SACE Stage 2 Essential Mathematics common mistakes
SACE Stage 2 Essential Mathematics · Understand the traps and how to avoid them.
When a question asks for a value 'per week' or 'per year', the candidate uses the rate exactly as given (e.g. a monthly rate) without multiplying or dividing by the time conversion factor.
The candidate focuses on the arithmetic of the calculation and treats the unit label as decoration, so the conversion step is skipped entirely rather than forgotten mid-way.
What to do instead
Before calculating, rewrite the required output unit at the top of the working (e.g. 'answer in $/week') and write the conversion as an explicit fraction (12 months / 1 year) that cancels the unwanted unit. Check that the units left after cancelling match the requested output.
The candidate rounds a running total at every intermediate step and then reports a final answer that differs from the exact value by a visible amount (often in money questions).
Habit from earlier years of writing every displayed calculator value to two decimal places, combined with not distinguishing 'displayed value' from 'stored value' on the calculator.
What to do instead
Keep full precision in calculator memory or the answer key, round only the final result, and state the rounding explicitly ('= $47.83 to the nearest cent'). Where a question specifies a rounding convention, underline it before starting.
In a percentage-change or mark-up/discount question, the candidate applies the percentage to the already-changed amount, or computes the new price by subtracting the discount from the percentage rather than from the original price.
The candidate pattern-matches on 'discount' and reaches for subtraction without identifying which quantity is the base of the percentage.
What to do instead
Write the base explicitly before calculating: 'base = original price'. Then use a multiplier (1 ± r) rather than two separate operations, and sanity-check that a 20% discount leaves 80% of the original, not 20% less than some other figure.
The candidate reads a value from a table, graph, or schedule but takes the figure from the wrong row, column, or time band (for example, the off-peak rate instead of the peak rate), and the rest of the working is correct.
Under time pressure the candidate scans for the number that looks relevant rather than tracing the row and column headers, and tables in these questions often place similar values close together.
What to do instead
Trace with a finger or the cursor from the row label and the column label to the intersection, and write the full label beside the number when copying it ('peak, weekday, first 100 units = ...'). Re-read the question's conditions and tick each one against the copied value.
When calculating a mean, median, or range from a frequency table or grouped data, the candidate divides by the number of rows instead of the total frequency, or takes the midpoint of the class containing the median without locating the position properly.
The candidate treats the table as a list of values and forgets that each row represents many observations.
What to do instead
Add a total-frequency column and compute n first. For the median, compute (n+1)/2 and find which class contains that position before estimating. For the mean from grouped data, use the class midpoint multiplied by frequency, and check that the frequencies sum to n.
The candidate constructs a scale drawing or uses a given scale but applies it in the wrong direction, giving an answer that is out by a factor of the scale (for example, 1:200 applied as multiply by 200 when converting a plan length to a real length, or vice versa).
The ratio notation is read as an operation rather than as a statement of equivalence between two lengths, so direction is guessed.
What to do instead
Write the scale as an equation with units: '1 cm on plan = 200 cm real'. Then substitute the known quantity on the correct side and solve. Check plausibility: a room should not come out 40 m long when the plan shows 20 cm at 1:200 unless the arithmetic supports it.
In a right-triangle or measurement problem the candidate substitutes into a formula without first converting all lengths to the same unit, mixing centimetres and metres in one calculation.
The numbers are extracted from a diagram or text in the order they appear, and unit labels are dropped once the numbers are on the page.
What to do instead
Convert every given quantity to a single working unit before writing the formula, and annotate each converted value with its unit. Carry units through the calculation so a mismatched result (e.g. cm·m) is visible.
The candidate gives a probability or relative-frequency answer as a count rather than as a proportion, or reports a probability greater than 1 after adding outcomes that are not mutually exclusive.
The candidate confuses 'how many' with 'how likely' and does not check whether the events being combined can occur together.
What to do instead
State the definition being used ('relative frequency = favourable outcomes / total outcomes') and finish with a value between 0 and 1 unless a percentage is requested. Before adding probabilities, ask whether the events can overlap; if they can, subtract the overlap.
The candidate answers a 'show that' or 'justify your answer' question with only the final number, omitting the reasoning or comparison that the question demands, and loses the communication marks even when the number is right.
The candidate treats every question as a calculation task and stops as soon as a number appears on the page.
What to do instead
Underline the command word (show, justify, compare, explain) and write a sentence that directly addresses it, referencing the calculated values. For comparisons, state both quantities and the direction of the difference explicitly.
The candidate produces a correct calculation but does not return to the question to check that the answer is sensible in context, so an implausible result (a negative time, a loan repayment larger than the loan, a fuel cost of thousands of dollars for a short trip) is submitted unchanged.
Once a number is obtained the candidate moves on to the next question, and there is no habitual final check against the real-world setting.
What to do instead
Reserve the last minute of each question for a plausibility test: estimate the answer roughly before calculating, then compare. If the two differ by more than a small factor, re-read the question and recheck the units and the operation before moving on.