## Statement on QCE Year 11 Maths C

QCE Year 11 Maths C is a:

- unique and powerful way of viewing the world to investigate patterns, order, generality and uncertainty
- way of thinking in which problems are explored through observation, reflection and logical,inductive or deductive reasoning
- powerful, concise and unambiguous symbolic system with written, spoken and visual components
- creative activity with its own intrinsic value, involving invention, intuition and exploration.

Mathematics C involves the study of mathematical concepts such as groups, Real and complex number systems, matrices, vectors, calculus, mathematical structures, linear programming, conics, dynamics, and advanced periodic and exponential functions.

These are used to develop:

- knowledge and skills in advanced computation and algebraic methods and procedures
- mathematical modelling and problem-solving strategies and skills
- the capacity to justify mathematical arguments and make decisions
- the capacity to communicate about mathematics in a variety of forms.

## Background of QCE Year 11 Maths C

Mathematics C has been designed to be taken in conjunction with Mathematics B. The subject contains topics in functions, calculus, probability and statistics that build on and deepen the ideas presented in Mathematics B and demonstrate their application in many areas. Vectors, complex numbers and matrices are introduced. Mathematics C is designed for students with a strong interest in mathematics, including those intending to study mathematics, statistics, all sciences and associated fields, economics or engineering at university.

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

#### Course Materials

#### Real Number System

- Representing Sets using Set Builder Notation
- Expressing Sets using Set Builder Notation
- Representing Sets using Interval Notation
- Natural Numbers
- Integers
- Rational Numbers
- Irrational Numbers
- Real Numbers
- Expressing to Recurring Decimals
- Representing Recurring Decimals to Repeated Pattern
- Converting to Recurring Decimals
- Definition of Surds
- Rational and Irrational Numbers
- 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
- Absolute Values
- Equations with Absolute Value
- Inequalities with Absolute Values

#### Complex Numbers

- 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
- Conjugate Pairs of Complex Numbers
- Real and Imaginary Parts
- Radian Measurement
- Modulus-Argument Form
- De Moivre`s Theorem
- Modulus
- Real and Imaginary Parts
- Conjugates
- Arguments

#### Matrices

- Matrix Definition
- Matrix Equality
- Matrix Addition
- Matrix Subtraction
- Scalar Multiples of Matrices
- Zero or Null Matrix
- Negative Matrix
- Simple Matrix Equations
- Single Row by Single Column
- Single Row by Multiple Columns
- Multiple Rows by Multiple Columns
- Commutative Law
- Identity Matrix
- Power of a Matrix
- Finding a Matrix Inverse
- Determinant of a Matrix
- Inverse Matrix using Determinant
- Matrix Equations
- Solving a Pair of Linear Equations
- Unique Solutions

#### Matrix Applications

- Finding Matrices
- Inverse of an Inverse matrix
- Inverse of Matrix Multiplications
- Inverse Matrix in a Linear Form
- Definition of Transpose of a Matrix
- Transpose of Transpose of a Matrix
- Distribution of Transpose of Matrices
- Multiplication of Transpose of Matrices
- Description of Transition Matrices
- Constructing Transition Matrices
- Underatanding Transition Matrices

#### Geometric Sequences and Series

- Identifying Geometric Sequences
- Finding the First Term and Common Ratio
- Finding a Term from a Rule
- 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
- Finding the Limiting Sum
- Finding the First Term and the Common Ratio
- Recurring Decimals
- Recurring Decimal with an Extra Value

#### Permutations and Combinations

- Counting Techniques with Repetitions
- Counting Techniques without Repetitions
- Definition of Factorial
- Arrangement
- Arrangements in a Round Table
- Removing Duplicates
- Definition
- Arrangements
- Arrangements in a Round Table
- Unknown Number of Arrangements
- Removing Duplicates
- Definition
- Selections
- Majority Decision
- Arrangements
- Probability