Mathematics Standard • Year 11 • Module 2 • Lesson 21
Time Zones and UTC — Skill Drill
Drill UTC ↔ local time conversions, city-to-city time differences, and the daylight-saving distinction across NSW, QLD, SA, WA and overseas.
1. Quick recall
Answer each question in the space provided. 1 mark each
Q1.1 Complete each Australian standard-time offset:
AEST = UTC ____. AWST = UTC ____. ACST = UTC ____.
Q1.2 During Australian daylight saving:
AEDT = UTC ____. ACDT = UTC ____. The states that do NOT observe daylight saving are: ____________, ____________, ____________.
Q1.3 To convert a local time to UTC, you ____________ the offset. To convert a UTC time to local, you ____________ the offset.
2. Worked example — Sydney to London (via UTC)
Every line of working has a reason on the right.
Problem. It is 3:00 pm Wednesday in Sydney during summer (AEDT = UTC+11). What is the local time in London (UTC+0, winter — no BST)?
Step 1 — Convert local time to UTC.
Sydney 1500 − 11 h = 0400 UTC Wednesday.
Reason: AEDT is UTC+11, so to recover UTC we subtract 11.
Step 2 — Convert UTC to destination local time.
London UTC+0: 0400 + 0 = 0400 Wednesday.
Reason: London winter time equals UTC, no adjustment.
Conclusion. When it is 3:00 pm Wednesday in Sydney, it is 4:00 am Wednesday in London.
3. Faded example — fill in the missing steps
It is 11:30 am Friday in Sydney during winter (AEST = UTC+10). Find the local time in Los Angeles (PST = UTC−8). 4 marks
Step 1 — Sydney → UTC: 1130 − ____ = ____________ UTC Friday.
Step 2 — UTC → LA local: ____________ + (____) = ____________
Step 3 — Negative? Adjust by adding 24 h: ____________ + 2400 = ____________
Step 4 — State the day: Result is on ____________ in LA.
Conclusion. Local time in LA = ____________ (____________ day).
4. Graduated practice — time-zone calculations
Show your working in 24-hour time and state the day where it changes.
Foundation — single-step UTC conversions (4 questions)
| Q | Problem | Answer |
|---|---|---|
| 4.1 1 | UTC = 0700 Monday. Find Sydney AEST (UTC+10). | |
| 4.2 1 | UTC = 1430 Monday. Find Perth AWST (UTC+8). | |
| 4.3 1 | UTC = 1100 Monday. Find New York EST (UTC−5). | |
| 4.4 1 | Sydney AEST = 1900 Tuesday. Convert to UTC. |
Standard — typical HSC difficulty (6 questions)
Always convert to UTC first, then to the destination local.
4.5 It is 2:00 pm in Sydney AEST. Find the time in Tokyo (UTC+9). 2 marks
4.6 It is 10:30 am Tuesday in Sydney AEST. Find the time and day in London (UTC+0). 2 marks
4.7 It is 9:00 am Friday in Perth AWST. Find the time and day in Los Angeles PST (UTC−8). 2 marks
4.8 It is 6:00 pm Wednesday in Sydney AEDT (UTC+11). Find the time and day in Brisbane AEST (UTC+10, no DST). 2 marks
4.9 It is 4:30 am Saturday in London (UTC+0). Find the time and day in Auckland NZST (UTC+12). 2 marks
4.10 It is 8:00 pm Sunday in Adelaide ACDT (UTC+10:30). Find the time and day in Dubai (UTC+4). 2 marks
Extension — daylight-saving complications (2 questions)
4.11 In January (Australian summer), the standard time difference between Sydney AEDT (UTC+11) and Brisbane AEST (UTC+10) is one hour. In July (Australian winter, no DST in either), they are both on UTC+10. (a) In January, if it is 7:00 am in Sydney, what is the time in Brisbane? (b) In July, if it is 7:00 am in Sydney, what is the time in Brisbane? 3 marks
4.12 A friend in Sydney messages a friend in London at 9:00 pm Sydney time. (a) If it is January (Sydney on AEDT = UTC+11; London on GMT = UTC+0), what is the London local time? (b) If it is July (Sydney on AEST = UTC+10; London on BST = UTC+1), what is the London local time? 3 marks
5. Self-check the easy 3
Tick once you've verified each.
How did this worksheet feel?
What I'll revisit before next class:
Q1.1 — Australian standard offsets
AEST = UTC +10. AWST = UTC +8. ACST = UTC +9:30.
Q1.2 — Daylight-saving offsets
AEDT = UTC +11. ACDT = UTC +10:30. States that do NOT observe DST: QLD, NT, WA.
Q1.3 — Direction of conversion
Local → UTC: subtract the offset. UTC → local: add the offset.
Q3 — Faded example (Sydney AEST 11:30 am → LA PST)
Step 1: Sydney → UTC: 1130 − 10 = 0130 UTC Friday. Step 2: UTC → LA: 0130 + (−8) = −0630. Step 3: add 2400 → 1730. Step 4: result is on Thursday in LA (previous day). Conclusion: LA local time = 1730 (5:30 pm) Thursday.
Q4.1 — UTC 0700 Mon → Sydney AEST
0700 + 10 = 1700 Monday (5:00 pm).
Q4.2 — UTC 1430 Mon → Perth AWST
1430 + 8 = 2230 Monday (10:30 pm).
Q4.3 — UTC 1100 Mon → New York EST
1100 − 5 = 0600 Monday (6:00 am).
Q4.4 — Sydney AEST 1900 Tue → UTC
1900 − 10 = 0900 UTC Tuesday.
Q4.5 — Sydney AEST 1400 → Tokyo
UTC = 1400 − 10 = 0400; Tokyo = 0400 + 9 = 1300 (1:00 pm).
Q4.6 — Sydney AEST 1030 Tue → London
UTC = 1030 − 10 = 0030 Tuesday; London = 0030 + 0 = 0030 Tuesday (12:30 am, just after midnight).
Q4.7 — Perth AWST 0900 Fri → LA PST
UTC = 0900 − 8 = 0100 Friday; LA = 0100 − 8 = −0700 → add 2400 → 1700 Thursday (5:00 pm previous day).
Q4.8 — Sydney AEDT 1800 Wed → Brisbane AEST
UTC = 1800 − 11 = 0700 Wed; Brisbane = 0700 + 10 = 1700 Wednesday (5:00 pm). (Brisbane is 1 h behind Sydney during AEDT.)
Q4.9 — London 0430 Sat → Auckland NZST
UTC = 0430 (London = UTC+0); Auckland = 0430 + 12 = 1630 Saturday (4:30 pm).
Q4.10 — Adelaide ACDT 2000 Sun → Dubai
UTC = 2000 − 10:30 = 0930 Sun; Dubai = 0930 + 4 = 1330 Sunday (1:30 pm).
Q4.11 — Sydney vs Brisbane in different seasons
(a) January: Sydney AEDT = UTC+11; Brisbane AEST = UTC+10. Sydney is 1 h ahead. Brisbane = 0700 − 1 = 0600 (6:00 am).
(b) July: both on UTC+10. Brisbane = 0700 (7:00 am) — same as Sydney.
Q4.12 — Sydney 2100 → London, two seasons
(a) January (Sydney UTC+11; London UTC+0): UTC = 2100 − 11 = 1000 same day; London = 1000 + 0 = 1000 (10:00 am).
(b) July (Sydney UTC+10; London UTC+1 BST): UTC = 2100 − 10 = 1100 same day; London = 1100 + 1 = 1200 (noon).