# Accreditation of VCE Specialist Mathematics Units 1 and 2

These units have been designed and published for complying Victorian Certificate of Education 1 January 2016 – 31 December 2018 and implementation of this course commences in January 2018.

VCE Specialist Mathematics Units 1 and 2 comprise a combination of prescribed and selected non-calculus based topics and provide courses of study for students interested in advanced study of mathematics, with a focus on mathematical structure and reasoning. They incorporate topics that, in conjunction with VCE Mathematical Methods Units 1 and 2, provide preparation for this subject and cover assumed knowledge and skills for those units.

#### Course Materials

Lessons

#### Number Systems: Surds

- Simplifying Surds
- Completing Surds
- Addition and Subtraction of Surds
- Multiplication and Division of Surds
- Multiplication of Surds
- Division with Surds
- Expansion Surds
- Binomial Products with Surds
- Square of Binomials with Surds
- Expansion and Simplify
- Difference of Squares with Surds
- Rationalising a Monomial Denominator
- Rationalising a Binomial Denominator
- Simplifying Fractional Surds

#### Number Systems: Complex Numbers

- Definition of Complex Numbers
- Conjugate Pairs of Complex Numbers
- Square Roots
- Definition of Complex Numbers
- Real Part and Imaginary Part of Complex Numbers
- Equality of Complex Numbers
- Addition and Subtraction of Complex Numbers
- Simplifying Complex Numbers using i
- Modulus
- Real and Imaginary Parts
- Conjugates
- Arguments
- Regions
- Factorising Quadratic Expressions over the Complex Field
- Solving Quadratic Equations over the Complex Field

#### Geometry in the Plane: Circle geometry

- Arcs, Angles and Chords
- Angle at the Circumference
- Chords and Centres
- Equidistant from the Centres
- Cut Internally and Externally
- Angles in the Same Segment
- Angle in a Semi-Circle
- Opposite Angles of a Cyclic Quadrilateral
- Exterior Angle of a Cyclic Quadrilateral
- Tangent to a Circle
- Alternate Segment
- Two Tangents to a Circle
- Secant from an External Point

#### Circular Functions

- Modelling with Trigonometric Functions
- Reciprocal Trigonometric Functions
- The Reciprocal Identities
- Graphs of Reciprocal Trigonometric Functions
- Trigonometric Identities
- Sums and Differences of Sine
- Sums and Differences of Cosine
- Sums and Differences of Tangent
- Double Angle Identity of Sine
- Double Angle Identities of Cosine
- Double Angle Identity of Tangent
- Transformations
- Equations using Transformations

#### Transformations: Logarithmic Graphs

- Dilation from the x-axis
- Dilation from the y-axis
- Dilation from the base
- Translation
- Reflection
- Stating the Transformations of Logarithmic Graphs to base e
- Dilation of Logarithmic Graphs to base e
- Translation of Logarithmic Graphs to base e
- Reflection of Logarithmic Graphs to base e
- Finding Equations for Graphs of Logarithmic Functions
- Absolute Values