General Mathematics · Past QCAA questions All simple familiar questions

2025 · Paper 1 · Simple familiar

Question 17

[4 marks] Scientific calculator

Topic guidesPremiumTopic guide 1 · Justifying an association

Game plansPremiumGame plan 1 · Bivariate data

The question

Students responded to a survey about their travel time to school.

	Travel less than 15 minutes	Travel 15 minutes or more
Year 6 students	11	6
Year 10 students	3	9

Determine the total number of students in each year level who responded to the survey.

[1 mark]

The survey results suggest there is an association between a student’s year level and their travel time.

Justify the suggested association by comparing the percentages of Year 6 and Year 10 students who travel less than 15 minutes.

[3 marks]

Watch the situation first

Different sized groups, so compare each one against its own total

Every dot is one student. Watch each year level become a bar out of 100%, then see how far apart the two orange shares are.

Year 6 has more students, so raw counts aren’t fair. Percentages of each year level put the two groups on the same scale.

Now for the mathematics

Choose what to divide by, then choose the sentence that earns the mark

The table now has its totals filled in. Pick the total each count should be divided by. The cells you use light up. Then pick the comparison you would write.

	Less than 15 min	15 min or more	Total
Year 6	11	6	17
Year 10	3	9	12
Total	14	15	29

Year 6: 11 travel less than 15 minutes, out of

Year 10: 3 travel less than 15 minutes, out of

Choose a total for each year level. The question asks for the percentage of Year 6 students, and the percentage of Year 10 students.

Which sentence justifies the association?

One of these earns the comparison mark. The other two each miss something the mark needs.

Not enough. The QCAA said it plainly in the 2025 subject report: stating there is a difference is not the same as stating there is a large difference. 45% and 55% are different too, and they would suggest no association. Say how big the gap is.

That’s it. It quotes both percentages, says the gap is large (more than double), and links it back to year level and travel time. The mark only counts if your percentages are worked out above it.

That compares counts, not percentages. There are 17 Year 6 students and only 12 in Year 10, so the counts aren’t on the same scale. The question asks you to compare percentages.

QCAA marking guide · 4 marks

Work through the solution one mark at a time

Try each step yourself before you reveal it. Part a) is one mark for both totals. Part b) has a mark for each percentage and one for the comparison.

Step 1 · part a)1 mark

Add along each row. Every student in a year level is in one column or the other.

$$\begin{aligned}\text{Year 6: }11+6&=17\\\text{Year 10: }3+9&=12\end{aligned}$$

Both totals must be right for this mark.

Marker: correctly identifies both totals

Step 2 · part b)1 mark

The percentage of Year 6 students who travel less than 15 minutes uses the Year 6 total from part a).

$$\frac{11}{17}\times100=64.7\%$$

Any value from 64 to 65 inclusive is accepted, so $65\%$ is fine. Follow-through applies if your total from part a) had a slip.

Marker: calculates percentage of Year 6 students who travel less than 15 minutes

Step 3 · part b)1 mark

Same again for Year 10, out of the Year 10 total.

$$\frac{3}{12}\times100=25\%$$

Dividing by 14 (the column total) or 29 (everyone surveyed) answers a different question and loses this mark.

Marker: calculates percentage of Year 10 students who travel less than 15 minutes

Step 4 · part b)1 mark

Compare the two percentages and say how big the gap is. Double 25% is 50%, and 64.7% is well past that.

The large difference in the percentages for the different year levels (64.7% is more than double 25%) suggests there is an association between a student’s year level and their travel time.

Words like large, significant, substantial or more than double all work. This mark is only awarded when your working above supports the comparison.

Marker: compares percentages to justify suggested association

Putting it all together

Each phrase of the question gave you something

“the total number of students in each year level”

Add along each row: 17 and 12. These become your denominators in part b).

“suggest there is an association”

The QCAA has told you the conclusion. Your job is the evidence.

“Justify”

Justify, don’t assert. Numbers plus a sentence that says how big the gap is.

“the percentages of Year 6 and Year 10 students”

Percentages of each year level, so divide by each row total, not 14 or 29.

“who travel less than 15 minutes”

The first column gives the counts on top: 11 and 3.

“[3 marks]” on part b)

One for each percentage, one for the comparison.

What makes this simple familiar

A two-way table with two rows, and a question that tells you exactly which percentages to compare. You don’t have to decide whether there is an association. The QCAA has already said there is one.

If I had to guess where you might lose marks, it would be the last sentence. The 2025 subject report points out that saying there is a difference is not the same as saying there is a large difference. Say the difference is large, or that 64.7% is more than double 25%. The other trap is dividing by the column total 14 or the grand total 29 instead of each year level’s own total.

Only mark this done when you could do it without help. Reading the solution does not count.

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Question wording and marking-guide steps are from the 2025 QCAA General Mathematics external assessment, © State of Queensland (QCAA) 2025, licensed under CC BY 4.0, and have been adapted. Tangent Tuition is not affiliated with the QCAA.

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