← Maths Standard 2 syllabus

NSWMaths Standard 2

Year 12: Measurement

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

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
A focused answer to the HSC Maths Standard 2 dot point on the area formula $A = \frac{1}{2} a b \sin C$ . When to use it, how it derives from the standard $\frac{1}{2}$ base times height formula, and worked Australian land surveying examples.
6 min answer →

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
A focused answer to the HSC Maths Standard 2 dot point on the cosine rule. Both forms of the rule, when to use it (SAS or SSS), the side-finding and angle-finding versions, and worked navigation and engineering examples.
7 min answer →

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
A focused answer to the HSC Maths Standard 2 dot point on 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.
8 min answer →

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
A focused answer to the HSC Maths Standard 2 dot point on 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 calculations with worked Australian examples.
8 min answer →

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
A focused answer to the HSC Maths Standard 2 dot point on ratios, scale drawings and the trapezoidal rule. Reading scale notation, converting distances, the trapezoidal rule formula with one or more applications, and worked examples for floor plans, maps and irregular Australian land areas.
9 min answer →

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
A focused answer to the HSC Maths Standard 2 dot point on the sine rule. Statement of the rule, when to use it, the ambiguous SSA case, and worked examples with Australian navigation and surveying contexts.
7 min answer →