Unit 1
Mathematical Methods (Queensland)
Topic 1: Surds and quadratic functions
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Surds: What they are and why we need them
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Proof that the square root is equal to the power of 1/2
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Simplifying surds
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Adding and Subtracting surds by grouping like terms
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Multiplying surds
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Surds and the distributive law
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Dividing Surds
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Surds Rationalising denominators
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Rationalising denominators using conjugates
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Infinite nested radicals
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Anatomy of a quadratic graph
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Solving Quadratics 3 ways
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3 forms of the quadratic equation
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Review of sketching quadratics two ways
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The quadratic formula and the discriminant
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Modelling and problem solving with quadratics
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solving simultaneous equations using quadratic and linear graphs
Topic 2: Binomial expansion and cubic functions
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Pascal’s Triangle and Selections
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Binomial expansion using pascal’s triangle
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Finding a linear factor of a polynomial
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Factorise solve and sketch a cubic
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Cubics in “Turning Point” Form: (But it’s not a turning point)
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Graphing and finding key points on the TI Nspire
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Determining intersections of functions graphically on the TI Nspire
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Sketching a graph on the TI Nspire
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Solving simultaneous equations using LinSolve TI Nspire
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Solving polynomials on the TI Nspire
Topic 3: Functions and relations
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Set Notation: Introduction
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Interval Notation and Number Lines
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Relations Domain and Range
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Relations, Functions and the vertical line test
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domain and range notation
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Domain and Range of functions and relations
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Graphing on calculator using restricted domains
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What’s a function
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Function notation
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Function Notation: Better ways of representing functions
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Piecewise Functions
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Function Transformations intro
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Functions Transformation fx+a
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Function transformation f(x+a)
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Function transformation afx
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Functions transformations f(ax)
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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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Sketching Hyperbolas and why there’s an asymptote
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Sketching circles and finding equations of circles
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The square root function
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Intersecting Functions
Topic 4: Trigonometric functions
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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 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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Finding exact trig ratios involving negative angles
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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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Pythagorean identity
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Pythagorean identity rearrangement
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Using Pythagorean Identities Part 1
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Solving trig identity equations using quadratics
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Solving trig identity equations using quadratics part 2
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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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Revision of radians and the unit circle
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Solving and simplifying using trig identities
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Solving Trig equations The Tricky 3 Quantum of Quadratics
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Solving Trig equations The Tricky 3 Square or Die
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Solving Trig equations The Tricky 3 Domain Domination
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Sketching f(x) = tan(x) and why it looks like that.
Topic 5: Probability
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The Language of Sets
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Theoretical Probability with sets
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All Probabilities sum to 1
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Venn Diagrams Intro
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Venn Diagrams simple Probabilities
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Venn Diagrams the complement
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Venn Diagrams the intersection
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Venn Diagrams The union
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Venn Diagrams: Calculating Probabilities including intersections, unions and complements
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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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Probability with two way tables
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Two way tables and conditional probability
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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