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Year 12: Mathematics Applications ATAR

Listed Mathematics syllabus content points at Year 12 · Units 3 and 4, in the words of the School Curriculum and Standards Authority (SCSA), Western Australia, with the practice on this site that covers it. Checked against the source on 4 September 2026.

For teaching from January 2025. Mathematical notation is flattened out of the syllabus PDF, so fractions and indices read on one line here. The wording is the syllabus's own.

  • 65syllabus content points
  • 32skills mapped
  • 98%have practice

Coverage is the percentage of listed syllabus content points with at least one linked practice skill; it does not measure how fully every part of an entry is practised. A skill can practise more than one syllabus content point, so some appear more than once below.

Topic 3.1: Bivariate data analysis

  1. 3.1.1review the statistical investigation process: identify a problem; pose a statistical question; collect or obtain data; analyse data; interpret and communicate results Identifying and describing associations between two categorical variables

  2. 3.1.2construct two-way frequency tables and determine the associated row and column sums and percentages

  3. 3.1.3use an appropriately percentaged two-way frequency table to identify patterns that suggest the presence of an association

  4. 3.1.4describe an association in terms of differences observed in percentages across categories in a systematic and concise manner, and interpret this in the context of the data Identifying and describing associations between two numerical variables

  5. 3.1.5construct a scatterplot to identify patterns in the data suggesting the presence of an association

  6. 3.1.6describe an association between two numerical variables in terms of direction (positive/negative), form (linear/non-linear) and strength (strong/moderate/weak)

  7. 3.1.7calculate, using technology, and interpret the correlation coefficient (r) to quantify the strength of a linear association

  8. 3.1.8identify the response variable and the explanatory variable for primary and secondary data

  9. 3.1.9use a scatterplot to identify the nature of the relationship between variables

  10. 3.1.10model a linear relationship by fitting a least-squares line to the data

  11. 3.1.11use a residual plot to assess the appropriateness of fitting a linear model to the data

  12. 3.1.12interpret the intercept and slope of the fitted line

  13. 3.1.13use the coefficient of determination to assess the strength of a linear association in terms of the explained variation

  14. 3.1.14use the equation of a fitted line to make predictions

  15. 3.1.15distinguish between interpolation and extrapolation when using the fitted line to make predictions, recognising the potential dangers of extrapolation

  16. 3.1.16report the results of the above analysis in a systematic and concise manner

    No practice for this one yet.

  17. 3.1.17recognise that an observed association between two variables does not necessarily mean that there is a causal relationship between them

  18. 3.1.18recognise 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

  19. 3.1.19implement the statistical investigation process to answer questions that involve identifying, analysing and describing associations between two categorical variables or between two numerical variables

Topic 3.2: Growth and decay in sequences

  1. 3.2.1use recursion to generate an arithmetic sequence

  2. 3.2.2display the terms of an arithmetic sequence in both tabular and graphical form and demonstrate that arithmetic sequences can be used to model linear growth and decay in discrete situations

  3. 3.2.3deduce a rule for the 𝑛𝑡ℎ term of a particular arithmetic sequence from the pattern of the terms in an arithmetic sequence, and use this rule to make predictions

  4. 3.2.4use arithmetic sequences to model and analyse practical situations involving linear growth or decay

  5. 3.2.5use recursion to generate a geometric sequence

  6. 3.2.6display the terms of a geometric sequence in both tabular and graphical form and demonstrate that geometric sequences can be used to model exponential growth and decay in discrete situations

  7. 3.2.7deduce a rule for the 𝑛𝑡ℎ term of a particular geometric sequence from the pattern of the terms in the sequence, and use this rule to make predictions

  8. 3.2.8use geometric sequences to model and analyse (numerically, or graphically only) practical problems involving geometric growth and decay

  9. 3.2.9use a general first-order linear recurrence relation to generate the terms of a sequence and to display it in both tabular and graphical form

