Applications of Measurement
Solve measurement problems involving perimeter, area, surface area and volume of standard and composite shapes and solids.
- 1.Find the volume of a cylinder with radius 5 cm and height 12 cm, correct to 2 decimal places.
- 2.A composite shape consists of a rectangle and a semicircle. Find its perimeter.
One of the heaviest topics — 6–10 marks across the paper.
- ·Using diameter instead of radius in circle formulas
- ·Forgetting to add all faces when computing surface area of composite solids
- ·Misidentifying the correct formula (e.g., using area instead of volume)
Working with Time
Perform calculations involving time and duration, time zones, and scheduling in practical contexts.
- 1.A flight departs Sydney (AEST) at 09:30 and lands in Perth (AWST) after 4 h 20 min. What is the local arrival time?
2–4 marks — often tested in context of travel and scheduling.
- ·Converting minutes to hours as a decimal incorrectly (e.g., treating 30 min as 0.30 h not 0.5 h)
- ·Errors with AM/PM conversion when calculating duration across midnight
Non-right-angled Trigonometry
Apply the sine rule, cosine rule, and area formula to solve problems with non-right-angled triangles.
- 1.Two ships leave a port. Ship A travels 12 km on a bearing of 040°; Ship B travels 9 km on a bearing of 120°. How far apart are the ships?
4–6 marks — often involving bearings and area-of-triangle problems.
- ·Using sine rule when cosine rule is required (ambiguous case misidentification)
- ·Errors in bearing problems — confusing true bearing and compass bearing
- ·Forgetting the ambiguous case of the sine rule
Rates and Ratios
Solve problems involving rates and ratios in practical contexts, including unit conversions and scale factors.
- 1.A scale map has a ratio of 1:50 000. If two towns are 8 cm apart on the map, what is the actual distance?
2–4 marks — practical calculation contexts.
- ·Incorrect unit conversion (e.g., km/h to m/s)
- ·Simplifying ratios without expressing in lowest terms
Other Standard 2 topics
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