The modules, one by one
Each area below lists the concepts named in the syllabus, what the NESA exam asks of them, and the mistake that most often costs marks.
Area 1 of 5
Algebra
Algebra in Standard 2 exists to describe real situations, so almost every question arrives wrapped in a context. You build and interpret linear models, reading the gradient as a rate and the intercept as a fixed charge, and you compare two linear models by solving them simultaneously, either algebraically or by finding where their graphs cross. Direct variation and inverse variation are treated as models in their own right, including relationships where one quantity varies with the square of another, and the constant of variation has to be found from given data before any prediction can be made. Non-linear work covers quadratic models and reading maximum values off a parabola, exponential growth and decay including the percentage rate implied by the model, and reciprocal relationships. Rearranging a formula to make a different variable the subject sits here too.
What the syllabus lists under this area · 3 points
- Types of relationships (linear, quadratic, exponential, inverse variation modelling)
- Simultaneous linear equations
- Non-linear relationships and their graphs
What the exam asks
Break-even comparisons are a staple: complete a table of charges, graph one plan against another, then state the usage where the plans cost the same. Other parts ask you to find the constant of variation and predict a new value, or to read a maximum and the times either side of it from a quadratic graph. Multiple-choice items test inverse variation and rearranging formulas.
Where marks go missing
Treating a squared relationship as if it were proportional. If braking distance varies with the square of speed, doubling the speed quadruples the distance, so the constant of variation must be calculated from the given pair before any prediction is attempted.
7 real NESA questions indexed on this area →
Area 2 of 5
Measurement
This is the largest practical topic. Non-right-angled trigonometry brings the sine rule, the cosine rule, the area formula using two sides and the included angle, the ambiguous case, and their use in bearings problems, compass radial surveys and angles of elevation and depression. Rates and ratios covers unit conversion, best buys, speed and fuel consumption, energy costs per kilowatt-hour, dividing quantities in a given ratio and applying formulas such as blood alcohol content, including rearranging them. The area and volume strand handles composite shapes, the trapezoidal rule for irregular areas and volumes, surface area of composite solids, and capacity, with density used to convert volume into mass. Latitude, longitude and time zones round the topic out, including working across UTC offsets and the International Date Line.
What the syllabus lists under this area · 4 points
- Non-right-angled trigonometry (sine rule, cosine rule, area of triangle, bearings, radial surveys)
- Rates and ratios (unit conversion, best buys, mixing ratios, speed)
- Further applications of area and volume (composite shapes, trapezoidal rule, surface area, volume of solids)
- Latitude, longitude and time zones
What the exam asks
Expect multi-step questions: two applications of the trapezoidal rule feeding a density calculation, a composite solid whose surface area must be found from a described arrangement, a bearings problem across two triangles, or a radial survey where a collinearity condition supplies the missing angle. Time-zone questions typically run backwards from an arrival time and flight duration.
Where marks go missing
Mixing units inside a single calculation. Lengths left in centimetres while a density is quoted per cubic metre, or a speed in kilometres per hour used with a distance in metres, produces an answer that is wrong by a factor of a thousand and is usually worth no marks.
18 real NESA questions indexed on this area →
Area 3 of 5
Financial Mathematics
Money is examined both by formula and by table. The investments and loans strand covers simple and compound interest, including compounding periods shorter than a year and daily-compounding credit card interest, appreciation and inflation, shares and dividends, GST, wages with overtime and commission, and income tax calculated from a marginal rate table. Loans are handled through reducing-balance amortisation spreadsheets and through tables giving the monthly repayment per one thousand dollars borrowed. Annuities are done using future value and present value factor tables, which you read to find a balance, a required contribution or a starting deposit. Depreciation covers both the straight-line method and the declining-balance method, and questions frequently ask you to compare the two over the same period. Budgeting and interpreting statements sit alongside all of this.
What the syllabus lists under this area · 3 points
- Investments and loans (simple and compound interest, GST, income tax, wages/overtime)
- Annuities (future value, present value, annuity tables)
- Depreciation (straight-line and declining-balance methods)
What the exam asks
Table-reading questions are common and multi-step: find a required periodic contribution from a future value annuity table, then repeat it for a different payment frequency, or use present value factors to size an initial deposit funding scheduled withdrawals. Others complete two rows of an amortisation spreadsheet and then explain, in words, why a repayment below the interest charged never clears the loan.
Where marks go missing
Reading an annuity or repayment table by years and annual rate when contributions are quarterly or monthly. The table is indexed by number of periods and rate per period, so five years of quarterly payments means twenty periods at a quarter of the annual rate.
16 real NESA questions indexed on this area →
Area 4 of 5
Statistical Analysis
The statistics topic is broad. Data displays cover box plots, histograms, dot plots, stem-and-leaf and two-way tables, together with the summary statistics behind them: mean, median, mode, range, interquartile range, standard deviation, outliers and shape. Sampling and data collection deals with random, stratified and systematic samples, self-selected samples and the bias they introduce. Bivariate analysis covers scatterplots, describing correlation by direction, strength and form, the correlation coefficient, and the least-squares regression line, which you may be given, read from a graph, or construct from the mean point and summary statistics, along with the difference between interpolation and extrapolation. The normal distribution introduces z-scores, the empirical rule and standard normal probability tables. Probability covers relative frequency, tree diagrams, complementary events, conditional probability and expected outcomes.
What the syllabus lists under this area · 5 points
- Bivariate data analysis (scatterplots, correlation, least-squares regression line)
- The normal distribution (z-scores, empirical rule)
- Sampling and data collection (sampling methods, bias)
- Data displays and summary statistics (box plots, histograms, two-way tables, measures of central tendency and spread)
- Probability (relative frequency, tree diagrams, conditional and compound probability)
What the exam asks
Questions ask you to plot the mean point and intercept of a regression line, state its equation and then identify a limitation of extrapolating it. Normal distribution parts use a supplied probability table with a stated mean and standard deviation to find an expected count or a cut-off score. Comparison parts ask for skewness, centre and spread from parallel box plots, in words.
Where marks go missing
Answering a 'describe the relationship' question with only a correlation value. Marks are awarded for direction, strength and form stated in the context of the variables, and for naming extrapolation as the reason a prediction beyond the data range cannot be trusted.
14 real NESA questions indexed on this area →
Area 5 of 5
Networks
Networks turns diagrams into decisions. The concepts strand covers drawing a network from a table of distances or connections, weighted edges, degree, connected graphs and trees, finding a shortest path between two vertices, constructing a minimum spanning tree and stating its total weight, and network flow, where cuts are used to bound the maximum flow between a source and a sink. Critical path analysis takes an activity chart with immediate predecessors, builds the network, then uses forward and backward scanning to find earliest start times, latest start times and float for each activity. The critical path is the sequence with zero float and it determines the minimum project duration; crashing asks which single activity to shorten, and by how much, to bring that duration down.
What the syllabus lists under this area · 2 points
- Network concepts (network diagrams, shortest path, minimum spanning trees, network flow/maximum flow)
- Critical path analysis (activity charts, forward/backward scanning, float time, project crashing)
What the exam asks
Typical parts have you complete a partially drawn network from a distance table, find a shortest path and then re-solve it after an edge is removed, or justify whether a given spanning tree is minimal and whether an alternative of equal weight exists. Critical path parts ask for an unknown duration from partial start-time data, the maximum float between two activities, or which task to crash.
Where marks go missing
Naming the critical path from the longest-looking route on the diagram. Only the forward and backward scans identify it, and an activity that looks long can still carry float and sit off the critical path, so shortening it changes nothing about the project duration.
8 real NESA questions indexed on this area →