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#### Unit 1: Money, measurement and relations

##### Topic 1: Consumer arithmetic

Applications of rates, percentages and use of spreadsheets

Unit 1: Money, measurement and relations > Topic 1: Consumer arithmetic > Applications of rates, percentages and use of spreadsheets

- Review definitions of rates and percentages

- Calculate weekly or monthly wages from an annual salary, and wages from an hourly rate, including situations involving overtime and other allowances and earnings based on commission or piecework

- Calculate payments based on government allowances and pensions, such as youth allowances, unemployment, disability and study

- Prepare a personal budget for a given income, taking into account fixed and discretionary spending

- Compare prices and values using the unit cost method

- Apply percentage increase or decrease in various contexts, e.g. determining the impact of inflation on costs and wages over time, calculating percentage mark-ups and discounts, calculating GST, calculating profit or loss in absolute and percentage terms, and calculating simple and compound interest

- Use currency exchange rates to determine the cost in Australian dollars of purchasing a given amount of a foreign currency, such as US$1500, or the value of a given amount of foreign currency when converted to Australian dollars, such as the value of €2050 in Australian dollars

- Calculate the dividend paid on a portfolio of shares, given the percentage dividend or dividend paid per share, for each share; and compare share values by calculating a price-to-earnings ratio

- Use a spreadsheet to display examples of the above computations when multiple or repeated computations are required, e.g. preparing a wage sheet displaying the weekly earnings of workers in a fast-food store where hours of employment and hourly rates of pay may differ, preparing a budget or investigating the potential cost of owning and operating a car over a year

##### Topic 2: Shape and measurement

Pythagoras' theorem

Unit 1: Money, measurement and relations > Topic 2: Shape and measurement > Pythagoras' theorem

- Review Pythagoras' theorem and use it to solve practical problems in two dimensions and simple applications in three dimensions

Mensuration

Unit 1: Money, measurement and relations > Topic 2: Shape and measurement > Mensuration

- Solve practical problems requiring the calculation of perimeters and areas of circles, sectors of circles, triangles, rectangles, trapeziums, parallelograms and composites

- Calculate the volumes and capacities of standard three-dimensional objects, including spheres, rectangular prisms, cylinders, cones, pyramids and composites in practical situations, such as the volume of water contained in a swimming pool

- Calculate the surface areas of standard three-dimensional objects, e.g. spheres, rectangular prisms, cylinders, cones, pyramids and composites in practical situations, such as the surface area of a cylindrical food container

Similar figures and scale factors

Unit 1: Money, measurement and relations > Topic 2: Shape and measurement > Similar figures and scale factors

- Review the conditions for similarity of two-dimensional figures, including similar triangles

- Use the scale factor for two similar figures to solve linear scaling problems

- Obtain measurements from scale drawings, such as maps or building plans, to solve problems

- Obtain a scale factor and use it to solve scaling problems involving the calculation of the areas of similar figures, including the use of shadow sticks, calculating the height of trees, use of a clinometer

- Obtain a scale factor and use it to solve scaling problems involving the calculation of surface areas and volumes of similar solids

##### Topic 3: Linear equations and their graphs

Linear equations

Unit 1: Money, measurement and relations > Topic 3: Linear equations and their graphs > Linear equations

- Identify and solve linear equations, including variables on both sides, fractions, non-integer solutions

- Develop a linear equation from a description in words

Straight-line graphs and their applications

Unit 1: Money, measurement and relations > Topic 3: Linear equations and their graphs > Straight-line graphs and their applications

- Construct straight-line graphs using ?? = ?? + ???? both with and without the aid of technology

- Determine the slope and intercepts of a straight-line graph from both its equation and its plot

- Interpret, in context, the slope and intercept of a straight-line graph used to model and analyse a practical situation

- Construct and analyse a straight-line graph to model a given linear relationship, such as modelling the cost of filling a fuel tank of a car against the number of litres of petrol required

Simultaneous linear equations and their applications

Unit 1: Money, measurement and relations > Topic 3: Linear equations and their graphs > Simultaneous linear equations and their applications

- Solve a pair of simultaneous linear equations in the format ?? = ???? + ??, using technology when appropriate; they must solve equations algebraically, graphically, by substitution and by the elimination method

- Solve practical problems that involve finding the point of intersection of two straight-line graphs, such as determining the break-even point where cost and revenue are represented by linear equations

Piece-wise linear graphs and step graphs

Unit 1: Money, measurement and relations > Topic 3: Linear equations and their graphs > Piece-wise linear graphs and step graphs

- Sketch piece-wise linear graphs and step graphs, using technology where appropriate

