QCAA General Mathematics Earth geometry and time zones

This option assumes a 4-hour time difference (UTC+12 vs UTC+8). However, the question explicitly states that New Zealand is UTC+13 during the winter, creating a 5-hour difference.

This result implies adding 4 hours to the time. Since Perth is west of New Zealand, the time there is earlier, so the time difference must be subtracted, not added.

This calculation incorrectly adds the 5-hour time difference to the scheduled time. Because Perth is in a time zone behind New Zealand (UTC+8 vs UTC+13), you must subtract the difference.

This option reverses the reference lines; latitude (North/South) is measured from the equator, and longitude (East/West) is measured from the prime meridian.

Latitude is measured relative to the equator, not the International Date Line, and longitude is measured relative to the prime meridian, not the equator.

While the latitude reference is correct, longitude is measured relative to the prime meridian ($0^\circ$), not the International Date Line (approx. $180^\circ$).

This value is incorrect and does not correspond to the proper calculation for the distance between these two coordinates.

This would be the distance if both locations were in the same hemisphere, which would involve subtracting the latitudes ($18.7^\circ - 12.4^\circ = 6.3^\circ$) instead of adding them.

This distance is incorrect and results from a miscalculation of the latitude difference or the Earth's radius.

The cities share the same longitude, but the latitude difference is only $1^\circ$ ($3^\circ$ N minus $2^\circ$ N). This results in a distance of approximately $111$ km, which is far less than $556$ km.

The latitude difference between these points is $55^\circ$ ($25^\circ$ N plus $30^\circ$ S). Multiplying by $111$ km per degree yields a distance of over $6,000$ km.

These cities share the same latitude, so the distance is calculated using the longitude difference ($5^\circ$) multiplied by the cosine of the latitude. The result is approximately $5 \times 111 \times \cos(25^\circ) \approx 503$ km.

This value represents latitude ($5^\circ$ N), but local time differences are determined by longitude (East/West coordinates).

This is a latitude coordinate ($65^\circ$ N). Time zones and local time are calculated based on longitude, not latitude.

This longitude is $30^\circ$ east of Osaka ($135^\circ + 30^\circ$), which would make the local time there 2 hours ahead of Osaka, rather than Osaka being ahead.

This assumes a 3-hour time difference, which incorrectly ignores daylight saving time and miscalculates the standard time zones.

This incorrectly assumes Western Australia is 3 hours ahead of New Zealand, rather than being behind.

This incorrectly assumes Western Australia is 5 hours ahead of New Zealand, rather than 5 hours behind.

This is incorrect because the longitude difference is $45^\circ$, which corresponds to a 3-hour time difference ($45^\circ / 15^\circ$ per hour), not 1 hour. Furthermore, City A is west of City B, so the sun rises later, not before.

While the direction (after) is correct, the time calculation is wrong. The difference in longitude is $45^\circ$, which results in a 3-hour difference ($45^\circ / 15^\circ$ per hour), not 1 hour.

This is incorrect because of the direction. Although the 3-hour difference is correct, City A ($120^\circ$ E) is west of City B ($165^\circ$ E), meaning the sun rises in City A later than in City B.