Question 9
The table shows the school start-time preferences of students in different year levels.
| 8 am | 9 am | |
|---|---|---|
| Years 7–9 | 124 | 74 |
| Years 10–12 | 82 | 120 |
What percentage of students in Years 10–12 prefer a start time of 8 am?
Not quite. 20.5% is $82\div400\times100$, a share of all 400 students surveyed. The question only asks about Years 10 to 12, so the whole is that row. In 2025, 7.8% of Queensland students chose (A).
Not quite. 39.8% is $82\div206\times100$, which uses the 8 am column total. That is the share of 8 am supporters who are in Years 10 to 12, a different question. In 2025, 10.0% of Queensland students chose (B).
That’s it. Step through the hints below to see why. In 2025, 77.6% of Queensland students chose (C).
Not quite. 66.1% is $82\div124\times100$, which compares the two 8 am counts. The 124 students are in Years 7 to 9, so they can’t be part of the Years 10 to 12 whole. In 2025, 4.1% of Queensland students chose (D).
| 8 am | 9 am | Total | |
|---|---|---|---|
| Years 7 to 9 | |||
| Years 10 to 12 | |||
| Total |
The part is always the 82 students in Years 10 to 12 who prefer 8 am. What changes the answer is which whole you divide by.
This is option (A). It answers “what percentage of all the students surveyed are in Years 10 to 12 and prefer 8 am?”
This is option (B). It answers “what percentage of the students who prefer 8 am are in Years 10 to 12?”
This is option (C). It answers the question that was asked: of the students in Years 10 to 12, what percentage prefer 8 am?
This is option (D). The 124 students are in Years 7 to 9, so they aren’t a whole that contains the 82. A percentage over 50% here should feel wrong once you see 82 is less than the 120 next to it.
Read the question for the group. “What percentage of students in Years 10 to 12 prefer 8 am?” The words after “of” name the whole.
The whole is the Years 10 to 12 row. Nobody in Years 7 to 9 belongs in this calculation.
The table doesn’t show totals, so add the row yourself.
$$\text{Years 10 to 12: }82+120=202\text{ students}$$
This is a row percentage, because the group the question names is a row.
$$\frac{82}{202}\times100=40.594\ldots\approx40.6\%$$
Check the size. 82 is a bit less than half of 202, so the answer should be a bit less than 50%. That rules out 66.1% straight away.
$$\begin{aligned}\text{Years 10 to 12 total}&=82+120=202\\\frac{82}{202}\times100&=40.594\ldots\approx40.6\%\end{aligned}$$
The group named in the question is Years 10 to 12, so divide by that row’s total.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording is from the 2025 QCAA General Mathematics external assessment, © State of Queensland (QCAA) 2025, licensed under CC BY 4.0, and has been adapted. Tangent Tuition is not affiliated with the QCAA.
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