# Learn the QCE Syllabus from the Largest FREE Video Resource in QLD

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#### Maths Standard

##### Relative Frequency and Probability

##### Perimeter, Area and Volume

- Area of Circles and Sectors
- Area of Composite Shapes
- Trapezoidal Rule
- Surface Area of Right Prisms
- Surface Area of Cylinders and Spheres
- Surface Area of Pyramids and Cones
- Volume of Right Prisms
- Volume of Cylinders and Spheres
- Volume of Pyramids and Cones
- Surface Area and Volume of Composite Solids
- Capacity

##### Interest and Depreciation

##### Exploring and Describing Data

##### Working with Time

##### Budgeting and Household Expenses

#### Maths Advanced

##### Working With Functions

- Linear Parametric Equations
- Quadratic Inequalities
- Sketching Square-Root Functions
- Index Laws and Surds
- Solving Quadratic Equations (Quadratic Formula and Completing the Square)
- Manipulation of Algebraic Expressions
- What is a Function and Relation?
- Function Notation for Domain and Range
- The Graph of a Function
- Identifying the Type of Function (Vertical Line Test)
- Odd and Even Functions
- Sum, Difference, Product and Quotient of Functions
- Composite Functions
- Finding the X-Intercepts
- Solving Linear Function Problems
- Solving Quadratic Function Problems
- Simultaneous Equations
- Solving Cubic Function Problems
- Defining a Real Polynomial
- Identifying the Coefficients and Degree of a Polynomial
- Identifying the Shape and Features of a Polynomial Function
- Hyperbolas
- Absolute Value
- Transformations of an Absolute Value Function
- Solving and Graphing Absolute Value Functions
- Reflecting Functions
- Circles

##### Trigonometric Functions

- Using Trigonometric Ratios to Solve Problems (Sine, Cosine, Tangent)
- Sine Rule, Cosine Rule, Area of a Triangle
- The Ambiguous Case of the Sine Rule (Obtuse Angle)
- Solving Problems in Two and Three Dimensions with the use of a Diagram
- Angles of Elevation and Depression and True and Compass Bearings
- Unit Circle in Degrees
- Defining a Radian
- Unit Circle in Radians
- Trigonometric Ratios of Any Magnitude In Degrees and Radians
- Sketching Sin, Cos and Tan Curves
- Arc Length and Area of a Sector for a Circle
- Solving Problems Involving Sector Areas, Arc Lengths and Combinations of Either Areas or Lengths
- Reciprocal Trigonometric Functions (Cosec, Sec, Cot)
- Sketching Cosec, Sec and Cot Graphs
- Proving and Applying Trigonometric Pythagorean Identities
- Using tan(x) = sin(x)/cos(x) provided that cos(x) is not equal 0
- Proving Trigonometric Identities
- Evaluating Trigonometric Expressions with Angles of Any Magnitude and Complementary Angles
- Simplifying Trigonometric Expressions and Solving Trigonometric Equations

##### Calculus

- Continuous and Discontinuous Functions
- Gradient of a Secant as an Approximation of the Tangent
- Relationship between Angle of Inclination, Tangent and Gradient
- Describing the Behaviour of a Function
- Using the Difference Quotient
- Distance-Time and Velocity-Time Graphs
- h Approaching 0 in the Difference Quotient
- Derivative as the Gradient of the Tangent of the Graph
- Estimating the Value of the Derivative at a Point
- Notation for Differentiation Using First Principles
- Differentiation Using First Principles for Simple Polynomials
- Derivative as a Function
- Sketching the Derivative Function
- Instantaneous Rate of Change
- Differentiating a Function
- Differentiating the Sum or Difference of Two Functions
- The Product, Quotient and Chain Rules
- Derivatives of Power Functions
- Finding the Equation of a Tangent or Normal of a Function at a Given Point
- Position, Velocity and Acceleration Using Derivatives