  10. 3.2.10generate a sequence defined by a first-order linear recurrence relation that gives long term increasing, decreasing or steady-state solutions

  11. 3.2.11use first-order linear recurrence relations to model and analyse (numerically or graphically only) practical problems

Topic 3.3: Graphs and networks

  1. 3.3.1demonstrate the meanings of, and use, 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

  2. 3.3.2identify practical situations that can be represented by a network, and construct such networks

  3. 3.3.3construct an adjacency matrix from a given graph or digraph and use the matrix to form multi-stage matrices to solve associated problems

  4. 3.3.4demonstrate the meanings of, and use, the terms: planar graph and face

  5. 3.3.5apply Euler’s formula, 𝑣 + 𝑓 − 𝑒 = 2 to solve problems relating to planar graphs

  6. 3.3.6demonstrate the meanings of, and use, the terms: walk, trail, path, closed walk, closed trail, cycle, connected graph, and bridge

  7. 3.3.7investigate and solve practical problems to determine the shortest path between two vertices in a weighted graph (by trial-and-error methods only)

  8. 3.3.8demonstrate the meanings of, and use, 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

  9. 3.3.9demonstrate the meanings of, and use, the terms: Hamiltonian graph and semi- Hamiltonian graph, and use these concepts to investigate and solve practical problems

Topic 4.1: Time series analysis

  1. 4.1.1construct time series plots

  2. 4.1.2describe 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

  3. 4.1.3smooth time series data by using a simple moving average, including the use of spreadsheets to implement this process

  4. 4.1.4calculate seasonal indices by using the average percentage method

  5. 4.1.5deseasonalise a time series by using a seasonal index, including the use of spreadsheets to implement this process

  6. 4.1.6fit a least-squares line to model long-term linear trends in time series data

  7. 4.1.7predict from regression lines, making seasonal adjustments for periodic data

  8. 4.1.8implement the statistical investigation process to answer questions that involve the analysis of time series data

Topic 4.2: Loans, investments and annuities

  1. 4.2.1use 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

  2. 4.2.2calculate 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

  3. 4.2.3with the aid of a calculator or computer-based financial software, solve problems involving compound interest loans, investments and depreciating assets Reducing balance loans (compound interest loans with periodic repayments)

  4. 4.2.4use 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

  5. 4.2.5with the aid of a financial calculator or computer-based financial software, solve problems involving reducing balance loans Annuities and perpetuities (compound interest investments with periodic payments made from the investment)

  6. 4.2.6use 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

  7. 4.2.7with the aid of a financial calculator or computer-based financial software, solve problems involving annuities (including perpetuities as a special case)

Topic 4.3: Networks and decision mathematics

  1. 4.3.1identify practical examples that can be represented by trees and spanning trees

  2. 4.3.2identify a minimum spanning tree in a weighted connected graph, either by inspection or by using Prim’s algorithm

  3. 4.3.3use minimal spanning trees to solve minimal connector problems Project planning and scheduling using critical path analysis (CPA)

  4. 4.3.4construct a network to represent the durations and interdependencies of activities that must be completed during the project

  5. 4.3.5use forward and backward scanning to determine the earliest starting time (EST) and latest starting times (LST) for each activity in the project

  6. 4.3.6use ESTs and LSTs to locate the critical path(s) for the project

  7. 4.3.7use the critical path to determine the minimum time for a project to be completed

  8. 4.3.8calculate float times for non-critical activities

  9. 4.3.9solve small-scale network flow problems, including the use of the ‘maximum flow-minimum cut’ theorem

  10. 4.3.10use a bipartite graph and/or its tabular or matrix form to represent an assignment/ allocation problem

  11. 4.3.11determine the optimum assignment(s), by inspection for small-scale problems, or by use of the Hungarian algorithm for larger problems

Other Year 12 skills

Year 12 skills not currently linked to an entry on this page. These may include revision, extension practice, or skills still awaiting a curriculum mapping.

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