SACE Stage 2 General Mathematics common mistakes
SACE Stage 2 General Mathematics · Understand the traps and how to avoid them.
When computing a reducing-balance loan or investment, the candidate applies the interest rate to the original principal each period instead of to the outstanding balance, or adds the annual interest once per year while repayments are monthly.
The formula sheet lists both simple and compound expressions side by side, and candidates pattern-match to the simpler one under time pressure. They also forget that the quoted annual rate must be divided by the compounding frequency and that interest is charged before the repayment is subtracted within each period.
What to do instead
Before any calculation, write a one-line recurrence such as B(n+1) = B(n) x (1 + r/12) - R and state the period unit explicitly. Test the recurrence on the first two periods by hand, checking that the interest amount shrinks as the balance falls, then use the finance solver or table only after the recurrence is verified.
The candidate reports a monthly repayment or a total interest figure to the nearest cent but leaves the final payment adjustment unmentioned, so the last payment in a schedule does not match the others and the balance does not reach exactly zero.
Candidates treat the computed level payment as exact rather than rounded, and they do not check the closing balance of their amortisation table. The discrepancy is small per period but accumulates, and the question often asks specifically for the final payment.
What to do instead
Always build the schedule to the final period and read the closing balance. If it is not zero, compute the adjusted final payment as the previous balance plus interest, and state it separately. Make a habit of writing the check 'balance after last payment = 0' at the bottom of every schedule.
Inflation, appreciation, or depreciation questions are answered by subtracting or adding a fixed dollar amount per year when the context is a percentage change, or the candidate applies the percentage to the wrong base year.
The words 'rises by 3% per year' and 'rises by $3000 per year' look similar in a wordy stem, and candidates skim. Depreciation by a flat percentage is also confused with straight-line depreciation, which is genuinely linear.
What to do instead
Underline the unit attached to the rate before starting: '% per annum' means a multiplicative model, '$ per annum' means a linear model. Write the model symbolically first, for example V = V0 x (1 - 0.15)^n versus V = V0 - 0.15 x V0 x n, and check that the two give different answers for n = 2 so the distinction is conscious.
The candidate computes a correlation coefficient or a regression line and then describes the relationship in causal language, or extrapolates the line well beyond the range of the data and treats the prediction as reliable.
Statistical software output invites over-interpretation, and candidates have seen 'strong correlation' rewarded in earlier years. The distinction between association and causation, and between interpolation and extrapolation, is a specific syllabus point that is easy to overlook when the arithmetic is the focus.
What to do instead
Adopt a fixed two-sentence reporting template: state strength and direction with the value of r, then state explicitly that the relationship is association only and that predictions are reliable only within the observed data range. Practise by writing the caveat sentence for every regression question attempted, even when it is not asked.
When asked whether a difference between two groups is meaningful, the candidate compares only the sample means and ignores the spread, sample size, and the overlap of the distributions.
The mean is the first statistic computed and the easiest to compare. Candidates have not internalised that a difference of two means can be swamped by within-group variation, and they lack a routine for describing overlap.
What to do instead
Use a structured comparison: report both means, both standard deviations, and the sample sizes, then describe overlap in terms of how many standard deviations separate the means. Conclude with a sentence on whether the difference is likely to be meaningful given the spread, and note that formal significance testing is outside this subject.
The candidate fits a straight line to data that is clearly curved, or fits an exponential to data that has been plotted on ordinary axes without checking whether a log transformation linearises it.
Linear regression is the most practised technique, so it becomes the default. Candidates do not routinely inspect a scatterplot before choosing a model, and they confuse 'the software produced a line' with 'a line is appropriate'.
What to do instead
Make plotting the residual or scatter graph a mandatory first step and record the shape in words. If curvature is present, test a transformation: take logs of the response variable and re-plot, then state whether the transformed data is linear and interpret the parameters in context. Compare the fit of at least two candidate models before choosing.
In a piecewise or step model, the candidate applies one rule across a boundary, for example charging the higher tier rate on the whole quantity rather than only on the portion above the threshold.
Tiered pricing, tax brackets, and stepped rates all require subtracting the threshold before applying the marginal rate, which is an extra algebraic step. Candidates read the table as a single rate schedule and apply it uniformly.
What to do instead
Redraw the rule as a labelled number line with the thresholds marked, then write the function in pieces with the domain of each piece stated. Evaluate the function at each threshold from both sides to confirm continuity where it should hold, and check one value just above a threshold by hand before trusting the formula.
When solving a network problem, the candidate counts a vertex's degree incorrectly because loops and multiple edges are treated as single connections, or they apply a shortest-path or critical-path routine without checking whether the graph is directed or whether all activities must be completed.
Hand-drawn networks in exams include loops and parallel edges that are easy to miss, and candidates carry over an algorithm from one problem type to another without confirming the question's structure. The distinction between a path, a walk, and a trail is also frequently blurred.
What to do instead
Before computing, list every vertex with its incident edges and mark loops as contributing 2 to the degree. Write one sentence classifying the problem: shortest path, minimum spanning tree, or critical path, and note whether the graph is directed. Then apply only the matching algorithm and check the result against the degree sum, which must equal twice the number of edges.
In matrix problems, the candidate multiplies matrices in the wrong order, or attempts a product whose inner dimensions do not match, and does not interpret the entries of the product in the context of the problem.
Matrix multiplication is not commutative, but the notation invites left-to-right reading as if it were. Candidates also focus on arithmetic mechanics and skip the step of naming what each row and column represents, so they cannot detect an order error from the answer.
What to do instead
Before multiplying, write the dimensions of both factors side by side and confirm the inner values agree. Label the rows of the first matrix and the columns of the second in words, then label the product's rows and columns the same way. If the labels do not make sense in the context, the order is wrong.
In a recurrence or difference-equation problem, the candidate generates terms from the wrong starting index, or answers a 'long-term' question by listing many terms instead of finding the steady state algebraically.
Conventions about whether the first term is index 0 or 1 vary between contexts, and candidates do not record which convention the question uses. Listing terms feels safer than solving, but it is slow and error-prone and does not establish the limit.
What to do instead
Write the initial condition explicitly, for example T(0) = 500, before writing the recurrence, and state the index convention in the answer. For long-term behaviour, set T(n+1) = T(n) = L, solve the resulting linear equation for L, and then verify by computing two terms either side to confirm convergence toward that value.