##### Exponential and Logarithmic Functions

- Logarithms
- Exponential Functions
- Relationship between Logarithms and Exponentials
- Logarithmic Laws
- Change of Base
- Interpreting and Using Logarithmic Scales (Seismic, pH, Acoustics)
- Solving Logarithmic Problems
- Introduction to Exponential Functions and Euler's Number (e)
- Differentiating the Exponential Function
- Natural Logarithms Problems
- Solving Equations Involving Indices Using Logarithms
- Graphing Exponential Functions and its Transformations
- Algebraic Properties of Exponential Functions
- Solving Exponential Problems
- Graphing Logarithmic Functions and its Transformations
- Modelling Situations with Logarithmic and Exponential Functions

##### Statistical Analysis

- Theoretical Probability, Relative Frequency and Probability Scale
- Solving Problems Involving Simulations or Trials of Experiments
- Array and Tree Diagrams
- Venn Diagrams
- Complement and Addition Theorem
- Conditional Probability
- Mutually Exclusive
- Multiplication Rule
- Defining and Categorising Random Variables
- Expected Value, Variance, and Standard Deviation
- Sample mean

#### Maths Extension

##### Further Work with Functions

- Introduction to Graphing Relationships
- Sketching Inverse Functions
- Sketching Squared Functions
- Graphing Absolute Functions
- Graphing Added Functions
- Graphing Multiplied Functions
- Graphing Questions
- Introduction to Inequalities
- Linear Inequalities
- Rational Inequalities
- Inequalities with Absolute Values
- Inequalities Questions
- Introduction Inverse Functions
- Graphing Inverse Functions
- Testing for a Function
- Restrictions in Inverse Functions
- Domain and Range for Inverse Functions
- Inverse Function Questions
- Introduction to Parametric Form
- Parabolic Parametric Equations
- Circular Parametric Equations
- Eliminating the Parameter in Parametric Form
- T Parametric Form
- Parametric to Cartesian form
- Sketch Parametric Functions
- Root of Cubic Polynomial
- Mutliplicity of roots

##### Further Trigonometric Identities

##### Rates of Change

- Questions on Exponential Growth
- Sketching the Exponential Function
- Questions on Exponential Growth & Decay
- Newton's Law of Cooling
- Sketching the Exponential Function
- Initial Value of the Exponential Model
- Growth Model
- Introduction to Rates of Change
- Language of Rates of Change
- Finding Derivatives with Time
- Displacement
- Velocity
- Acceleration
- Exponential Growth and Decay

##### Working with Combinatorics

- Counting Principle
- Factorials
- Circular Combinations
- Pigeonhole Principle
- Permutations
- Permutations with Repetitions
- Permutations without Repeats
- Combinations
- Questions on Permutations & Combinations
- Pascals Triangle
- Binomial Expansion
- Combinations and Binomials
- Derive and Simple Identities Associated with Pascal’s Triangle

#### Chemistry

##### Module 1: Properties and Structure of Matter

- Introduction to Properties of Matter
- Separation Techniques
- Percentage Composition
- IUPAC Nomenclature of Inorganic Substances
- Physical and Chemical Properties
- Introduction to Atomic Structure and Atomic Mass
- Energy Levels in Atoms
- Electronic Configuration and spdf Notation
- Examining Energy Levels
- Relative Atomic Mass
- Properties of Unstable Isotopes
- Introduction to Periodicity
- Atomic Radii
- Ionisation Energy and Electronegativity
- Reactivity with Water
- Introduction to Bonding
- Role of Electronegativity in Determining Bonding
- Allotropy
- Intermolecular and Intramolecular Bonding
- Different Chemical Structures of Atoms and Elements

##### Module 2: Introduction to Quantitative Chemistry

- Introduction to the Mole Concept
- Models of Chemical Reactions
- Molar Mass
- Percentage Composition and Empirical Formulae
- Limiting Reagents
- Introduction to Chemical Reactions and Stoichiometry
- Stoichiometry and The Law of Conservation of Mass
- Introduction to Concentration and Molarity
- Calculating Concentration
- Making a Standard Solution via Dilution
- Introduction to Gas Laws
- The Ideal Gas Law

##### Module 3: Reactive Chemistry

- Introduction to Chemical Reactions
- Aboriginal and Torres Strait Islander (ATSI) Applications of Chemical Processes
- Common Chemical Reactions
- Introduction to Predicting Reactions of Metals
- Metal Activity Series
- Patterns in Metal Activity
- Oxidation and Reduction
- Galvanic Cells and Half Cells
- Predicting Reactions of Metals and Spontaneity Using Standard Reduction Potentials
- Introduction to Rates of Reactions
- Factors that Influence the Rate of Reaction
- Using Collision Theory to Explain Reaction Rate

