General Mathematics · Past QCAA questions All simple familiar questions
2023 · Paper 1 · Simple familiar

Question 18

[4 marks] Scientific calculator
The question

The locations of three space research sites in Australia are listed in the table.

Site Coordinates
A32° S 116° E
B32° S 136° E
C12° S 136° E
120° E 130° E 140° E 110° E 120° E 130° E 140° E Northern Territory Western Australia South Australia 10° S 20° S 30° S 40° S 10° S 20° S 30° S 40° S
a)

Which site is closest to the equator?

[1 mark]
b)

Name the state or territory in which site A is located.

[1 mark]
c)

Determine and explain which two sites are in the same standard time zone.

[2 marks]
Watch the situation first

Latitude answers part a), longitude answers part c)

Watch the three sites go on the map. Then follow a parallel for part a), the state border for part b), and the sun’s noon line sweeping west for part c).

Plot the three sites from the table Part a) Latitude measures distance from the equator Part b) Site A is west of the 129° E border Part c) Longitude sets the clock Same longitude, same standard time zone Northern Territory Western Australia South Australia 12° S 32° S 129° E 136° E A B C A 32° S 116° E B 32° S 136° E C 12° S 136° E C is at 12° S. A and B are at 32° S. 12° is the smaller latitude, so site C is closest to the equator. A is at 116° E, west of the 129° E border, so site A is in Western Australia. The sun’s noon line moves west, 15° an hour. It reaches B and C at the same moment, and A later, 20° further west. B and C share 136° E. Same longitude, same sun time, so the same standard time zone.

Latitude says how far north or south. Longitude says what time the sun is overhead. The question is checking that you know which one each part needs.

Now for the mathematics

Pick the pair, then the reason that earns the second mark

Answer part a), then choose a pair of sites and an explanation for part c). The map draws the line or distance your reason relies on, and the feedback tells you which marks your choice would earn.

Northern Territory Western Australia South Australia 12° S 32° S 116° E 136° E A B C

Sites plotted from the table: A (32° S 116° E), B (32° S 136° E), C (12° S 136° E). A ring marks your part a) choice.

a) Closest to the equator
c) Same standard time zone
c) Because they have
Marks so far
a) c)

Part a): which latitude is nearest to 0°?

Part a): that’s it. 12° S is the smallest latitude, so site C is closest to the equator. Writing 12° S is also accepted.

Part c): choose a pair, then the reason. Which coordinate decides what time the sun is overhead?

Part c): now choose the explanation. “Determine and explain” is two marks, and the reason is the second one.

Part c): choose the pair as well. Naming the two sites is its own mark.

QCAA marking guide · 4 marks

Three short answers and one reason

Try each step yourself before you reveal it. Parts a) and b) are one mark each. Part c) has a mark for the pair and a separate mark for the explanation.

Step 1 · part a)1 mark

Latitude is the angle north or south of the equator, so the smallest latitude is closest. Sites A and B are at 32° S and site C is at 12° S.

Site C

Answering “12° S” instead of naming the site is also accepted. Longitude plays no part here, so ignore the 116° E and 136° E.

Marker: correctly names the site

Step 2 · part b)1 mark

Find 116° E on the map. It is a little to the left of the 120° E meridian, and the whole of that strip is west of the dashed border at 129° E. Follow it down to 32° S, a little below the 30° S parallel, and you reach the south-west coast near Perth.

Western Australia

The abbreviation WA is also accepted. The map in the question doesn’t mark the sites, so this part checks that you can read coordinates against the grid.

Marker: correctly names the state

Step 3 · part c)1 mark

Time depends on longitude, so compare the longitudes in the table: 116° E, 136° E and 136° E. Two of them match.

Sites B and C are in the same standard time zone.

Sites A and B share a latitude, 32° S, which is the distractor. Latitude doesn’t affect the time.

Marker: correctly determines sites B and C are in the same standard time zone

Step 4 · part c)1 mark

“Explain” needs a reason written down, and the reason is the shared longitude.

Sites B and C are in the same standard time zone because they have the same longitude, 136° E.

Similar statements are accepted, such as “both sites are at 136° E”. In real life B is in South Australia and C is in the Northern Territory, and both use the same standard time, UTC +9:30, while Western Australia uses UTC +8. Real time zone borders follow state lines, so longitude explains the overall pattern, and it is the reasoning the marker wants. The word “standard” matters too: South Australia uses daylight saving and the Northern Territory doesn’t, so in summer their clocks differ.

Marker: correctly explains using longitude

Putting it all together

Each phrase of the question gave you something

“The locations of three space research sites … are listed in the table.”
Parts a) and c) come straight from the table. Part b) needs the map.
“Which site is closest to the equator?”
Compare latitudes only. The smallest wins: site C at 12° S.
“Name the state or territory in which site A is located.”
116° E is west of the 129° E border, so Western Australia.
“which two sites are in the same standard time zone”
Compare longitudes only. B and C share 136° E.
“Determine and explain”
Two marks. Name the pair, then give the reason, and the reason has to mention longitude.
What makes this simple familiar

Reading coordinates from a table and locating them on a map is Unit 3 Earth geometry at its most direct, and there is no calculation at all. The 2023 subject report listed explaining which two sites share a standard time zone among the things students did well, and used part c) as a sample of effective practice: responses that named both sites and then explained why using longitude, in syllabus terms.

If I had to guess where you might lose marks, it would be part c). A and B share a latitude, 32° S, and the matching numbers make them look like a pair, but latitude says nothing about the clock. The other way to drop a mark is to write “B and C” and stop. “Determine and explain” is two marks, and the second one needs the reason: the shared longitude, 136° E.

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 2023 QCAA General Mathematics external assessment, © State of Queensland (QCAA) 2023, licensed under CC BY 4.0, and have been adapted. Tangent Tuition is not affiliated with the QCAA.