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Skills available for Australia year 12 maths curriculum

Objectives are in black and IXL maths skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.

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11-12.1.1 Consumer arithmetic

  • 11-12. Applications of rates and percentages:

    • 11-12.ACMGM001 review rates and percentages

    • 11-12.ACMGM002 calculate weekly or monthly wage from an annual salary, wages from an hourly rate including situations involving overtime and other allowances and earnings based on commission or piecework

    • 11-12.ACMGM003 calculate payments based on government allowances and pensions

    • 11-12.ACMGM004 prepare a personal budget for a given income taking into account fixed and discretionary spending

    • 11-12.ACMGM005 compare prices and values using the unit cost method

    • 11-12.ACMGM006 apply percentage increase or decrease in various contexts; for example, 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

    • 11-12.ACMGM007 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

    • 11-12.ACMGM008 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.

  • 11-12. Use of spreadsheets:

    • 11-12.ACMGM009 use a spreadsheet to display examples of the above computations when multiple or repeated computations are required; for example, 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.

11-12.1.2 Algebra and matrices

11-12.1.3 Shape and measurement

11-12.2.1 Univariate data analysis and the statistical investigation process

  • 11-12. The statistical investigation process:

    • 11-12.ACMGM026 review the statistical investigation process; for example, identifying a problem and posing a statistical question, collecting or obtaining data, analysing the data, interpreting and communicating the results.

  • 11-12. Making sense of data relating to a single statistical variable:

    • 11-12.ACMGM027 classify a categorical variable as ordinal, such as income level (high, medium, low), or nominal, such as place of birth (Australia, overseas), and use tables and bar charts to organise and display the data

    • 11-12.ACMGM028 classify a numerical variable as discrete, such as the number of rooms in a house, or continuous, such as the temperature in degrees Celsius

    • 11-12.ACMGM029 with the aid of an appropriate graphical display (chosen from dot plot, stem plot, bar chart or histogram), describe the distribution of a numerical dataset in terms of modality (uni or multimodal), shape (symmetric versus positively or negatively skewed), location and spread and outliers, and interpret this information in the context of the data

    • 11-12.ACMGM030 determine the mean and standard deviation of a dataset and use these statistics as measures of location and spread of a data distribution, being aware of their limitations

  • 11-12. Comparing data for a numerical variable across two or more groups:

    • 11-12.ACMGM031 construct and use parallel box plots (including the use of the 'Q1 – 1.5 x IQR' and 'Q3 + 1.5 x IQR' criteria for identifying possible outliers) to compare groups in terms of location (median), spread (IQR and range) and outliers and to interpret and communicate the differences observed in the context of the data

    • 11-12.ACMGM032 compare groups on a single numerical variable using medians, means, IQRs, ranges or standard deviations, as appropriate; interpret the differences observed in the context of the data; and report the findings in a systematic and concise manner

    • 11-12.ACMGM033 implement the statistical investigation process to answer questions that involve comparing the data for a numerical variable across two or more groups; for example, are Year 11 students the fittest in the school?

11-12.2.2 Applications of trigonometry

11-12.2.3 Linear equations and their graphs

11-12.3.1 Bivariate data analysis

  • 11-12. The statistical investigation process:

    • 11-12.ACMGM048 review the statistical investigation process; for example, identifying a problem and posing a statistical question, collecting or obtaining data, analysing the data, interpreting and communicating the results.

  • 11-12. Identifying and describing associations between two categorical variables:

  • 11-12. Identifying and describing associations between two numerical variables:

    • 11-12.ACMGM052 construct a scatterplot to identify patterns in the data suggesting the presence of an association

    • 11-12.ACMGM053 describe an association between two numerical variables in terms of direction (positive/negative), form (linear/non-linear) and strength (strong/moderate/weak)

    • 11-12.ACMGM054 calculate and interpret the correlation coefficient (r) to quantify the strength of a linear association.

  • 11-12. Fitting a linear model to numerical data:

    • 11-12.ACMGM055 identify the response variable and the explanatory variable

    • 11-12.ACMGM056 use a scatterplot to identify the nature of the relationship between variables

    • 11-12.ACMGM057 model a linear relationship by fitting a least-squares line to the data

    • 11-12.ACMGM058 use a residual plot to assess the appropriateness of fitting a linear model to the data

    • 11-12.ACMGM059 interpret the intercept and slope of the fitted line

    • 11-12.ACMGM060 use the coefficient of determination to assess the strength of a linear association in terms of the explained variation

    • 11-12.ACMGM061 use the equation of a fitted line to make predictions

    • 11-12.ACMGM062 distinguish between interpolation and extrapolation when using the fitted line to make predictions, recognising the potential dangers of extrapolation

    • 11-12.ACMGM063 write up the results of the above analysis in a systematic and concise manner.

  • 11-12. Association and causation:

    • 11-12.ACMGM064 recognise that an observed association between two variables does not necessarily mean that there is a causal relationship between them

    • 11-12.ACMGM065 identify possible non-causal explanations for an association, including coincidence and confounding due to a common response to another variable, and communicate these explanations in a systematic and concise manner.

  • 11-12. The data investigation process:

    • 11-12.ACMGM066 implement the statistical investigation process to answer questions that involve identifying, analysing and describing associations between two categorical variables or between two numerical variables; for example, is there an association between attitude to capital punishment (agree with, no opinion, disagree with) and sex (male, female)? is there an association between height and foot length?

