Session Length:     2 hours per week

Cost:    \$60 per session (includes ALL resources, notes, examples, tests. 10% discount if you pay for a full term in advance)

Skills Test:
0.4 hours

Teaching:
1.6 hours

Resources Provided:
Weekly notes and examples, weekly questions, practice harder test questions, access to worked solutions (by hand and video), exam style questions.

Calculator:
All aspects of the course taught on CASIO Classpad and TI Inspire CAS

The jump from Year 10 Mathematics to the Unit 1/2 Maths Methods course is definitely the area where the largest amount of new content is introduced in secondary school (excluding Specialist Maths Unit 1/2). Many new topics are introduced and students can drop the subject as they feel that it is too much! However, it is very similar to the Unit 3/4 course, so if they can hang in, they can still achieve great results. It's extremely important to know how to use the CAS, which I focus on and run through with every example (many teachers in schools seem to skip over this!).. It begins with a 20-25 minute test on the previous weeks content, then teaching of the new course content in sequence and is finished off with any questions students might have in regards to SAC preparation questions etc.

The following content is taught throughout the course:

#### Reviewing linear equations

- Linear Equations
- Constructing Linear Equations
- Simultaneous Equations
- Constructing simultaneous Linear Equations
- Solving Linear inequalities
- Using and transposing formulas

#### Coordinate Geometry and linear relations

- Distance and midpoint
- The gradient of a straight line
- The equation of a straight line
- Graphing straight lines
- Parallel and perpendicular lines
- Families of straight lines
- Linear models
- Simultaneous linear equations

- Expanding and factorising
- Solving and graphing
- Completing the square and turning point form
- Solving inequalities and the general quadratic formula
- The discriminant
- Solving simultaneous and linear quadratic equations

#### A Gallery of graphs

- Rectangular hyperbolas and the truncus
- The graph of the square root of x
- Graphing circles and determining rules

#### Functions and Relations

- Set notation
- Types of functions and implied domains
- One to one functions
- Piece wise defined functions
- Applying function notation
- Inverse functions
- Applications of Functions

#### Polynomial Functions

- The language of polynomials
- Division and factorisation of polynomials
- The general cubic function and solving cubic equations
- Graphs of cubics in different forms and solving cubic inequalities
- Quartics and other polynomial functions
- Applications of polynomial functions

#### Transformations

- Translations
- Dilations & Reflections
- Combinations of transformations
- Determining transformations
- Using transformations to sketch graphs
- Determining the rule for a function from it's graph
- Transformations of graphs using matrices

#### Probability

- Sample spaces and estimating probabilities
- Multi stage events and combining events
- Probability tables and conditional probability
- Independent events

#### Counting Methods

- Arrangements and selections
- Applications to probability
- Pascal's triangle and the binomial theorem

#### Discrete probability distributions

- Discrete random variables
- Sampling without replacement
- Sampling with replacement (the binomial distribution)

#### Exponential and Logarithmic functions

- Index laws and rational indices
- Graphs of exponential functions
- Solving exponential equations and inequalities
- Logarithms
- Graphing logarithmic functions
- Using logarithms to solve exponential equations and inequalities
- Exponential models and applications

#### Circular Functions

- Defining sine, cosine and tangent
- Symmetry properties and the pythagorean identity
- Graphs of sine, cosine and tangent
- Solving trigonometric equations
- Sketching trigonometric equations with transformations
- Determining rules for graphs of circular functions
- General solutions of trigonometric equations
- Applications of circular functions

#### Rates of change

- Recognising relationships and constant rates of change
- Average and instantaneous rates of change
- Position and average velocity

#### Differentiation

- First principles
- Differentiating functions of the form x^n, where n is negative
- Differentiating rational functions
- Graphing the derivative function
- The chain, product and quotient rules
- Antidifferentiation of polynomial functions
- Limits and Continuity
- When is a function differentiable?

#### Applications of Differentiation

- Tangents and Normals
- Rates of change
- Stationary points
- Types of stationary points
- Absolute minimum and maximum values
- Applications of differentiation and antidifferentiation to kinematics
- Families of functions and transformations
- Newton's method

#### Further differentiation and antidifferentiation

- The chain rule
- Differentiating rational powers
- Antidifferentiating rational powers
- The second derivatives
- Sketching graphs

#### Integration

- Estimating the area under a graph
- Antidifferentiation: indefinite integrals
- Finding the exact area under a curve