- Interpret piece-wise linear and step graphs used to model practical situations

#### Unit 2: Applied trigonometry, algebra, matrices and univariate data

##### Topic 1: Applications of trigonometry

Applications of trigonometry

Unit 2: Applied trigonometry, algebra, matrices and univariate data > Topic 1: Applications of trigonometry > Applications of trigonometry

- Review the use of the trigonometric ratios to find the length of an unknown side or the size of an unknown angle in a right-angled triangle

- Determine the area of a triangle given two sides and an included angle, or given three sides by using Heron's rule, and solve related practical problems

- Solve two-dimensional problems involving non-right-angled triangles using the sine rule (ambiguous case excluded) and the cosine rule

- Solve two-dimensional practical problems involving the trigonometry of right-angled and non-right-angled triangles, including problems involving angles of elevation and depression and the use of true bearings

##### Topic 2: Algebra and matrices

Linear and non-linear relationships

Unit 2: Applied trigonometry, algebra, matrices and univariate data > Topic 2: Algebra and matrices > Linear and non-linear relationships

- Substitute numerical values into linear algebraic and simple non-linear algebraic expressions, and evaluate, e.g. order two polynomials, proportional, inversely proportional

- Find the value of the subject of the formula, given the values of the other pronumerals in the formula

- Transpose linear equations and simple non-linear algebraic equations, e.g. order two polynomials, proportional, inversely proportional

- Use a spreadsheet or an equivalent technology to construct a table of values from a formula, including two-by-two tables for formulas with two variable quantities, e.g. a table displaying the body mass index (BMI) of people with different weights and heights

Matrices and matrix arithmetic

Unit 2: Applied trigonometry, algebra, matrices and univariate data > Topic 2: Algebra and matrices > Matrices and matrix arithmetic

- Use matrices for storing and displaying information that can be presented in rows and columns, e.g. tables, databases, links in social or road networks

- Recognise different types of matrices (row matrix, column matrix (or vector matrix), square matrix, zero matrix, identity matrix) and determine the size of the matrix

- Perform matrix addition, subtraction, and multiplication by a scalar

- Perform matrix multiplication (manually up to a 3 x 3 but not limited to square matrices)

- Determining the power of a matrix using technology with matrix arithmetic capabilities when appropriate

- Use matrices, including matrix products and powers of matrices, to model and solve problems, e.g. costing or pricing problems, squaring a matrix to determine the number of ways pairs of people in a communication network can communicate with each other via a third person

##### Topic 3: Univariate data analysis

Making sense of data relating to a single statistical variable

Unit 2: Applied trigonometry, algebra, matrices and univariate data > Topic 3: Univariate data analysis > Making sense of data relating to a single statistical variable

- Define univariate data

- Classify statistical variables as categorical or numerical

- Classify a categorical variable as ordinal or nominal and use tables and pie, bar and column charts to organise and display the data, e.g. ordinal: income level (high, medium, low); or nominal: place of birth (Australia, overseas)

- Classify a numerical variable as discrete or continuous, e.g. discrete: the number of rooms in a house or continuous: the temperature in degrees Celsius

- Select, construct and justify an appropriate graphical display to describe the distribution of a numerical dataset, including dot plot, stem-and-leaf plot, column chart or histogram

- Describe the graphical displays in terms of the number of modes, shape (symmetric versus positively or negatively skewed), measures of centre and spread, and outliers and interpret this information in the context of the data

- Determine the mean and standard deviation (using technology) of a dataset and use statistics as measures of location and spread of a data distribution, being aware of the significance of the size of the standard deviation

Comparing data for a numerical variable across two or more groups

Unit 2: Applied trigonometry, algebra, matrices and univariate data > Topic 3: Univariate data analysis > Comparing data for a numerical variable across two or more groups

- Construct and use parallel box plots to compare datasets in terms of median, spread (IQR and range) and outliers to interpret and communicate the differences observed in the context of the data

- Compare datasets using medians, means, IQRs, ranges or standard deviations for a single numerical variable, interpret the differences observed in the context of the data and report the findings in a systematic and concise manner

#### Unit 3: Bivariate data, sequences and change, and Earth geometry

view_agenda query_stats##### Topic 1: Bivariate data analysis

view_agenda query_statsIdentifying and describing associations between two categorical variables

view_agenda query_statsUnit 3: Bivariate data, sequences and change, and Earth geometry > Topic 1: Bivariate data analysis > Identifying and describing associations between two categorical variables

Identifying and describing associations between two numerical variables

view_agenda query_statsUnit 3: Bivariate data, sequences and change, and Earth geometry > Topic 1: Bivariate data analysis > Identifying and describing associations between two numerical variables

