Understand and use Coordinated Universal Time (UTC) and the relationship between time zones around the world expressed as offsets from UTC, including the link between longitude and time, to calculate the local time in different locations

One mark for the time difference: $10 - 1 = 9$ hours. One mark for choosing the correct direction - Madrid has the smaller offset, so it is west of Sydney and its clock is behind, meaning subtract $9$ hours. One mark for the local time WITH the correct date: $7{:}00$ am minus $9$ hours goes back past midnight, so $7 - 9 = -2$, then $-2 + 24 = 22$, that is $10{:}00$ pm on Tuesday (the previous day). A marker awards full marks only if the day change is stated; a bald '$10{:}00$ pm' without 'Tuesday/previous day' typically loses the final mark, because the date is the point of the question.

Part (a), one mark: the cities are on opposite sides of Greenwich, so the longitudes ADD, $20\degree + 130\degree = 150\degree$ - a frequent error is to subtract and get $110\degree$. Part (b), one mark: $150 \div 15 = 10$ hours. Part (c), two marks: City B is east of City A (it is the eastern longitude), so it is ahead - add $10$ hours; $9{:}00$ am $+ 10$ h $= 19{:}00 = 7{:}00$ pm the same day, ahead of City A. Markers reward an explicit 'add because B is east/ahead' statement and the correct same-day note; choosing the wrong direction caps the part at one mark.

Part (a), one mark: $11 - (-10) = 21$ hours, with Sydney ahead (keep the minus sign on Honolulu's offset). Part (b), two marks: Sydney is ahead, so add $21$ hours to Honolulu time. Write $11{:}00$ pm Thursday as $23{:}00$; then $23 + 21 = 44$. Since $44$ exceeds $24$, subtract $24$ and advance the date one day: $44 - 24 = 20$, so $20{:}00 = 8{:}00$ pm on Friday. A marker awards the second mark for the correct add direction and the third for the correctly advanced date; stating $8{:}00$ pm without 'Friday' loses the final mark.

Part (a) - a positive offset is east, so add. A UTC offset is just how many hours to add (if positive) or subtract (if negative):

so Tokyo is at $23{:}00$, that is $11{:}00$ pm the same day.

Part (b) - a negative offset is west, so subtract.

so Buenos Aires is at $11{:}00$, that is $11{:}00$ am the same day. (Neither answer crosses midnight, so the date does not change. Always check whether subtracting takes you before $0{:}00$ or adding takes you past $24{:}00$.)

Find the time difference between the two cities. Subtract the offsets:

so the two cities are $2$ hours apart.

Decide the direction. Perth has the smaller offset, so Perth is west of Sydney and its clock is behind - subtract:

so it is $11{:}00$ am in Perth, the same day. (Sanity check: Australia's east coast is ahead of the west coast, so when Sydneysiders are at lunch, Perth has not reached lunch yet.)

Find the time difference. Subtract the offsets:

Decide the direction. London has the smaller offset, so London is west of Sydney and behind - subtract $10$ hours:

Track the date carefully. Going back $8$ hours from $8{:}00$ am reaches $0{:}00$ (midnight), the start of the same day. There are still $2$ more hours to subtract, which steps into the previous day:

so in London it is $10{:}00$ pm on the previous day. (Subtracting past midnight is the trap here - whenever a westward subtraction goes below $0{:}00$, add $24$ hours and step the date back one day.)

Use the daylight-saving offsets, not the standard ones. In January Sydney is UTC$+11$ and London is UTC$+1$, so find the difference from those:

Decide the direction. London has the smaller offset, so it is west of Sydney and behind - subtract $10$ hours. Write $7{:}00$ pm as $19{:}00$:

Check the date. The result $9{:}00$ stays inside the same day (it did not drop below $0{:}00$), so London is at $9{:}00$ am on the same Saturday. The London answer is $9{:}00$ am Saturday. (Both cities ran their clocks forward by an hour, so the $10$ hour gap happens to be unchanged here - but you must still read each city's correct seasonal offset rather than assume.)

Find the time difference, keeping the half hour. Subtract the offsets, treating New York's as negative:

so the two cities are $14$ hours $30$ minutes apart.

Decide the direction. New York has the smaller offset, so it is west of Adelaide and behind - subtract $14{:}30$ from $8{:}00$ am:

Track the date. Subtracting $8$ hours reaches $0{:}00$, the start of the same day, with $6{:}30$ still to subtract, which steps into the previous day:

so New York is at $5{:}30$ pm on the previous day. (The half-hour zones - Adelaide, Darwin and the central states - are exactly where students drop marks by rounding $9{:}30$ to $9$ or $10$; carry the $30$ minutes through.)

Part (a) - difference in longitude. Both are east of Greenwich, so subtract:

Part (b) - convert degrees to time. The Earth turns $15\degree$ of longitude every hour, so divide the longitude difference by $15$:

so the cities are $7$ hours apart.

Part (c) - apply the difference. City Q is at the larger eastern longitude, so it is further east and its clock is ahead - add $7$ hours:

so City Q is at $5{:}00$ pm, the same day, and it is ahead of City P. (The Sun rises in the east, so the more easterly city reaches each hour first - hence "east is ahead".)

Part (a) - time difference. Subtract the offsets, being careful with the negative:

so Sydney and Los Angeles are $18$ hours apart, with Sydney ahead (it has the larger offset).

Part (b) - Los Angeles time to Sydney time. Sydney is ahead, so add $18$ hours to the Los Angeles time. Start at $6{:}00$ pm Friday, written as $18{:}00$ Friday:

Since $36{:}00$ is past $24{:}00$, subtract $24$ and step the date forward one day:

so kick-off is at $12{:}00$ noon Saturday in Sydney.

Part (c) - Sydney time back to Los Angeles time. Now go the other way: Los Angeles is behind, so subtract $18$ hours from the Sydney time. Start at $9{:}00$ am Sunday, written as $9{:}00$ Sunday:

A negative result means we crossed back over midnight, so add $24$ and step the date back one day:

so it is $3{:}00$ pm Saturday in Los Angeles. (Both parts use the same $18$ hour gap; the only decisions are add-versus-subtract and adjusting the date whenever you pass $0{:}00$ or $24{:}00$.)