of a quadratic graph
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Solving Quadratics 3 ways
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Review of sketching quadratics two ways
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Modelling and problem solving with quadratics
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solving simultaneous equations using quadratic and linear graphs
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Direct vs inverse proportion
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Equations of hyperbola and sketching
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Finding equation of reciprocal function from sketch
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Equation of a circle sketching and finding coordinates
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Sketching a circle on a cartesian plane
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Equation of a circle finding intersection using simultaneous equations
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Finding a linear factor of a polynomial
Topic 2: Trigonometric Functions
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Trig Ratios fast
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The Sine Rule Fast
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The sine rule ambiguous case
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The cosine rule
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Area of a triangle using trigonometry
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True Bearings
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Bearings and Trigonometry an example
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How to Draw the Diagrams for Trig Applications Questions (Bearings and Elevation/Depression
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Draw in 3D
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Introduction to Radians
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Converting Radians to Degrees and Degrees to Radians
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Radians quick angles
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Standard triangles
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The Unit Circle
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The Unit Circle The Tan Ratio
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The Unit Circle and Symmetry
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The unit circle CAST and why CAST works
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Finding exact trig ratios involving negative angles
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Finding exact values of trig ratios around the unit circle
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The Unit Circle Finding exact values of negative trig ratios
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The unit circle Boundary angles
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The unit circle solving unknown angles
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Solving Simple Trig Equations Worksheet (worksheet in Description)
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The unit circle solving unknowns in trig equations
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Sketching SinX and CosX
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Sketching y = AsinX and AcosX
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Sketching y = AsinX +D and AcosX + D
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Sketching y = AsinBx + D or y = AcosBx +D
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Sketching y = AsinB(x+C)+D
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Finding the equation of a periodic function from a graph or sketch
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Complementary trig functions
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Trig Addition identities part 1
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Trig Addition Identities Part 2
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Trig Addition Identities Part 3
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Trig Identities part 4
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Revision of radians and the unit circle
Topic 3: Counting and Probability
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Pascal’s Triangle and Selections
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Binomial expansion using pascal’s triangle
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Factorials!
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Combinations
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The Language of Sets
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Basic Set Theory
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The inclusion exclusion principle for 2 and 3 sets
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Theoretical Probability with sets
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All Probabilities sum to 1
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Venn Diagrams the complement
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Experimental probability
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simplified tree diagram
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The Addition rule of probability
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Probability Tables intro
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Conditional Probability formula
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Conditional Probability Do you watch the bachelorette
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Conditional probability rearranging the formula
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Conditional Probability and Tree Diagrams
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Independent events intro and tests
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Independent events 2
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Addition and Multiplication principles