##### Module 4: Drivers of Reactions

- Introduction to Energy Changes in Chemical Reactions
- Enthalpy
- Energy Profile Diagrams
- The Role of Catalysts
- Introduction to Enthalpy and Hess’s Law
- Hess's Law and Energy Cycles
- Hess's Law
- Introduction to Entropy and Gibbs Free Energy
- Predicting Entropy Changes
- Explaining Spontaneous Reactions
- Temperature and Spontaneity

#### Biology

##### Module 1: Cells as the Basis of Life

- Introduction to Cellular Structures
- Technologies Used to Determine Cell Structures
- Drawing Scaled Diagrams
- Cell Organelles and Arrangements
- The Fluid Mosaic Model
- Introduction to Cell Function
- Active Transport
- The Balance of Surface Area to Volume
- Cell Requirements
- Photosynthesis and Cell Respiration
- Enzymes and Their Role in Cells

##### Module 2: Organisation of Living Things

- Introduction to The Organisation of Cells
- Structure and Function of Tissues, Organs and Systems
- The Hierachy of Structure in Organisms
- Introduction to Nutrient and Gas Requirements
- Special Plant Structures
- Structure and Function of Plants
- Digestion in Mammals
- Microscopic Gas Exchange Structures
- Gas Exchange Structures in Different Animals
- Autotrophs and Heterotrophs Requirements
- Introduction to Transport
- Vascular Systems in Plants and Animals
- Open and Closed Systems in Animals
- Changing Composition of Blood Through The Body

##### Module 3: Biological Diversity

- Introduction to Effects of the Environment on Organisms
- Selection Pressures in Action
- Introduction to Adaptations
- The Theory of Evolution by Natural Selection
- Introduction to The Theory of Evolution by Natural Selection
- Microevolutionary Changes
- Convergent and Divergent Evolution
- Introduction to Evolution - the Evidence
- Modern-Day Examples

##### Module 4: Ecosystem Dynamics

- Introduction to Population Dynamics
- Ecological Niches
- Predicting Consequences Based on Changes to Ecosystems
- Sampling Techniques
- Extinction Events
- Introduction to Past Ecosystems
- Determining Past Changes with Technology
- Evidence of Evolution of Present-Day Organisms in Australia
- Reasons for Changes in Past Ecosystems
- Introduction to Future Ecosystems
- Climate Change and Ecosystems
- Restoring Damaged Ecosystems

#### Physics

##### Module 1: Kinematics

- Describing Motion Using Scalar and Vector Quantities
- Instantaneous and Average Velocity
- Relative Velocity
- Motions of Objects in One Dimension (Time, Distance, Displacement, Speed, Velocity, Acceleration)
- Modelling Relationships between Variables in Rectilinear Motion
- Vectors in One and Two Dimensions
- Vector Addition
- Analysing the Motion of Objects Algebraically, Graphically and with Vector Diagrams
- Relative Motion of Objects in Two Dimensions

##### Module 2: Dynamics

- Describing Static and Dynamic Interactions (Newton's Laws of Motion)
- Net Force and Equilibrium
- Solving Problems Involving Resultant and Component Forces
- Practical Investigation: Motion of Objects on Inclined Planes
- Newton’s First Two Laws of Motion to a Variety of Everyday Situations (Friction)
- Acceleration of a Single Object Subjected to a Force (Newton’s Second Law of Motion)
- The Special Case of Conservation of Mechanical Energy (Work Done and Gravitational Potential Energy)
- Average Power
- Interactions Between Objects in Simple Closed Systems
- Law of Conservation of Momentum (Elastic Collisions)
- Force as a Function of Time
- Impulse
- Momentum and Kinetic Energy of Elastic and Inelastic Collisions

