Units 3 & 4 Specialist Maths
These lessons are for the 2016 - 2022 Study Design
These lessons are for the 2016 - 2022 Study Design
Functions & Graphs
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Circular Functions
Circles, Ellipses, Hyperbolae
Reciprocal Circular Functions
Note: There are a couple of arithmetic errors in an example. The process is correct.
Inverse Circular Functions
Graphing Rational Functions
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Modulus Function
Parametric Equations
Compound and Double Angle Formulae
Note: There is a domain error in the last part of the last example. The process is correct.
Solving Equations with Sec, Cosec, Cot
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Algebra and Complex Numbers
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Definitions and Properties
Polar Form (modulus-argument)
Solving quadratic equations over the Complex Field
Solving Equations using De Moivre’s theorem
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Modulus, Conjugate & Division
Operations in Polar form (modulus–argument)
Solving polynomial equations over the Complex Field
Sketching subsets of the complex plane
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Differential Calculus
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Chain, Product & Quotient Rules
Derivative of Inverse Circular Functions
Points of Inflection
Rational Functions
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Derivative of x = f(y)
Second Derivatives
Related Rates
Implicit Differentiation
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Integral Calculus
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Antidifferentiation
Integration by Substitution
Integration using Trigonometric Identities
Integration Review
Area Between Curves
There is an error in the third example for the integration of sin(2x). It should be -1/2cos(2x). It gets fixed in the end.
Volume of Revolution
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Antiderivatives of Inverse Circular Functions
Definite Integrals by Substitution
Integration using Partial Fractions
Fundamental Theorem of Calculus (area)
Integration with CAS
Lengths of Curves
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Differential Equations
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Verifying Solutions
Function of the Dependent Variable
Separation of Variables
Using a Definite Integral
Slope (direction) field for a differential equation
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Function of the Independent Variable
Applications
Differential Equations with related rates
Euler's Method
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Kinematics
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Position, Velocity & Acceleration
Velocity-time graphs
Expressions for acceleration
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Constant Acceleration Formula
D.E.'s of the form v = f(x) and a = f(v)
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Vectors & Vector Calculus
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Vector Operations & Resolution of Vectors
The notes referred to in the above video are below
Vector Projections (components, resolutes)
Geometric Proofs using Vectors
Vector calculus
Velocity and acceleration for motion along a curve |
Scalar (dot) Product of Vectors
Collinearity
Vector functions - Position vectors as function of time
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Dynamics (Mechanics)
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Force
Resolution of Forces, Inclined Plane
Variable Force
Vector Functions
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Newton's Second Law
Connected Particles
Equilibrium
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Probability and Statistics
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Linear Combinations of Random Variables and Independent Normal Random Variables
The Central Limit Theorem
Hypothesis Testing for the Mean
Errors in Hypothesis Testing
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The Distribution of the Sample Mean of a normally distributed random variable
Confidence Intervals for the Population Mean
One-Tail and Two-Tail tests
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