## Statement on QCE Year 12 Maths B

The Senior Syllabus in QCE Year 12 Maths B is a recommended precursor to 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 B

The global aims are statements of the long-term achievements, attitudes and values that are developed by students through studying Mathematics B 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 B

The subject matter has been organised into seven topics. All topics must be studied. The order in which topics are presented does not imply a teaching sequence. The topics are:

- Introduction to functions
- Rates of change
- Periodic functions and applications
- Exponential and logarithmic functions and applications
- Optimisation
- Introduction to integration
- Applied statistical analysis.

Throughout the course, certain fundamental knowledge and procedures are required. Time should be provided to revise the fundamental knowledge and procedures within topics as they are required. This maintenance takes time, and should be allowed for in designing the course sequence.

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

#### Quadratic Graphs

- Transformations
- Vertex and Intercepts
- Coefficients
- Finding the Vertex using Completing the Square
- Finding Quadratic Equations
- Axis of Symmetry and Vertex
- Finding y given x
- Substituting Points
- Finding x given y
- Applications of Quadratic Functions
- Finding Quadratics using Intercepts
- Finding Quadratics for Touching x-axis
- Finding Quadratics using Axes of Symmetry
- Finding Quadratics using Coefficients
- Finding Quadratics using Vertices
- Axes Intercepts

#### Exponential and Logarithmic Functions

- Index Laws
- Negative Indices
- Fractional Indices
- Definition of Logarithms
- Addition of Logarithms
- Subtraction of Logarithms
- Indices of Logarithms
- Zero Value of Logarithms
- Unity of Logarithms
- Changing the Base of Logarithms
- Equations involving Logarithms
- Simplifying Logarithms in base 10
- Finding Exponents using Logarithms in base 10
- Equations involving Logarithms in base 10
- Interchangeable Logarithmic Forms
- Simplifying involving any Bases
- Equations involving Indices
- Negative Base
- Equations by Changing the Base
- Reducible to Quadratic Equations
- Equations using Logarithms
- Equivalent Natural Logarithms
- Equations involving Natural Logarithms

#### Derivatives of Exponential and Logarithmic Functions

- Inverse of Logarithmic Functions
- Inverse of Exponential Functions
- Differentiation of Logarithmic Functions
- Differentiation of the Exponential Function
- Basic Exponential Growth and Decay to base e
- Exponential Growth
- Exponential Decay
- Finding the Values to base e
- Working without Initial Values to base e
- Further Applications to base e

#### Calculus of Periodic Functions

- Differentiation of Sine Function : Chain Rule
- Differentiation of Sine Function : Product Rule
- Differentiation of Sine Function : Quotient Rule
- Differentiation of Cosine Function : Chain Rule
- Differentiation of Cosine Function : Product Rule
- Differentiation of Cosine Function : Quotient Rule
- Differentiation of Tangent Function
- Applications of Differentiation

#### Introductory Integration

- Antidifferentiation
- Antidifferentiation of Fractions
- Antidifferentiation of Surds
- Antidifferentiation of Linear Expressions
- Antidifferentiation for finding Equations
- Standard Integral of Cosine
- Standard Integral of Sine
- Standard Integral of Tangent
- Integration of Logarithmic Functions
- Integration of the Exponential Function
- Using Chain Rule
- Using Derivative of Exponential Functions
- Using Derivative of SINE function
- Using Derivative of COSINE function
- Using Derivative of TANGENT function
- Using Derivative of Logarithmic function
- Using Product Rule
- Using Long Division

#### Probability Distributions

- Continuous or Discrete
- Corresponding Probabilities
- Probability Distribution Graphs
- Characteristics of Discrete Probability Distribution
- Find the missing Values From the Discrete Probability Distribution
- Probability Functions
- Using Probability Distributions
- Finding the Expected Value
- Finding the Unknown Value
- Finding Multiple Unknown Values
- Applciations
- Expectation Theorems
- Applications of Expectation Theorems
- Mean
- Mode

#### Binomial Distribution

- Bernulli Trials and Sequences
- Probability Function
- Probability with a specific Order
- Probability without a specific Order
- Finding the Number of Trials
- Using Tables
- Using Parameters
- Conditional Probability
- Finding the Expected Value Variance and Standard Deviation of Binomial Probability Distribution
- Finding the Probability using the Expected Value
- Finding the number of Trials