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VCE Mathematical Methods - Units 1 and 2
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Appendices
Appendix A - Using the Casio ClassPad II in senior mathematics
A.1 - The Main Menu
Applying values to pronumerals
Combine
Define
Expand
Factor
rFactor
Simplify
Solve
A.2 - Graphical representation in the Main Menu
G-Solve
Resizing the graph screen
Restricting the domain
Sketch
A.3 - Graphs & Tables
G-Solve
Generate a table of values for a specified rule
Resizing the graph screen
Restricting the domain
Sketch
A.4 - Conics
Appendix B - Using the TI N-Spire in senior mathematics
Appendix C - Matrices
Online Textbook
Section 1 - Mathematical Skills
1A - Organising numbers
1B - Rational Numbers
1C - Irrational Numbers
1D - Rules of algebra
1E - Index Laws
1F - Binomial expansion
1G - Substitution into a formula
1H - Transposing basic equations
Section 1 - Resources
Section 10 - Rates of Change
10A - Analysing relationships
10B - Constant rates of change
10C - Average rate of change
10D - Instantaneous rate of change
10E - Rates of particle motion
Section 10 - Resources
Section 11 - Differential Calculus
11A - An introduction to limits
11B - Differentiation from first principles
11C - Conditions for differentiability
11D - Differentiation of polynomial functions
11E - Differentiation of power functions
11F - Differentiation of other functions
11G - Nature of stationary points
11H - Relationship between functions and derivatives
11H - Relationship between functions and derivatives
11I - Applications of differentiation
11I.1 - Tangents and normals
11I.2 - Optimisation
11I.3 - Kinematics
11I.3 - Kinematics
11J - Continuity and smoothness
Section 11 - Resources
Section 12 - Integral Calculus
12A - Introduction to antidifferentiation
12B - Integration of rational powers
12C - Definite integrals
12D - Area under a curve
Section 12 - Resources
Section 13 - Probability
13A - Introduction to probability
13B - Representing sample spaces
13B.1 - Venn Diagrams
13B.2 - Tables and Grids
13B.3 - Tree Diagrams
13B.4 - Karnaugh Maps
13C - The addition rule of probability
13D - Conditional probability
13E - The law of total probability
13F - Independent events
13G - Simulations with probability
Section 13 - Resources
Section 14 - Methods for counting
14A - Addition and multiplication principles
14B - Permutations and probability
14C - Combinations and probability
Section 14 - Resources
Section 15 - Further Probability and Statistics
15A - Discrete random variables
15B - Sampling without replacement
15C - Sampling with replacement
Section 2 - Coordinate Geometry
2A - Review of the Cartesian plane
2B - Transformations: Dr.T
2C - Matrix representations
2D - Combining transformations
2E - The midpoint of a line
2F - The distance between two points
2G - Angles of straight lines
Section 2 - Resources
Section 2 - Linear functions
2A - Linear equations
Section 3 - Linear Functions
3A - Linear equations
3B - Simultaneous linear equations
3C - Linear inequations
3D - The gradient
3E - Sketching linear graphs
3F - Finding the equation of a straight line
Section 3 - Resources
Section 4 - Quadratic Functions
4A - Expanding quadratics
4B - Factorising quadratic trinomials
4C - Solving quadratic equations
4D - The general quadratic formula
4E - The discriminant
4F - Completing the square
4G - Graphing quadratic functions
4H - Solving quadratic simultaneous equations
4I - Solving quadratic inequations
4J - Determining the rule of a quadratic
4K - Applications and modelling with quadratics
Section 4 - Resources
Section 5 - Polynomial Functions
5A - Introduction to polynomials
5B - Identifying factors of a polynomial
5C - Methods for solving polynomial equations
5C.1 - Long division
5C.2 - Synthetic division
5D - Families of cubics
5E - Families of quartics
5F - Other polynomial functions
5G - Solving cubic inequalities
5H - Determining the rule of a polynomial
5I - The bisection method
5J - Applications of polynomial functions
Section 5 - Resources
Section 6 - Power Functions
6A - Square-root function
6B - Cubed root function
6C - Hyperbola function
6D - Truncus function
6E - Circles and semicircles
Section 6 - Resources
Section 7 - Functions and Relations
7A - Types of functions
7B - Domain and range
7C - Piecewise functions
7D - Composite functions
7E - Inverse functions
7F - Transformations
7F.1 - Translations
7F.2 - Dilations and reflections
7F.3 - Transformations using Dr.T
7I - Transformations using matrices
7J - Functions not defined by a rule
Section 7 - Resources
Section 8 - Exponential and Logarithmic Functions
8A - Index laws
8B - Rational indices
8C - The exponential function
8D - Transformations of the exponential function
8E - Logarithmic laws and properties
8F - The logarithmic function
8G - Transformations of the logarithmic function
8H - Exponentials and logarithms are inverses
8I - Applications of exponentials and logarithms
Section 8 - Resources
Section 9 - Circular Functions
9A - Degrees and radians
9B - The unit circle
9C - The sine function
9D - The cosine function
9E - Transformations of sine and cosine functions
9F - The tangent function
9G - Exact values
9H - The Pythagorean identity
9I - Special triangles
9J - Solving trigonometric equations
9K - Graphing trigonometric functions
9L - Applications of circular functions
Section 9 - Resources
VCE Mathematical Methods - Units 1 and 2
1C - Irrational Numbers
What is an irrational number?
Operations involving rational numbers
Simplifying surds
Rationalising the denominator
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