## Statement on QCE Year 11 Maths B

QCE Year 11 Maths B is:

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

Mathematics B involves the study of mathematical functions and their applications, differential and integral calculus and applied statistical analysis.

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 B

Mathematics B aims to provide the opportunity for students to participate more fully in lifelong learning. This subject provides a foundation for further studies in disciplines within which mathematics and statistics have important roles. It is also advantageous for further studies in the health and social sciences. In summary, Mathematics B is designed for students whose future pathways may involve mathematics and statistics, and their application, in a range of disciplines at the tertiary level.

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

#### Linear Lines

- Gradient given the Angle at the x-axis
- Gradient Form (Standard Form)
- Finding the Equation in Gradient Form
- General Form
- Intercept Form
- Point-Gradient Formula
- Gradient from Rise and Run
- Gradient from two Points
- Gradient from an Angle
- Finding the Positive Angle ot the x-axis
- Finding the Equation of a Straight Line using the Gradient and a Point
- Finding the Equation of a Straight Line using Two Points
- Basic Simultaneous Equations
- Simultaneous Equations involving Quadratics
- Simultaneous Equations involving Absolute Values
- Substitution Method
- Elimination Method
- Applications

#### Relations and Functions

- Set Notation
- Union Sets and Intersection Sets
- Disjoint or Mutually Exclusive
- Set Builder Notations
- Complement Sets
- Venn Diagram
- Counting Elements of Sets
- Domain and Range
- Types of Relations
- Vertical Line Test
- Inequalities
- Simple Regions
- Function Notation
- Hybrid Functions
- Basic Circles
- SemiCircles
- General Equation of a Circle
- General form of a Circle

#### Logarithmic Functions

- Definition of Logarithms
- Addition
- Subtraction
- Indices
- Zero Value
- Unity
- Changing the Base
- 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
- Varialbes in Logarithms
- Varialbes in Base
- Varialbes in Other Side
- Varialbes in Multiple Terms
- Converting to an Index Form
- Multiple Terms

#### Geometric Progressions

- 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
- 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

#### Summary Statistics

- Calculating the Mean
- Mean from UnGrouped Data
- Mean from Grouped Data
- Calculating the Median
- Median from a Table
- Median from a Cumulative Frequency Graph
- Median from a Grouped Cumulative Frequency Graph
- Range
- Interquartile Range
- Population Standard Deviation
- Box-and-Whisker Plots
- Double Box-and-Whisker Plots
- Back-to-back Stem Plots
- Parallel Boxplots

#### Differentiation

- Limits
- Continuity
- the First Principles
- Differentiation of Constant Functions
- Differentiation of Linear Functions
- Methods of Differentiation
- Differentiation of Rational Functions
- Differentiation of Rational Powers
- Differentiation of Polynomial Functions
- Basic Rates of Change
- using Rates of Change
- Maximum and Minimum Speed
- Maxima and Minima
- Maximum Velocity and Speed