11-12.3.2 Growth and decay in sequences

11-12.3.3 Graphs and networks

  • 11-12. The definition of a graph and associated terminology:

    • 11-12.ACMGM078 explain the meanings of the terms: graph, edge, vertex, loop, degree of a vertex, subgraph, simple graph, complete graph, bipartite graph, directed graph (digraph), arc, weighted graph, and network

    • 11-12.ACMGM079 identify practical situations that can be represented by a network, and construct such networks; for example, trails connecting camp sites in a National Park, a social network, a transport network with one-way streets, a food web, the results of a roundrobin sporting competition

    • 11-12.ACMGM080 construct an adjacency matrix from a given graph or digraph.

  • 11-12. Planar graphs:

    • 11-12.ACMGM081 explain the meaning of the terms: planar graph, and face

    • 11-12.ACMGM082 apply Euler's formula, v + f – e = 2, to solve problems relating to planar graphs

  • 11-12. Paths and cycles:

    • 11-12.ACMGM083 explain the meaning of the terms: walk, trail, path, closed walk, closed trail, cycle, connected graph, and bridge

    • 11-12.ACMGM084 investigate and solve practical problems to determine the shortest path between two vertices in a weighted graph (by trial-and-error methods only)

    • 11-12.ACMGM085 explain 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; for example, the Königsberg Bridge problem, planning a garbage bin collection route

    • 11-12.ACMGM086 explain the meaning of the terms: Hamiltonian graph and semi-Hamiltonian graph, and use these concepts to investigate and solve practical problems; for example, planning a sight-seeing tourist route around a city, the travelling-salesman problem (by trial-and-error methods only).

11-12.4.1 Time series analysis

  • 11-12. Describing and interpreting patterns in time series data:

    • 11-12.ACMGM087 construct time series plots

    • 11-12.ACMGM088 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; for example, one-off unanticipated events.

  • 11-12. Analysing time series data:

    • 11-12.ACMGM089 smooth time series data by using a simple moving average, including the use of spreadsheets to implement this process

    • 11-12.ACMGM090 calculate seasonal indices by using the average percentage method

    • 11-12.ACMGM091 deseasonalise a time series by using a seasonal index, including the use of spreadsheets to implement this process

    • 11-12.ACMGM092 fit a least-squares line to model long-term trends in time series data

  • 11-12. The data investigation process:

    • 11-12.ACMGM093 implement the statistical investigation process to answer questions that involve the analysis of time series data.

11-12.4.2 Loans, investments and annuities

  • 11-12. Compound interest loans and investments:

    • 11-12.ACMGM094 use a recurrence relation to model a compound interest loan or investment, and investigate (numerically or graphically) the effect of the interest rate and the number of compounding periods on the future value of the loan or investment

    • 11-12.ACMGM095 calculate the effective annual rate of interest and use the results to compare investment returns and cost of loans when interest is paid or charged daily, monthly, quarterly or six-monthly

    • 11-12.ACMGM096 with the aid of a calculator or computer-based financial software, solve problems involving compound interest loans or investments; for example, determining the future value of a loan, the number of compounding periods for an investment to exceed a given value, the interest rate needed for an investment to exceed a given value.

  • 11-12. Reducing balance loans (compound interest loans with periodic repayments):

    • 11-12.ACMGM097 use a recurrence relation to model a reducing balance loan and investigate (numerically or graphically) the effect of the interest rate and repayment amount on the time taken to repay the loan

    • 11-12.ACMGM098 with the aid of a financial calculator or computer-based financial software, solve problems involving reducing balance loans; for example, determining the monthly repayments required to pay off a housing loan.

  • 11-12. Annuities and perpetuities (compound interest investments with periodic payments made from the investment):

    • 11-12.ACMGM099 use a recurrence relation to model an annuity, and investigate (numerically or graphically) the effect of the amount invested, the interest rate, and the payment amount on the duration of the annuity

    • 11-12.ACMGM100 with the aid of a financial calculator or computer-based financial software, solve problems involving annuities (including perpetuities as a special case); for example, determining the amount to be invested in an annuity to provide a regular monthly income of a certain amount.

11-12.4.3 Networks and decision mathematics

  • 11-12. Trees and minimum connector problems:

    • 11-12.ACMGM101 explain the meaning of the terms tree and spanning tree identify practical examples

    • 11-12.ACMGM102 identify a minimum spanning tree in a weighted connected graph either by inspection or by using Prim's algorithm

    • 11-12.ACMGM103 use minimal spanning trees to solve minimal connector problems; for example, minimising the length of cable needed to provide power from a single power station to substations in several towns

  • 11-12. Project planning and scheduling using critical path analysis (CPA):

    • 11-12.ACMGM104 construct a network to represent the durations and interdependencies of activities that must be completed during the project; for example, preparing a meal

    • 11-12.ACMGM105 use forward and backward scanning to determine the earliest starting time (EST) and latest starting times (LST) for each activity in the project

    • 11-12.ACMGM106 use ESTs and LSTs to locate the critical path(s) for the project

    • 11-12.ACMGM107 use the critical path to determine the minimum time for a project to be completed

    • 11-12.ACMGM108 calculate float times for non-critical activities.

  • 11-12. Flow networks

    • 11-12.ACMGM109 solve small-scale network flow problems including the use of the 'maximum-flow minimum- cut' theorem; for example, determining the maximum volume of oil that can flow through a network of pipes from an oil storage tank (the source) to a terminal (the sink).

  • 11-12. Assignment problems

    • 11-12.ACMGM110 use a bipartite graph and/or its tabular or matrix form to represent an assignment/ allocation problem; for example, assigning four swimmers to the four places in a medley relay team to maximise the team's chances of winning

    • 11-12.ACMGM111 determine the optimum assignment(s), by inspection for small-scale problems, or by use of the Hungarian algorithm for larger problems.