##### Module 3: Waves and Thermodynamics

- Practical Investigation: Creation of Mechanical Waves
- Practical Investigation: Transverse, Longitudinal, Mechanical and Electromagnetic Waves
- Graphs of Displacement as a Function of Time (Transverse and Longitudinal Waves)
- Solving problems using v=fλ and f=1/T
- Reflection, Refraction, Diffraction and Wave Superposition
- Progressive and Standing Waves
- Resonance in Mechanical Systems (Driving Frequency, Natural Frequency, Amplitude, Transfer of Energy)
- Practical Investigation: Pitch and Loudness of a Sound
- Sound in Air as a Longitudinal Wave
- Displacement of Air Molecules as Variations in Pressure
- Relationship Between Distance and Intensity of Sound
- Reflection, Diffraction, Resonance and Superposition of Sound Waves
- Behaviour of Standing Waves on Strings and Pipes
- The Doppler Effect and Beats
- Practical Investigation: Formation of Images in Mirrors and Lenses
- Refraction and Total Internal Reflection
- Snell's Law
- Practical Investigation: Phenomenon of the Dispersion of Light
- Relationship Between the Inverse Square Law, the Intensity of Light and the Transfer of Energy
- Applying Equations and Relationships to Solve Questions (Refraction Index, Snell's Law, Critical Angle, Intensity of Light)
- Relationship Between the Temperature of an Object and Kinetic Energy
- Thermal Equilibrium
- Relationship between the Change in Temperature of an Object and its Specific Heat Capacity (Q = mc△T)
- Conduction, Convection and Radiation
- Latent Heat Involved in a Change of State
- Thermal Conductivity

##### Module 4: Electricity and Magnetism

- Introduction to Electrostatics
- Electric Field Lines Representation
- Applying the Electric Field Model using Formulas
- Moving Charge in an Electric Field
- Flow of Electric Currents in Metals (I=q/t)
- Current-Voltage Relationship and Ohm's Law
- The Rate of Conversion of Electrical Energy in Components of Electrical Circuits, as Heat and Light (P=VI and E=Pt)
- Series and Parallel Circuits (Kirchhoff's Laws, Series and Parallel Formula)
- Law of Conservation of Energy to the Heating Effects of Electric Currents
- Force Produced Between Magnetised and Magnetic Materials in the Context of Ferromagnetic Materials
- Using Magnetic Field Lines to Model Properties of Magnets, Current-Carrying Wires and Solenoids.
- The Magnetic Field Produced by Wires and Solenoids
- How do Ferromagnetic Materials Become Magnetised
- Applying Models to Represent Features of Magnetic Fields

#### Economics

##### Preliminary Topic 1 - Introduction to Economics

##### Preliminary Topic 3 - Markets

- Law of Demand
- Factors Affecting Demand
- Movements and Shifts in the Demand Curve
- The Law of Supply
- Factors Affecting Supply
- Movements and Shifts Along the Supply Curve
- Market Equilibrium
- Effects of Changes in Supply and Demand on the Market Equilibrium
- Price Ceilings and Price Floors
- Market Failure, Merit Goods, Public Goods and Externalities
- Price Elasticity, Inelasticity and Unit Elasticity of Demand
- Calculating Price Elasticity Using the Total Outlay Method
- Factors Affecting the Price Elasticity of Demand
- Elastic and Inelastic Supply
- Factors Affecting the Price Elasticity of Supply
- Market Structures and Variations in Competition

##### Preliminary Topic 5 - Financial Markets

- Primary and Secondary Markets
- Types of Financial Markets
- The Role and Function of the Share Market
- The Reserve Bank of Australia (RBA)
- The Australian Prudential Regulation Authority (APRA)
- The Australian Securities and Investments Commission (ASIC)
- Transactions and Speculative Motives
- Currency and Broad Money
- The Role of the Reserve Bank in Determining the Cash Rate
- Influence of the Cash Rate on Market Interest Rates

##### Preliminary Topic 6 - Government and the Economy

- The Provision of Public Goods and Merit Goods
- Inequality and the Distribution of Income
- Externalities and the Environment
- Monopoly Power
- The Levels of Government and Constitutional Powers
- The Reallocation of Resources
- The Redistribution of Income through Taxation and Government Spending
- Monetary and Fiscal Policies
- Types of Budgets - Surplus, Balanced and Deficit