Essential Mathematics 2025 v 1.3 Applied (Essential) senior syllabus
IA 1 and IA 3 are problem-solving and modelling tasks. IA 2 is the Unit 3 common internal assessment:5 minutes perusal and 60 minutes working, with the provided formula book and technology, and no personal notes. IA 4 is a school-developed Unit 4 short-response assessment. The 20 original CIA-format papers here use 50 marks, divided into 40 simple familiar,5 complex familiar and 5 complex unfamiliar marks. The current syllabus permits small variation around its 80/10/10 complexity proportions.
Past papers on this subject span more than one syllabus. Papers written under an older one still work as practice, but the units and topics they test have changed — the index labels every paper with the syllabus it was set under.
Historical CIA scope before 2026 · 2023–2025
The units and topics, one by one
Each area below lists the concepts named in the syllabus, what the QCAA exam asks of them, and the mistake that most often costs marks.
- Unit 3 — Calculations
- Unit 3 — Measurement
- Unit 3 — Scales, plans and models
- Unit 3 — Probability and relative frequencies
- Unit 4 — Bivariate graphs and linear models
- Unit 4 — Summarising and comparing data
- Unit 4 — Loans and compound interest
Area 1 of 7
Unit 3 — Calculations
Estimation, decimal rounding, percentages, ratios and consistent units support every topic. Check whether a context requires rounding up, down or to a given precision. Show a formula or a clear calculation pathway, carry unrounded intermediate values, then interpret the answer in context.
What the syllabus lists under this area · 1 point
- Estimation, decimal rounding, percentages, ratios and consistent units support every topic. Check whether a context requires rounding up, down or to a given precision. Show a formula or a clear calculation pathway, carry unrounded intermediate values, then interpret the answer in context.
What the exam asks
Current Unit 3 CIA and school assessment.
Where marks go missing
Distinguish a calculated value from a practical whole-number purchase or count.
Area 2 of 7
Unit 3 — Measurement
Describe prisms, pyramids and their nets. Work with metric length, area, volume, capacity and mass; calculate perimeter, arcs, surface area and volume. Identify exposed surfaces in compound objects and state when a base or join is excluded. Convert squared and cubed units using the correct powers of the conversion factor.
What the syllabus lists under this area · 1 point
- Describe prisms, pyramids and their nets. Work with metric length, area, volume, capacity and mass; calculate perimeter, arcs, surface area and volume. Identify exposed surfaces in compound objects and state when a base or join is excluded. Convert squared and cubed units using the correct powers of the conversion factor.
What the exam asks
Current Unit 3 CIA and school assessment.
Where marks go missing
A diameter is not a radius, and square-unit conversions do not use the linear conversion factor.
Area 3 of 7
Unit 3 — Scales, plans and models
Read scale drawings and find actual dimensions before calculating perimeter, area, quantity or cost. Use Pythagoras and right-triangle trigonometry for lengths and angles, including elevation and depression. Label a diagram, identify the relevant angle and distinguish slant length from perpendicular height.
What the syllabus lists under this area · 1 point
- Read scale drawings and find actual dimensions before calculating perimeter, area, quantity or cost. Use Pythagoras and right-triangle trigonometry for lengths and angles, including elevation and depression. Label a diagram, identify the relevant angle and distinguish slant length from perpendicular height.
What the exam asks
Current Unit 3 CIA and school assessment.
Where marks go missing
A resized plan no longer has its original scale unless it is recalibrated.
Area 4 of 7
Unit 3 — Probability and relative frequencies
List possible outcomes systematically with arrays and tree diagrams. Use probabilities in everyday settings, compare observed relative frequency with a theoretical model, and conduct or interpret simulations. Describe replacement, independence and equal-likelihood assumptions; increasing the number of trials does not guarantee exact agreement with a theoretical probability.
What the syllabus lists under this area · 1 point
- List possible outcomes systematically with arrays and tree diagrams. Use probabilities in everyday settings, compare observed relative frequency with a theoretical model, and conduct or interpret simulations. Describe replacement, independence and equal-likelihood assumptions; increasing the number of trials does not guarantee exact agreement with a theoretical probability.
What the exam asks
Current Unit 3 CIA and school assessment.
Where marks go missing
Probability is current CIA content despite its absence from the selected older CIA papers.
Area 5 of 7
Unit 4 — Bivariate graphs and linear models
Use Cartesian coordinates and linear functions. Describe scatterplot direction, form and strength, use a line of best fit and correlation coefficient, and distinguish prediction within the data from extrapolation. Explain why association alone cannot establish causation and interpret each variable in its context.
What the syllabus lists under this area · 1 point
- Use Cartesian coordinates and linear functions. Describe scatterplot direction, form and strength, use a line of best fit and correlation coefficient, and distinguish prediction within the data from extrapolation. Explain why association alone cannot establish causation and interpret each variable in its context.
What the exam asks
Unit 4 school assessment; outside the current Unit 3 CIA.
Where marks go missing
A straight line need not represent direct proportionality; that additionally requires passage through the origin.
Area 6 of 7
Unit 4 — Summarising and comparing data
Calculate and interpret mean, median, mode, range, interquartile range and standard deviation. Read quartiles, deciles and percentiles from displays, construct or interpret box plots, histograms and back-to-back stem plots, and compare groups with context, centre, spread and unusual values.
What the syllabus lists under this area · 1 point
- Calculate and interpret mean, median, mode, range, interquartile range and standard deviation. Read quartiles, deciles and percentiles from displays, construct or interpret box plots, histograms and back-to-back stem plots, and compare groups with context, centre, spread and unusual values.
What the exam asks
Unit 4 school assessment; outside the current Unit 3 CIA.
Where marks go missing
These statistics appeared in older CIAs but belong to Unit 4 under the syllabus examined from 2026.
Area 7 of 7
Unit 4 — Loans and compound interest
Compare simple and compound interest with consistent rate and time units. Use the annual compound-interest relationship and technology to investigate payment periods. Build and interpret reducing-balance loan tables or spreadsheets, separating interest charged, repayment and remaining principal. Treat every supplied rate or fee as a hypothetical task input.
What the syllabus lists under this area · 1 point
- Compare simple and compound interest with consistent rate and time units. Use the annual compound-interest relationship and technology to investigate payment periods. Build and interpret reducing-balance loan tables or spreadsheets, separating interest charged, repayment and remaining principal. Treat every supplied rate or fee as a hypothetical task input.
What the exam asks
Unit 4 school assessment; outside the current Unit 3 CIA.
Where marks go missing
A nominal annual rate divided by the number of periods is not the same as converting an effective annual rate.