Year 11
Mathematics Advanced (New South Wales)
MA-F1: Working With Functions
F1.1: Algebraic Techniques
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Introduction to index laws and using them to simplify algebraic expressions
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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 Law 8 Fractional Indices – moving from index form to radical form
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Index Laws equating bases to solve for unknown exponent or power part 1
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Index Laws equating bases to solve for unknown exponent or power part 2
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Index Laws Negative bases
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Index Laws Fractional indices
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Harder Indicial Equations
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Solving Indicial equations
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Indicial equations super hard quadratic action
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Indicial equations The hardest one
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Surds what is a surd
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Simplifying surds
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Simplifying Surds
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Surds simplifying algebraic surds
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Surds adding and subtracting surds
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Adding and subtracting surds
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Multiplying surds
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Multiplying surds and the distributive law
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Surds square numbers
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Surds dividing
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Dividing Surds
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Solving Quadratics 3 ways
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The quadratic formula and the discriminant
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Completing the square part 1
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Completing the square part 2
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Solving by completing the square
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Algebraic fractions cancelling common factors
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Algebraic fractions multiplying and dividing
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Algebraic fractions adding and subtracting
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Algebraic fractions adding and subtracting part 2
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Algebraic fractions adding and subtracting part 3
F1.2: Introduction to Functions
F1.3: Linear, Quadratic and Cubic Functions
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Find x and y values from a graph
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Plotting Linear graphs
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Equations of horizontal and vertical lines
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The equation of a line y = mx + c
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Determining the rule of a linear graph
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Anatomy of a linear graph
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Finding the gradient of a line revision
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Parallel lines and their gradients
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Perpendicular lines and their gradients
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3 forms of the quadratic equation
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The quadratic formula and the discriminant
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solving simultaneous equations using quadratic and linear graphs
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Modelling and problem solving with quadratics
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Cubics quartics and greater polynomials in Turning Point Form
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Factor form of Quadratics cubics and Quartics
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Factorise solve and sketch a cubic
F1.4: Further Functions and Relations
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Factor form of Quadratics cubics and Quartics
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Cubics quartics and greater polynomials in Turning Point Form
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Finding a linear factor of a polynomial
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Intersecting Functions
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Direct and Indirect Proportion
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Equations of hyperbola and sketching
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Sketching Hyperbolas and why there’s an asymptote
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Finding equation of reciprocal function from sketch
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The modulus or absolute value function introduction
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The modulus or absolute value solving equations
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Absolute Value Functions
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Sketch Absolute Value Functions with a vertical shift
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Sketching an absolute value function worked example
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Reflecting Functions in the y axis using absolute value 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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Functions transformations f(ax)
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Sketching circles and finding equations of circles
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Equation of a circle sketching and finding coordinates
MA-T1: Trigonometry And Measure of Angles
T1.1: Trigonometry
T1.2: Radians
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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
MA-T2: Trigonometric Functions and Identities
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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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Solving and simplifying using trig identities
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Sketching f(x) = tan(x) and why it looks like that.
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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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Reciprocals of Trigonometric Functions
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Complementary Trigonometric Relationships
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Exact values of reciprocal trigonometric functions
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Solving reciprocal trig functions
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The pythagorean Identity and reciprocal trigonometric functions
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Proving Trigonometric identities
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2 more pythagorean identities
MA-C1: Introduction to Differentiation
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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
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Derivatives of polynomials, negative and fractional powers by rule
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Composite functions and the chain rule
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The chain rule the fast way
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The product rule
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The quotient rule
MA-E1: Logarithms and Exponentials
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Log laws as fast as possible
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Logs 1 Intro to Logarithms
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Logs 2 Log Law 1
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Logs 3 Log Law 2
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Logs 4 Log Law 3
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Logs 5 Log Law 4
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Logs 6 Log Law 5
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Logs 7 Log Law 6
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Logs 8 solving exponentials
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Solving Indicial equations using logarithms
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Logs 9 Solving logarithmic equations
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Solving Log equations examples
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Solving equations involving natural log
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Solving logarithmic equations with an unknown power
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Solving logarithmic equations with an unknown base
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Logs 10 Solving logarithmic equations part 2
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Logarithms 12 Simplifying Log equations
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Logarithmic functions Basic shape
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Logarithmic functions Sketching
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Finding equations of log functions
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Logarithmic functions 3 Find equation from a sketch
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Logarithmic Functions 4 Regression analysis
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Exponential and logarithmic modelling
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Solving Indicial equations
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Harder Indicial Equations
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Indicial equations super hard quadratic action
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Indicial equations The hardest one
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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 2 Sketching
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Exponential functions 3 Finding equation from a sketch
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Exponential Model and Applications
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Derivatives of Exponential, Logarithmic and Trigonmetric functions
MA-S1: Probability & Discrete Probability Distributions
S1.1: Probability and Venn diagrams
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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 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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Pascal’s Triangle and Selections
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Binomial expansion using pascal’s triangle
S1.2: Discrete probability distributions
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Discrete Random Variables: Introduction and Examples
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Discrete Random Variables Uniform Distribution
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Discrete Random Variable Worked Example
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The Geometric Probability Distribution
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Expected Value of discrete random distributions
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Discrete random distributions Expected value challenging but important
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Variance and Standard Deviation: Discrete Random Variables
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Properties of Expected Value: aE(X)+b = E(aX + b)
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The alternative Variance formula Proof
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Alternative Variance Formula Worked Example