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Stage 1 & 2 -Mathematics (Methods & Specialist)
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Theorems
Mathematical Methods
Methods LAP & Schedule
Differential Calculus
Functions
Polynomial Functions
Exponential Functions
Logarithmic Functions (& Log Laws)
Trigonometric Functions
Differentiate with first principles
Differentiate using rules
Derivative of constants, Polynomials, Addition rule
The Chain Rule
The Product Rule
The Quotient Rule
Derivatives of Exponential Functions
Derivatives of Logarithmic Functions
Derivatives of Trigonometric Functions
The Second Derivative
Applications of Differential Calculus
The equation of a tangent
Increasing and Decreasing Functions
Stationary Points
Inflections & Shape
Kinematics
Rates of Change
Optimisation
Integration (or Integral Calculus)
The area under a curve
The definite integral
Antidifferentiation
The Fundamental Theorem of Calculus
Integration
Rules of integration
Integrating f(ax+b)
Definite integrals
Applications of integratation
The area under a curve.
The area between two functions
Kinematics (integration)
Problem Solving by integration
Discrete Random Variables
Discrete probability distributions
Expected value (and fair games)
Variance and Standard Deviation
Properties of aX+b
The Bernoulli distribution
The binomial Distribution
Continuous Random Varaibles
Continuous Random Variable (review from Yr11))
Sampling and Confidence Intervals
Sampling distributions
Distributions of sample means
Central Limit Theorem
Confidence intervals for means
Sample proportions
Confidence intervals for proportions
Study Routines
Specialist Mathemtaics
Specialist Maths LAP & Schedule
Complex Numbers
The complex plane (or Argand Plane)
Modulus and Argument
Polar Form
Euler's Form
De Moivre's Theorem
Roots of Complex Numbers
Polynomials
Operations with Polynomials
Zeros, Roots and Factors
Polynomial Equality
Polynomial Division
The Remainder Theorem
The Factor Theorem
The Fundamental Theorem of Algebra
Graphing Real Polynomials
Polynomial Equations
Functions and Sketching graphs
Composite functions
Inverse Functions
Reciprocal functions and reciprocals of other functions
Rational functions
Absolute Value Functions
Vectors
Vectors in space
Operations with vectors in space
Vector algebra
The vector between two points
Parallelism (3D)
The scalar product of two vectors
The angle between two vectors (3D)
Proof using vector geometry (3D)
The vector product of two vectors
Vector Applications
Area (3D vectors)
Lines in 2 and 3 dimensions
The angle between two lines
Constant velocity problems
The shortest distance from a point to a line
Intersecting lines
Relationships between lines
Planes
Angles in space
Solving 3x3 linear systems
Intersecting planes
Rates of Change & Differential Equations
Implicit Differentiation
Related Rates
Differential Equations
differential equations of the form dy/dx=f(x)
Separable Differential Equations
Slope fields
Problem Solving (Differential Equations)
Vector Calculus
Parametric Equations (vector calculus)
Pairs of uniformly varying quantities
Pairs of non-uniformly varying quantities
Bezier Curves
Trigonometric parameterisation
Arc length of parametric curves
Pre-Methods
Semester 1 - LAP & Schedule
Topic 1 - Functions & graphs
Subtopic 1.1: Lines and linear relationships
Subtopic 1.2: Inverse proportion
Subtopic 1.3: Relations
Subtopic 1.4: Functions
Topic 2 - Polynomials
2.1 - Quadratic relationships
2.2 - Cubic and quartic polynomials
Pre-Specialist
Semester 1 - LAP & Schedule
Arithmetic and Geometric Sequence and Series
Arithmetic sequences and series
Geometric sequences and series
Geometry (Topic 8)
8.1 Circle Properties
8.2 The Nature of Proof
Geometry Booklet
Vectors in 2D
Vectors and scalars
Geometric operations with vectors
Vectors in the plane
The magnitude of a vector
Operations with Plane Vectors
The Vector Between Two Points
Parallelism
Problems involving vector operations
The scalar product of two vectors
The angle between two vectors
Vector Projection
Proof using vector geometry
Further Trigonometry
The general tangent function
General trigonometric functions
Reciprocal trigonometric functions
Solving Trigonometric equations
Modelling using trigonometric functions
Trigonometric relationships
Double angle identities
Angle sum and difference identities
Trigonometric equations in quadratic form
Matrices
Matrix Structure
Matrix operations and definitions
Matrix Multiplication
The inverse of a 2x2 matrix
Simultaneous linear equations (Matrices)
Translations and lines in 2D (Matrices)
Linear Transformations (Matrices)
Rotations about the origin
Reflections (Matrices)
Dilations (Matrices)
Compositions of transformations
The inverse of a linear transformation
Solving using Technology
Mathematical Investigations
Haese Textbook Links
Glossary
Prior Knowledge
Stage 1 & 2 -Mathematics (Methods & Specialist)
Integrating f(ax+b)
Integrating f(ax+b)
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