QCAA General Maths EA common mistakes
QCAA General Maths EA · Understand the traps and how to avoid them.
When asked for a bivariate data association, the candidate reports Pearson's r and a conclusion of 'strong positive' without first inspecting the scatterplot for curvature or outliers, and without checking whether the relationship is linear.
Students treat r as an automatic first step because it is the most practised calculation, and the formula gives a number for any data set, so nothing flags non-linearity. The syllabus emphasis on choosing a model based on the shape of the scatterplot is easily lost under exam time pressure.
What to do instead
Adopt a fixed written sequence for every bivariate question: sketch or describe the scatterplot, state the form (linear/non-linear), direction and strength, check for outliers, then only calculate r if the form is linear. Practise on data sets that are clearly curved or contain a single influential point so the mismatch between 'r = 0.9' and 'obviously curved' becomes familiar.
The candidate computes a least-squares regression line, then uses it to predict for an x-value far outside the observed data range and states the prediction as reliable, without commenting on extrapolation.
Prediction questions look like simple substitution tasks, and the arithmetic works for any x. Students conflate 'the model gives an answer' with 'the model is trustworthy', and the requirement to justify reliability is a separate skill from calculating.
What to do instead
Build a two-part answer template: (1) substitute and compute, (2) state whether the value is within the data range and therefore interpolation, or outside it and therefore extrapolation whose reliability cannot be assumed. Always quote the actual minimum and maximum x-values from the data when justifying.
When interpreting a coefficient of determination, the candidate writes 'r-squared = 0.81, so the correlation is 0.81' or '81% of the data points lie on the line', rather than describing the proportion of variation in the response variable explained by the regression on the explanatory variable.
The squared relationship and the word 'determination' invite confusion with r itself, and percentage language tempts students toward a 'percentage of points' reading. Textbooks and software output present r-squared without interpretation practice, so the phrase is memorised loosely.
What to do instead
Memorise one exact sentence frame and rehearse it aloud: 'Approximately [X]% of the variation in [response variable] can be explained by the linear relationship with [explanatory variable].' Explicitly contrast this with r in a comparison table, and practise converting between r and r-squared in both directions.
The candidate calculates a residual as observed minus predicted reversed, or reports a residual without units and sign meaning, so that a positive residual is described as 'below the line'.
The order of subtraction is arbitrary unless memorised deliberately, and students often compute quickly under time pressure. The graphical meaning of a residual (vertical distance from point to line) is understood but not linked to the arithmetic sign.
What to do instead
Fix the definition as residual = observed − predicted and always annotate a sketch: a point above the line has a positive residual. Practise by plotting residuals against the explanatory variable and checking that the pattern of signs matches the position of points relative to the line.
In a normal distribution question, the candidate finds a probability or proportion but does not convert it to the number of individuals asked for, or uses the population standard deviation instead of the standard error when the question concerns the mean of a sample.
Two separate slips combine: forgetting the final multiplication by the total, and failing to distinguish the distribution of individual values from the sampling distribution of the mean. Both produce plausible-looking numbers, so no alarm is raised.
What to do instead
Before calculating, write down what the random variable represents: a single observation or a sample mean. If it is a sample mean, immediately write the standard error as sigma over root n. After obtaining a proportion, always ask 'does the question want a proportion or a count?' and multiply by the total if needed.
The candidate states a conclusion about a hypothesis test or confidence interval in terms of the sample statistic rather than the population parameter, for example 'there is evidence that the sample mean is greater than 50'.
The calculation is about the sample, so the language of the working bleeds into the conclusion. Students also avoid the more abstract population phrasing because it feels less concrete, and the distinction is rarely drilled as a writing task.
What to do instead
Write conclusions using a fixed stem that names the population: 'There is sufficient evidence at the 5% level to conclude that the population mean ... is greater than ...'. Underline the word 'population' in every draft conclusion and check the direction of the claim matches the alternative hypothesis.
When a question asks whether a result is statistically significant, the candidate compares the p-value to the wrong threshold, or treats a small p-value as proof that the null hypothesis is false rather than as evidence against it.
The logic of hypothesis testing is conditional and probabilistic, which is genuinely counterintuitive. Students default to binary 'true or false' reasoning and to memorised phrases without understanding the strength-of-evidence idea.
What to do instead
Practise writing conclusions at three p-values (0.001, 0.04, 0.20) for the same scenario and note how the strength of language changes. Always state the significance level being used before comparing, and include the phrase 'evidence against' rather than 'proof' in every written conclusion.
The candidate constructs a confidence interval but interprets it as 'there is a 95% probability that the population mean lies in this particular interval', rather than describing the long-run capture rate of the procedure.
The interval is a fixed set of numbers once computed, but the probability statement belongs to the method, not the realised interval. This subtlety is frequently taught quickly and the intuitive (but wrong) reading is reinforced by everyday language.
What to do instead
Use the exact phrasing 'We are 95% confident that the population mean lies between ...' and be able to explain in one sentence why 'probability' is wrong for a computed interval. Also practise checking that the interval is centred on the sample mean and that the margin of error equals the half-width.
In a question involving a transition matrix or a recurrence relation, the candidate multiplies matrices in the wrong order, or applies the recurrence without matching the initial state to the correct time index, producing an answer that is off by one step.
Matrix multiplication is not commutative, and the convention for whether the state vector is a row or column is easy to mix up. Off-by-one errors arise because the initial state is often labelled period 0 while the question asks for period n.
What to do instead
Always write the state vector and transition matrix dimensions explicitly before multiplying, and confirm the order gives a vector of the correct size. For recurrences, build a small table of values for the first three or four periods so the indexing convention is visible, then read the requested period directly from the table.
The candidate solves a network or scheduling problem by inspection and reports a route or duration without demonstrating that it is optimal, or finds the critical path but does not report the float times or the effect of a delay on a non-critical activity.
These problems reward a plausible-looking answer, so students stop once they have one number. The requirement to justify optimality and to interpret float values is a separate skill from finding a path, and it is often under-practised.
What to do instead
For every network question, produce the full forward and backward pass table with earliest and latest start times, then derive the critical path from zero float rather than by eye. When asked about a delay, compare the delay to the float of that activity and state explicitly whether the project duration changes.