Year 12
Mathematics Extension 1 (New South Wales)
ME-P1: Proof by Mathematical Induction
MA-C3: Applications of Differentiation
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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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Equations of tangents and normals revisited
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Rates of change application
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Motion in a straight line An application of rates
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Motion in a straight line acceleration recap
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Concave up and Concave down Part 1: 2 useful definitions
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Concave up and Concave Down Part 2 A more useful definition
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Concavity and the second derivative
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Points of Inflection and the 2nd derivative
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The 2nd Derivative test
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Sketching Functions with the second derivative and Points of Inflection
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Introduction to Kinematics
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Applications of Integration in motion questions
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Optimisation when the function is unknown
ME-V1: Introduction to Vectors
V1.1: Introduction to Vectors
V1.2: Further Operations with Vectors
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Vectors finding the magnitude
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Vectors finding the unit vector
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Finding direction of a vector
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Defining a vector between 2 points
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Vector Revision part 1
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The dot product part 1
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The dot product part 2
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The dot product part 3
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The scalar product or dot product of a vector revisited
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Force Vector Diagrams
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Resolving Force Vectors
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Resolving forces into their components
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Resolving Forces into components part 2
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Vector midpoints
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Vectors in component form recap
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Vectors in polar form
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What’s a vector projection?
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Calculating vector projections
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Resolving a vector into components parallel and perpendicular to a second vector
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Applications of vectors displacement and velocity
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Applications of vectors displacement and velocity collisions
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Applications of vectors relative velocity
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Triangle of forces
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Inclined plane recap part 1
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Solving equilibrium questions using resolution of forces
V1.3: Projectile Motion
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Vector Functions Introduction and converting vector functions to cartesian functions
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Vector equations and finding collision points
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Vector Calculus Displacement, velocity Acceleration
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Vector Calculus Anti differentiation worked example
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Vector Calculus Differentiation worked examples
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Vector Calculus Motion in a straight line
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Vector Calculus Projectile Motion Calculating Launch Angle
ME-T3: Trigonometric Equations
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Express the sum of trigonometric functions as a single function
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Express the sum of trigonometric functions as a single function part 2
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Solving trig equations of the form sin(ax+b) = c
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Exact values of reciprocal trigonometric functions
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Solving reciprocal trig functions
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Proving Trigonometric identities
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2 more pythagorean identities
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Angle sum and difference indentities
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Angle sum and difference identities part 2
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Double angle identity proofs and an example
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More proofs of trig identities
ME-C2: Further Calculus Skills
ME-C3: Applications of Calculus
C3.1: Further Area & Volumes of Solids of Revolution
C3.2: Differential Equations
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Implicit differentiation
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Solving differential equations
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Solving differential equations given in terms of f(y)
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Setting up differential equations
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Isaac Newton & My Cup of Coffee: Differential Equations Applications
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Differential equations: Mixing Problems
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Modelling Population Growth: The Logistic Equation – Differential Equations
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Verifying solutions to differential equations
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Separable differential equations
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Displacement velocity acceleration etc
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Velocity in terms of displacement Acceleration in terms of velocity
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Other Expressions for acceleration part 1
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Other Expressions for acceleration part 2
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Simple Harmonic Motion
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Resultant forces
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Momentum
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Newton’s laws of motion
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Newtons laws of motion examples
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Calculating the Normal Reaction Force in an Elevator
ME-S1: The Binomial Distribution
S1.1: Bernoulli & Binomial Distributions
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Bernoulli sequence
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Binomial distribution introduction
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Developing Binomial Distribution Intuition
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The binomial Probability Formula
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Binomial Probability Distribution formula Worked Example
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Binomial Probability formula at most and at least
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Binomial Distribution on the Casio FX CG50AU
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Binomial Probability Conditional Probability
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Binomial distribution expected value variance and standard deviation
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Construct a Binomial Distribution Graph
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Binomial Distribution finding a sample size
S1.2: Normal Approximation for the Sample Proportion
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Why is sample proportion interesting and important
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Sampling from a small population
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Sampling from a large population
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Sample proportion mean and standard deviation
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Approximating the distribution of sample proportions using the normal distribution
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Determining required Sample size for a given Margin of error
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Binomial Approximation to the normal and sample proportion, one question two ways