VCE General Mathematics Units 1 and 2 – Geometry, Measurement and Trigonometry

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Description

4.1 Measurement
4.2 Perimeter
4.3 Area
4.4 Surface Area
4.5 Volume
4.6 Similarity
4.7 Pythagoras Theorem
4.8 Trigonometry
4.9 Non-right Angled Triangles




Additional information

Outcome

Shape and measurement
Key knowledge
• the measures of length, area, volume and capacity and their units of measurement
• Pythagoras’ theorem and its application
• the perimeter and areas of triangles, quadrilaterals, circles and composites
• the volumes and surface areas of solids (spheres, cylinders, pyramids, prisms and their composites)
• similarity and scaling, and the linear scale factor k and its extension to areas and volumes.
Key skills
• solve practical problems involving the use of Pythagoras’ theorem in two and three dimensions
• calculate the perimeter and areas of triangles, quadrilaterals, circles and composites in practical situations
• calculate the volumes and surface areas of solids (spheres, cylinders, pyramids and prisms and their composites) in practical situations
• use a linear scale factor to scale lengths, areas and volumes of similar figures and shapes in practical situations.

Applications of trigonometry
Key knowledge
• trigonometric ratios sine, cosine and tangent
• angles of elevation and depression and three figure bearings
• the definition of sine and cosine for angles up to 180°
• the sine rule (including the ambiguous case) and cosine rule.
Key skills
• use trigonometric ratios sine, cosine and tangent to find the length of an unknown side or the size of an unknown angle, in a right-angled triangle
• solve practical problems involving right-angled triangles including the use of angles of elevation and depression, and the use of three-figure (true) bearings in navigation
• calculate the areas of triangles in practical situations using the rule Area = \( \displaystyle \frac{1}{2} ab \sin C \) and Heron's formula
• solve practical problems requiring the calculation of side lengths or angles in non-right angled triangles using the sine rule or the cosine rule as appropriate
• identify sufficient sets of information to determine a triangle.

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