Fitting a linear model to numerical data

view_agenda query_statsUnit 3: Bivariate data, sequences and change, and Earth geometry > Topic 1: Bivariate data analysis > Fitting a linear model to numerical data

Association and causation

view_agenda query_statsUnit 3: Bivariate data, sequences and change, and Earth geometry > Topic 1: Bivariate data analysis > Association and causation

##### Topic 2: Time series analysis

view_agenda query_statsDescribing and interpreting patterns in time series data

view_agenda query_statsUnit 3: Bivariate data, sequences and change, and Earth geometry > Topic 2: Time series analysis > Describing and interpreting patterns in time series data

- Describe time series plots by identifying features such as trend (long-term direction), seasonality (systematic, calendar-related movements) and irregular fluctuations (unsystematic, short-term fluctuations), and recognise when there are outliers, e.g. one-off unanticipated events

Analysing time series data

view_agenda query_statsUnit 3: Bivariate data, sequences and change, and Earth geometry > Topic 2: Time series analysis > Analysing time series data

##### Topic 3: Growth and decay in sequences

view_agenda query_statsThe arithmetic sequence

view_agenda query_statsUnit 3: Bivariate data, sequences and change, and Earth geometry > Topic 3: Growth and decay in sequences > The arithmetic sequence

- Use arithmetic sequences to model and analyse practical situations involving linear growth or decay, such as analysing a simple interest loan or investment, calculating a taxi fare based on the flag fall and the charge per kilometre, or calculating the value of an office photocopier at the end of each year using the straight-line method or the unit cost method of depreciation

The geometric sequence

view_agenda query_statsUnit 3: Bivariate data, sequences and change, and Earth geometry > Topic 3: Growth and decay in sequences > The geometric sequence

- Use geometric sequences to model and analyse (numerically or graphically only) practical problems involving geometric growth and decay (logarithmic solutions not required), such as analysing a compound interest loan or investment, the growth of a bacterial population that doubles in size each hour or the decreasing height of the bounce of a ball at each bounce; or calculating the value of office furniture at the end of each year using the declining (reducing) balance method to depreciate

##### Topic 4: Earth geometry and time zones

view_agenda query_statsLocations on the Earth

view_agenda query_statsUnit 3: Bivariate data, sequences and change, and Earth geometry > Topic 4: Earth geometry and time zones > Locations on the Earth

- Use a local area map to state the position of a given place in degrees and minutes, e.g. investigating the map of Australia and locating boundary positions for Aboriginal language groups, such as the Three Sisters in the Blue Mountains or the local area's Aboriginal land and the positions of boundaries

Time zones

view_agenda query_statsUnit 3: Bivariate data, sequences and change, and Earth geometry > Topic 4: Earth geometry and time zones > Time zones

#### Unit 4: Investing and networking

view_agenda query_stats##### Topic 1: Loans, investments and annuities

view_agenda query_statsCompound interest loans and investments

view_agenda query_statsUnit 4: Investing and networking > Topic 1: Loans, investments and annuities > Compound interest loans and investments

Reducing balance loans (compound interest loans with periodic repayments)

view_agenda query_statsUnit 4: Investing and networking > Topic 1: Loans, investments and annuities > Reducing balance loans (compound interest loans with periodic repayments)

Annuities and perpetuities (compound interest investments with periodic payments made from the investment)

view_agenda query_statsUnit 4: Investing and networking > Topic 1: Loans, investments and annuities > Annuities and perpetuities (compound interest investments with periodic payments made from the investment)

##### Topic 2: Graphs and networks

view_agenda query_statsGraphs, associated terminology and the adjacency matrix

view_agenda query_statsUnit 4: Investing and networking > Topic 2: Graphs and networks > Graphs, associated terminology and the adjacency matrix

Planar graphs, paths and cycles

view_agenda query_statsUnit 4: Investing and networking > Topic 2: Graphs and networks > Planar graphs, paths and cycles

- Understand the meaning of the terms Eulerian graph, Eulerian trail, semi-Eulerian graph, semi-Eulerian trail and the conditions for their existence, and use these concepts to investigate and solve practical problems, e.g. the Königsberg bridge problem, planning a garbage bin collection route

##### Topic 3: Networks and decision mathematics

view_agenda query_statsTrees and minimum connector problems

view_agenda query_statsUnit 4: Investing and networking > Topic 3: Networks and decision mathematics > Trees and minimum connector problems

Project planning and scheduling using critical path analysis (CPA)

view_agenda query_statsUnit 4: Investing and networking > Topic 3: Networks and decision mathematics > Project planning and scheduling using critical path analysis (CPA)

Flow networks

view_agenda query_statsAssigning order and the Hungarian algorithm

view_agenda query_stats