Year 12: Measurement

6 dot points across 6 inquiry questions, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

How are rates used to solve practical problems involving fuel consumption, energy use and dosage, and how do we convert between units?

Use rates and unit conversions to solve practical problems including fuel consumption, dosage, power consumption and energy efficiency

Rates and unit conversions. Definition of a rate, the unitary method, converting between SI units, fuel consumption (L per 100 km), energy use (kWh) and dosage, with unit-cancellation chains and worked Australian examples.

12 min read →

How are ratios and scale drawings used to read maps and plans, and how does the trapezoidal rule estimate irregular areas?

Use ratios and scale drawings to interpret maps and plans, and use the trapezoidal rule to estimate the area of an irregular region

Ratios, scale drawings and the trapezoidal rule. Reading scale notation, converting distances, the trapezoidal rule formula with a strip-by-strip stepped build, and worked examples for floor plans, maps and irregular Australian land areas.

13 min read →

How is the cosine rule used to find missing sides and angles in non-right-angled triangles?

Use the cosine rule to find a side given two sides and the included angle, or an angle given three sides

Cosine rule. Both forms of the rule, when to use it (SAS or SSS), a stage-by-stage SAS solve, exam wording, the link to Pythagoras, and worked navigation and paddock examples.

12 min read →

How is the sine rule used to find missing sides and angles in non-right-angled triangles, and when does the ambiguous case arise?

Use the sine rule to find unknown sides and angles in non-right-angled triangles, including the ambiguous case

Sine rule. Statement of the rule, when to use it, the ambiguous SSA case shown stage by stage, exam wording, and worked examples with Australian navigation and surveying contexts.

12 min read →

How are bearings and radial surveys used to find distances and directions in navigation and surveying?

Use compass and true bearings, and radial surveys, to solve practical navigation and surveying problems

Bearings and radial surveys. Compass vs true bearings, back-bearings, the structure of a radial survey, and worked Australian navigation examples using the sine and cosine rules, with stage-by-stage diagrams.

13 min read →

How is the area of a non-right-angled triangle calculated using two sides and the included angle?

Use the formula

A = \frac{1}{2} a b \sin C

to find the area of any triangle given two sides and the included angle

Area formula $A = \frac{1}{2} a b \sin C$ . Where it comes from, choosing the included angle, a stage-by-stage diagram, exam wording, and worked Australian land and sail examples including SSS via the cosine rule.

11 min read →