Mathematics Standard • Year 11 • Module 2 • Lesson 21
Time Zones and UTC — Past-Paper Style
HSC Mathematics Standard 2-style writing on time zones: short answers and one structured extended response with explicit marking criteria.
1. Short-answer questions
1.1 It is 0400 UTC on a Tuesday. Find the local time and day in Sydney (AEST = UTC+10) and in Los Angeles (PST = UTC−8). 3 marks Band 3
1.2 A sporting event begins at 7:30 pm Saturday in London (GMT = UTC+0, winter).
(a) Convert this time to UTC.
(b) State the local time and day in Sydney (AEDT = UTC+11, summer). 3 marks Band 3–4
1.3 In January (Australian summer), Sydney observes AEDT (UTC+11) but Brisbane stays on AEST (UTC+10). In July (Australian winter) both cities are on AEST (UTC+10).
(a) If it is 10:00 am in Sydney in January, what time is it in Brisbane?
(b) If it is 10:00 am in Sydney in July, what time is it in Brisbane?
(c) Explain in one sentence why the difference between Sydney and Brisbane changes with the season. 4 marks Band 4
2. Extended response
2.1 A flight departs Sydney at 9:40 pm on a Thursday in January, when Sydney is on AEDT (UTC+11). The flight takes 14 hours 30 minutes to reach Dubai (UTC+4, all year — no DST).
(a) Convert the Sydney departure time to UTC.
(b) Calculate the UTC arrival time, stating the day.
(c) Convert the UTC arrival to Dubai local time, stating the day in Dubai.
(d) The traveller has a connecting flight from Dubai to London that departs Dubai at 9:00 am the following morning. How many hours and minutes does the traveller have to wait in Dubai? 7 marks Band 5–6
Explicit marking criteria
Part (a) — 1 mark
• 1 mark — correctly converts 2140 AEDT to 1040 UTC by subtracting 11.
Part (b) — 2 marks
• 1 mark — correctly adds 14 h 30 min to UTC departure including midnight handling.
• 1 mark — correct UTC arrival 0110 Friday.
Part (c) — 2 marks
• 1 mark — adds Dubai offset (+4) to UTC arrival.
• 1 mark — correct Dubai local 0510 Friday.
Part (d) — 2 marks
• 1 mark — correctly computes elapsed time between 0510 Fri and 0900 Sat Dubai local.
• 1 mark — final answer 27 h 50 min, clearly stated.
Your response:
Stuck on (b)? 1040 + 14 h = 0040 next day; + 30 min = 0110 next day.How did this worksheet feel?
What I'll revisit before next class:
1.1 — UTC 0400 Tue → Sydney and LA (3 marks)
Sample response.
Sydney AEST = 0400 + 10 = 1400 Tuesday (2:00 pm).
Los Angeles PST = 0400 − 8 = −0400 → add 2400 → 2000 Monday (8:00 pm previous day).
Marking notes. 1 mark — Sydney value correct. 1 mark — LA value correct numerically. 1 mark — explicit "Monday" (previous day) noted for LA. A bare "2000" without the day rollover loses a mark.
1.2 — London 7:30 pm Sat → Sydney (3 marks)
(a) Sample response. London = UTC+0 → 7:30 pm = 1930 → 1930 UTC Saturday.
(b) Sample response. Sydney AEDT = 1930 + 11 = 3030 → subtract 2400 = 0630 Sunday (6:30 am next day).
Marking notes. (a) 1 mark — correct UTC. (b) 1 mark — correct local time. 1 mark — explicit "Sunday" day rollover stated.
1.3 — Sydney/Brisbane in two seasons (4 marks)
(a) Sample response. January: Sydney AEDT (UTC+11), Brisbane AEST (UTC+10). Sydney is 1 h ahead → Brisbane = 1000 − 1 = 0900 (9:00 am).
(b) Sample response. July: both on UTC+10. Brisbane = 1000 (10:00 am) — same.
(c) Sample response. Sydney observes daylight saving in summer (AEDT = UTC+11) but Brisbane does not — Queensland keeps AEST year-round, so the gap opens up to 1 h in summer and closes to 0 in winter.
Marking notes. (a) 1 mark. (b) 1 mark. (c) 1 mark — correctly identifies which state observes DST. 1 mark — clear cause-effect explanation in one sentence.
2.1 — Sydney → Dubai → London, sample Band-6 (7 marks)
Sample Band-6 response.
(a) Sydney departure in UTC.
Sydney 9:40 pm AEDT = 2140; UTC = 2140 − 11 = 1040 UTC Thursday. [1 mark.]
(b) UTC arrival.
UTC arrival = 1040 + 14 h 30 min. 1040 + 14 h = 2440 → subtract 2400 → 0040 next day (Friday). [1 mark — midnight crossing handled.]
+ 30 min: 0040 + 30 min = 0110 Friday. UTC arrival = 0110 UTC Friday. [1 mark.]
(c) Dubai local arrival.
Dubai = UTC+4: 0110 + 4 = 0510 Friday. [1 mark — offset applied. 1 mark — local time and day correctly stated.]
(d) Wait time in Dubai.
Connecting flight departs 0900 Saturday (Dubai local). Wait = from 0510 Friday to 0900 Saturday.
From 0510 Friday to 0510 Saturday = 24 h. From 0510 Saturday to 0900 Saturday = 3 h 50 min. [1 mark — correct interval calculation.]
Total wait = 24 + 3 h 50 min = 27 h 50 min in Dubai. [1 mark — clear final wait.]
Conclusion: the traveller arrives in Dubai at 0510 Friday local time and waits 27 h 50 min for the 0900 Saturday connection to London.
Total: 7/7.
Band descriptors for marker.
Band 3: Correctly converts Sydney departure to UTC but errors when adding the long 14 h 30 min flight time (forgets midnight rollover); does not attempt (d). ≈ 2–3 marks.
Band 4: Parts (a)–(c) numerically correct but does not state the day in (b) or (c); attempts (d) but only computes within one day (gives 3 h 50 min instead of 27 h 50 min). ≈ 4–5 marks.
Band 5: Full correct calculation including day rollover; bare answer in (d) ("27 h 50 min") without a clear conclusion sentence. ≈ 6 marks.
Band 6: Complete and correct throughout, with day stated at every conversion, midnight handled cleanly, and a clear conclusion sentence in (d). 7/7.