WACE Maths Applications common mistakes
WACE Maths Applications · Understand the traps and how to avoid them.
Reading a value off a hand-drawn or supplied graph (e.g. a break-even point or a trend value) and quoting it to the nearest whole unit or to more precision than the grid allows, rather than stating the value with the accuracy the scale supports.
Students treat graph-reading as exact arithmetic and default to calculator-style precision, forgetting that a point located by eye carries uncertainty of roughly half a grid square, so the answer is over-precise and often outside the accepted range.
What to do instead
Before reading, note the value of one small grid square on each axis and quote answers to that increment (or half of it), and where the question says 'estimate', explicitly round to the nearest marked division. Practise by reading the same point three times and checking the spread of your readings.
When a question gives data with units in different scales (e.g. grams and kilograms, or minutes and hours), substituting the raw numbers straight into a formula without converting, then reporting a final answer that is wrong by a factor of 1000 or 60.
The formula is recalled as a string of letters with no attached units, so students plug in whatever number appears next to each variable, and the unit mismatch is invisible on the calculator display.
What to do instead
Write the unit beside every substituted number in the working line, and carry units through the calculation as if they were algebraic symbols; if the resulting unit is not the one asked for, a conversion is missing. Convert all data to a single consistent unit set before starting.
Drawing a line of best fit by joining the first and last data points, or by eye through the middle, instead of placing it so that the vertical deviations of points above and below the line roughly balance, and then using that line to predict.
Joining extreme points is a quick visual shortcut that feels objective, and students have often only seen 'draw a line through the points' without the balancing-of-residuals idea being made explicit.
What to do instead
Use the mean point (mean of x, mean of y) as an anchor the line must pass through, then rotate the line until the total vertical distance above equals the total below. Check by counting points above and below and by confirming the line passes through the mean point.
Treating a strong correlation coefficient as proof that one variable causes the other, and writing a conclusion such as 'increasing study time causes higher scores' from observational data alone.
The numerical strength of r is visually compelling and the syllabus spends much time computing it, so students conflate strength of association with causal mechanism and overlook lurking variables.
What to do instead
Adopt a fixed sentence pattern: 'There is a strong positive association between X and Y; this does not establish that X causes Y because a third variable such as Z could influence both.' Always name at least one plausible confounding variable before making any recommendation.
Computing a seasonal index and then applying it by multiplying the raw value by the index, when the index was calculated as an average percentage of the overall mean and should be used as a ratio to deseasonalise by division, or to forecast by multiplication onto a trend value.
The direction of the operation depends on how the index was defined, and students memorise 'multiply by the index' without tracking whether they are removing or imposing seasonality.
What to do instead
State in words what the index means before using it ('a value of 112 means this quarter is typically 12% above the annual average'). To deseasonalise, divide the actual by the index; to forecast, multiply the trend by the index. Sanity-check that a high index produces a high forecast.
In a loan or investment, applying the interest rate per compounding period but using the number of years as the number of periods (or vice versa), and mixing a nominal annual rate into a formula that expects a periodic rate.
Recurrence and compound interest formulas both contain a rate and a count, and both letters look familiar, so the periodic conversion step is dropped under time pressure.
What to do instead
Always write the two conversion lines first: periodic rate = annual rate divided by compounds per year, and number of periods = years times compounds per year. Only then substitute. Finish by checking the answer is plausible against a simple single-year estimate.
Confusing the present value and future value roles in annuity and loan formulas, for example reporting the total of all repayments as the amount borrowed, or using the future value formula when the question asks for the lump sum needed today.
The formula sheet lists several similar-looking expressions, and students select by pattern-matching the words in the question rather than by identifying which quantity is at which point in time.
What to do instead
Draw a timeline before choosing a formula, marking each cash flow with its date, and label the unknown as 'value now' or 'value later'. For loans, separately compute the total repaid and the interest paid as total repayments minus principal, and state both if asked.
When constructing or interpreting a network diagram, counting an activity's earliest start time from the immediately preceding activity only, ignoring that other parallel paths into the same node may finish later, so float and critical path are wrong.
Students scan left to right and take the nearest predecessor, whereas the earliest start is the maximum of all incoming path completions, a maximisation step that is easy to skip.
What to do instead
At every node, write down the finish time arriving along each incoming path and circle the largest; that is the earliest start. Then do the backward pass taking the minimum. Confirm the critical path has zero float at every node and that its duration equals the project duration.
Reading a matrix or transition diagram as if rows and columns were interchangeable, so a transition probability is taken from the wrong cell, or a state vector is multiplied on the wrong side of the matrix.
The convention that rows sum to one and that the state vector is a row vector multiplied on the left is a notational habit, and students who have seen both conventions in different contexts apply the wrong one.
What to do instead
Before any calculation, label the rows and columns in words on the matrix and check that each row sums to 1. Write the multiplication explicitly as a row vector times the matrix, and verify the resulting entries still sum to 1, which catches a transposed matrix immediately.
Giving a bare numerical answer to a modelling question with no statement of what the number represents, no units, and no comment on the reasonableness of the result in the context of the original problem.
Students treat the final calculation as the end of the task because practice exercises often stop there, but the syllabus and marking keys reward interpretation and evaluation of the model against the real situation.
What to do instead
End every response with a context sentence containing the quantity, its units and its meaning, plus one sentence judging plausibility (for example whether a predicted value lies outside the range of the data or implies an impossible negative quantity). Build this into a checklist used on every practice question.