Session Length:     2 hours per week

Cost:    \$60 per session (includes ALL resources, notes, tests and discounted if taking more than 1 course)

Skills Test:
0.4 hours

Teaching:
1.6 hours

Resources Provided:   weekly notes, weekly questions, practice SAC 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 Unit 1/2 Specialist Maths course is very intensive and a huge jump from Year 10 Mathematics (hopefully you will have been doing an advanced maths course in year 10). Some of the topics chosen may be school dependent, so I will decide what to cover in these cases based on the students. 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:

Algebra 1

- Indices and standard form
- Solving linear equations and simultaneous linear equations
- Substitution and transposition of formulas
- Algebraic fractions and Literal equations
- Using the CAS for algebra

Number systems and sets

- Set notation and sets of numbers
- The modulus function
- Surds
- Natural Numbers
- Linear Diophantine equations
- The Euclidean algorithm
- Problems involving sets

Variation

- Direct and Inverse variation
- Fitting data
- Joint and part variation

Sequences and series

- Introduction to sequences
- Arithmetic sequences and series
- Geometric sequences and series
- Zeno's paradox and infinite geometric series

Algebra 2

- Polynomial identities
- Applying quadratic equations to rate problems
- Partial Fractions
- Simultaneous equations

Principles of counting

- Basic counting methods
- Factorial notation and permutations
- Permutations with restrictions
- Permutations of like objects
- Combinations and combinations with restrictions
- Pascal's triangle
- The pigeon hole principle
- The inclusion-exclusion principle

Number and proof

- Direct proof
- Proof by contrapositive
- Equivalent and disproving statements
- Proof by induction

Geometry in the plane and proof

- Points, lines and angles
- Triangles and polygons
- Congruence and proof
- Pythagoras' theorem and ratios
- Similarity
- Areas, volumes and similarity
- The golden ratio

Circle Geometry

- Angle properties of a circle
- Tangents
- Chords in circles

Sampling and sampling distributions

- Populations and samples
- The distribution of the sample proportion
- Investigating the distribution of sample proportion and sample mean using simulation

Trigonometric ratios and applications

- Reviewing trigonometry
- The sine and cosine rule
- The area of a triangle and circle mensuration
- Angles of elevation, depression and bearings
- Problems in three dimensions
- Angles between planes and more difficult 3D problems

Further Trigonometry

- Symmetry properties
- The tangent function
- Reciprocal functions and the Pythagorean identity
- Addition formulas and double angle formulas
- Simplifying a cos(x) + b sin(x)

Graphing Techniques

- Reciprocal functions
- Locus of points
- Parabolas, ellipses and hyperbolas
- Parametric equations
- Polar coordinates/br> - Graphing using polar coordinates

Complex Numbers

- Starting to build complex numbers
- Multiplication and division of Complex Numbers
- Argand diagrams
- Solving equations of Complex Numbers
- Polar form of a complex number

Matrices

- Matrix notation
- Addition, subtraction and multiplying by a scalar
- Multiplying matrices
- Identities, inverses and determinants for 2x2 matrices
- Solving simultaneous equations using matrices

Vectors

- Introduction to vectors
- Resolution of a vector into rectangular components
- Scalar product of vectors
- Vector projections
- Geometric proofs
- Vectors in three dimensions

Kinematics

- Position, velocity and acceleration
- Applications of antidifferentiation to kinematics
- Constant Acceleration
- Velocity Time Graphs

Statics of a particle

- Force and triangles of forces
- Resolution of forces

Transformations of the plane

- Linear and geometric transformations
- Rotations and general reflections
- Compositions of transformations
- Inverse transformations
- Transformations of straight lines and other graphs
- Area and determinant
- General transformations