- 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.
Find the angular distance between two coordinates on the earth
Convert angular distance to nautical miles
Convert nautical miles to kilometres
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
Solve problems involving international time zones
Calculate the difference in latitude 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 longitude between two given points that lie on any small/great circle
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 distance between two coordinates on the Earth
Terminology associated with the Earth
Write the latitude of a point that lies on any small/great circle
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 lower and upper limits of the volume of a shape
Find the surface areas of triangular prisms
Find the surface area of a cylinder
Find the surface area of rectangular prisms
Surface areas of spheres
Calculate the volume of of right pyramids
Calculate the volume of a cone
Calculate the volume of an annular cylinder
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
Convert between metric units of volume and capacity
Determine the scale factor of two similar figures
Solve problems using ratio and scale factors in similar figures
Use a scale factor to find unknown sides
Solve practical problems using scale diagrams and factors, similarity and trigonometry
use appropriate trigonometric ratios and formulae in 'two-triangle problems', where one triangle is right-angled and the diagram is given
Conduct a plane table survey
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
Conduct a radial survey
Calculate the perimeter of a radial survey
Calculate the area of a radial survey
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
Use the sine rule to find unknown sides and angles of a non-right-angled triangle including the ambiguous case
Solve worded problems involving bearings and angles of elevation and depression of non-right-angled triangles
Divide a quantity in a given ratio
Convert between metric units of area
Convert between metric units of volume and capacity
Convert units of measurement using standard form of metric prefixes, index laws and scientific notation
Determine the limit of reading of a measurement or measuring tool
Determine the absolute error based on the limit of reading
Find the lower and upper limit of the true measurement based on the absolute error
Use formulae to calculate the percentage error
Solve problems involving repeated percentage change
Apply the unitary method to ratio problems
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
Increase a quantity by a percentage
Decrease a quantity by a percentage
Use the unitary method to find an average or simplified rate
Construct a field diagram from a notebook entry
Construct a notebook entry from a field diagram
Recognise a traverse survey and apply your understanding to calculate the area of the field
Recognise a traverse survey and apply your understanding to calculate the perimeter of the field
Use formulae for Simpson's Rule to find the area under a curved surface.
Find the areas of simple composite figures that may be dissected into rectangles, squares, parallelograms and triangles
Use formulae to find the arc length of a sector
Find the perimeter of sectors including quadrants and semicircles
Find the perimeters of a range of plane shapes, including composite figures
Find the areas of quadrants, semicircles and sectors
Calculate the area of an annulus
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