- Mathematics General
- Year 12
Measurement
approx. 20 hrs
6 topics
74 concepts
Develop an aptitude for Measurement and approach your examinations with confidence.
approx. 20 hrs
6 topics
74 concepts
Develop an aptitude for Measurement and approach your examinations with confidence.
Year 12 Measurement addresses outcomes from the Measurement and Geometry Strand contained in the NSW General Senior Syllabus. Students who study Year 12 Measurement apply estimation of quantities to achieve appropriate levels of accuracy to particular situations relating to measurement. In addition, students apply understanding of length, area, volume, similarity and trigonometry to a variety of problems.
This learning program is made up of the following 6 topics, broken down into 74 concepts.
Convert units of measurement using standard form of metric prefixes, index laws and scientific notation
Convert between metric units of volume and capacity
Determine the limit of reading of a measurement or measuring tool
Determine the absolute error based on the limit of reading
Use formulae to calculate the percentage error
Find the lower and upper limit of the true measurement based on the absolute error
Solve problems involving repeated percentage change
Convert between metric units of area
Divide a quantity in a given ratio
Scale drawing - convert scale distance to actual distance and vice versa
Solve a variety of real-life problems involving rates
Use the unitary method to solve problems involving percentages
Use the unitary method to find an average or simplified rate
Decrease a quantity by a percentage
Increase a quantity by a percentage
Apply the unitary method to ratio problems
Use formulae for Simpson's Rule to find the area under a curved surface.
Construct a notebook entry from a field diagram
Recognise a traverse survey and apply your understanding to calculate the perimeter of the field
Construct a field diagram from a notebook entry
Recognise a traverse survey and apply your understanding to calculate the area of the field
Find the areas of simple composite figures that may be dissected into rectangles, squares, parallelograms and triangles
Find the areas of quadrants, semicircles and sectors
Calculate the area of an annulus
Find the perimeters of a range of plane shapes, including composite figures
Find the perimeter of sectors including quadrants and semicircles
Use formulae to find the arc length of a sector
Find the lower and upper limits of the volume of a shape
Calculate the volume of composite solids including right cones and right pyramids
Find the lower and upper limits of the area of a shape
Find the surface area of a cylinder
Find the surface area of rectangular prisms
Find the surface areas of triangular prisms
Surface areas of spheres
Develop and use the formula for the volume of right prisms and find the capacity
Develop and use the formula for the volume of cylinders and find the capacity
Calculate the volume of an annular cylinder
Calculate the volume of a cone
Calculate the volume of of right pyramids
Convert between metric units of volume and capacity
Solve problems using ratio and scale factors in similar figures
Use a scale factor to find unknown sides
Determine the scale factor of two similar figures
Solve practical problems using scale diagrams and factors, similarity and trigonometry
Conduct a plane table survey
Use appropriate trigonometric ratios and formulae in 'two-triangle problems', where one triangle is right-angled and the diagram is given
Identify the hypotenuse, adjacent sides and opposite sides on a right angles triangle
Find the lengths of unknown sides in right-angled triangles using SOH CAH TOA where the given angle is measured in degrees and minutes
Find the size in degrees and minutes of unknown angles using SOH CAH TOA in right-angled triangles
Solve a variety of practical problems involving angles of elevation and depression of right-angled triangles
Solve worded problems involving bearings using SOH CAH TOA
Calculate the perimeter of a plane table survey
Calculate the area of a plane table survey
Calculate the perimeter of a radial survey
Calculate the area of a radial survey
Conduct a radial survey
Solve worded problems involving bearings and angles of elevation and depression of non-right-angled triangles
Use the sine rule to find unknown sides and angles of a non-right-angled triangle including the ambiguous case
Use the cosine rule to find unknown sides and angles of a non-right-angled triangle
Apply the appropriate rule to find unknowns in non-right-angled triangles
Calculate the time taken to travel a distance using speed that may be measured in knots or as a rate of nautical miles per hour
Calculate time differences between locations on the Earth given the difference in longitude
Convert angular distance to nautical miles
Convert nautical miles to kilometres
Find the angular distance between two coordinates on the earth
Solve problems involving international time zones
Write the coordinates of a point that lies on any small/great circle
Identify the location of a place on the world map given latitude and longitude
Calculate the difference in longitude between two given points that lie on any small/great circle
Write the longitude of a point that lies on any small/great circle
Calculate the difference in latitude between two given points that lie on any small/great circle
Calculate the distance between two coordinates on the Earth
Write the latitude of a point that lies on any small/great circle
Terminology associated with the Earth
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