## Background of QCE Year 12 Maths C

The Senior Syllabus in QCE Year 12 Maths C is a recommended companion subject to Mathematics B. It provides additional preparation for tertiary studies in subjects with high demand in mathematics, especially in the areas of science, medicine, mining and engineering, information technology, mathematics, finance, and business and economics.

## Global Aims of QCE Year 12 Maths C

The global aims are statements of the long-term achievements, attitudes and values that are developed by students through studying Mathematics C but which are not directly assessed by the school.

By the end of this course, students should develop:

- broad mathematical knowledge and skills
- the ability to recognise when problems are suitable for mathematical analysis and solution, and be able to attempt such analysis and solve problems with confidence
- an awareness of the uncertain nature of their world and be able to use mathematics to help make informed decisions in life-related situations
- an understanding of the diverse applications of mathematics
- an ability to comprehend mathematical information which is presented in a variety of forms
- an ability to communicate mathematical information in a variety of forms
- an ability to use mathematical procedures to justify conclusions
- an ability to benefit from the availability of a wide range of technologies
- an ability to choose and use mathematical instruments appropriately
- positive attitudes to the learning and practice of mathematics.

## Course Organisation of QCE Year 12 Maths C

The syllabus contains both core and option topics. A course of study in Mathematics C must contain all core topics and a minimum of two complete option topics. Although some topics contain material which is required in other topics, the order in which they are presented does not imply a teaching sequence.

#### Core topics

- Introduction to groups
- Real and complex number systems
- Matrices and applications
- Vectors and applications
- Calculus
- Structures and patterns

#### Option topics

- Linear programming
- Conics
- Dynamics
- Introduction to number theory
- Introductory modelling with probability
- Advanced periodic and exponential functions
- School option(s).

*referred from Mathematics C Senior Syllabus 2008 (amended 2014) Queensland Studies Authority 2014*

#### Differential Equations

- Basic Rates of Change
- using Rates of Change
- Rates of Change and Integration
- Velocity and Speed
- at Rest
- Maximum and Minimum Speed
- Distance Travelled
- Combining Rates of Change
- Eliminating Pronumerals
- Rate of Change Involving Angles
- Basic Exponential Growth and Decay to base e
- Finding the Values to base e
- Working without Initial Values to base e
- Further Applications to base e

#### Sequences and Series

- Set up a Rule
- Finding the number of Terms
- Applications
- Sum of an Arithmetic Series
- Set up a Sum Formula
- Finding the Sum using a Formula
- Finding Terms from Sum
- Sigma Notation of Arithmetic Series
- Set up a Rule
- Finding the number of Terms
- Applications
- Compound Interest
- Finding Unknown Values
- Set up a Sum Formula
- Finding the Sum using a Formula
- Finding Number of Terms
- Sigma Notation of Geometric Series
- Finding the Number of Terms

#### Mathematical Induction

- Proof by Mathematical Induction
- Finding the Initial Value
- Working with Indices
- Induction with Factorials
- using Formulae
- Two Initial Values
- Basic Divisibility
- Multiple Index
- Increasing More than One
- Two Indices
- Three Indices
- Basic Comparison
- using the Difference
- Finding the Initial Value
- using the Assumption

#### Advanced Periodic Functions

- Reciprocal Trigonometric Ratios
- The Reciprocal Identities
- Reciprocal Functions
- Miscellaneous Graphs
- Exact Ratios with Radian Measurement
- 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

#### Conics

- A Locus and its Equation
- Circle as a Locus
- Parabola as a locus
- Parabola Symmetrical to y-axis
- Parabola Symmetrical to x-axis
- Transformation of Parabola Symmetrical to y-axis
- Transformation of Parabola Symmetrical to x-axis
- Eccentricity of Ellipse
- Definition of Ellipse
- Transformation of Ellipse
- Locus of Ellipse
- Drawing Hyperbolae
- Eccentricity of Hyperbola
- Transformation of Hyperbola
- Find the Equation of Hyperbola
- Rotation of Hyperbola
- Directrices of Hyperbola
- Foci of Hyperbolae
- Modulus
- Real and Imaginary Parts
- Conjugates
- Arguments
- Regions

#### Parametric Equations

- Definition of Parametrices
- Cartesian Equations in Parametrices
- Parametric Equations in Parametrices
- Parametric Coordinates
- Chords in Parametrices
- Tangents in Parametrices
- Normals in Parametrices
- Focal Chords in Parametrices
- Parametric Equations of Ellipse
- using Parametric Equations of Ellipse
- Parametric Equations of Hyperbola
- Applications of Hyperbola
- Parametric Equations of Rectangular Hyperbola
- Tangents of Rectangular Hyperbola
- Normals of Rectangular Hyperbola