• Mathematics General
  • Year 12

Measurement

approx. 20 hrs

6 topics

74 concepts

Develop an aptitude for Measurement and approach your examinations with confidence.

Available in
ACT NSW NT QLD SA TAS VIC WA

Overview

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.

Topics & Concepts We Cover

This learning program is made up of the following 6 topics, broken down into 74 concepts.

  • Spherical Geometry 14 concepts

    1. Find the angular distance between two coordinates on the earth

    2. Convert angular distance to nautical miles

    3. Convert nautical miles to kilometres

    4. 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

    5. Calculate time differences between locations on the Earth given the difference in longitude

    6. Solve problems involving international time zones

    7. Calculate the difference in latitude between two given points that lie on any small/great circle

    8. Write the longitude of a point that lies on any small/great circle

    9. Calculate the difference in longitude between two given points that lie on any small/great circle

    10. Write the coordinates of a point that lies on any small/great circle

    11. Identify the location of a place on the world map given latitude and longitude

    12. Calculate the distance between two coordinates on the Earth

    13. Terminology associated with the Earth

    14. Write the latitude of a point that lies on any small/great circle

  • Application of area and volume to 3D shapes 13 concepts

    1. Calculate the volume of composite solids including right cones and right pyramids

    2. Find the lower and upper limits of the area of a shape

    3. Find the lower and upper limits of the volume of a shape

    4. Find the surface areas of triangular prisms

    5. Find the surface area of a cylinder

    6. Find the surface area of rectangular prisms

    7. Surface areas of spheres

    8. Calculate the volume of of right pyramids

    9. Calculate the volume of a cone

    10. Calculate the volume of an annular cylinder

    11. Develop and use the formula for the volume of right prisms and find the capacity

    12. Develop and use the formula for the volume of cylinders and find the capacity

    13. Convert between metric units of volume and capacity

  • Similarity of two-dimensional shapes 3 concepts

    1. Determine the scale factor of two similar figures

    2. Solve problems using ratio and scale factors in similar figures

    3. Use a scale factor to find unknown sides

  • Applications of Trigonometry 17 concepts

    1. Solve practical problems using scale diagrams and factors, similarity and trigonometry

    2. use appropriate trigonometric ratios and formulae in 'two-triangle problems', where one triangle is right-angled and the diagram is given

    3. Conduct a plane table survey

    4. Identify the hypotenuse, adjacent sides and opposite sides on a right angles triangle

    5. Find the lengths of unknown sides in right-angled triangles using SOH CAH TOA where the given angle is measured in degrees and minutes

    6. Find the size in degrees and minutes of unknown angles using SOH CAH TOA in right-angled triangles

    7. Solve a variety of practical problems involving angles of elevation and depression of right-angled triangles

    8. Solve worded problems involving bearings using SOH CAH TOA

    9. Calculate the perimeter of a plane table survey

    10. Calculate the area of a plane table survey

    11. Conduct a radial survey

    12. Calculate the perimeter of a radial survey

    13. Calculate the area of a radial survey

    14. Use the cosine rule to find unknown sides and angles of a non-right-angled triangle

    15. Apply the appropriate rule to find unknowns in non-right-angled triangles

    16. Use the sine rule to find unknown sides and angles of a non-right-angled triangle including the ambiguous case

    17. Solve worded problems involving bearings and angles of elevation and depression of non-right-angled triangles

  • Units of Measurement and Applications 16 concepts

    1. Divide a quantity in a given ratio

    2. Convert between metric units of area

    3. Convert between metric units of volume and capacity

    4. Convert units of measurement using standard form of metric prefixes, index laws and scientific notation

    5. Determine the limit of reading of a measurement or measuring tool

    6. Determine the absolute error based on the limit of reading

    7. Find the lower and upper limit of the true measurement based on the absolute error

    8. Use formulae to calculate the percentage error

    9. Solve problems involving repeated percentage change

    10. Apply the unitary method to ratio problems

    11. Scale drawing - convert scale distance to actual distance and vice versa

    12. Solve a variety of real-life problems involving rates

    13. Use the unitary method to solve problems involving percentages

    14. Increase a quantity by a percentage

    15. Decrease a quantity by a percentage

    16. Use the unitary method to find an average or simplified rate

  • Application of perimeter, area and volume 11 concepts

    1. Construct a field diagram from a notebook entry

    2. Construct a notebook entry from a field diagram

    3. Recognise a traverse survey and apply your understanding to calculate the area of the field

    4. Recognise a traverse survey and apply your understanding to calculate the perimeter of the field

    5. Use formulae for Simpson's Rule to find the area under a curved surface.

    6. Find the areas of simple composite figures that may be dissected into rectangles, squares, parallelograms and triangles

    7. Use formulae to find the arc length of a sector

    8. Find the perimeter of sectors including quadrants and semicircles

    9. Find the perimeters of a range of plane shapes, including composite figures

    10. Find the areas of quadrants, semicircles and sectors

    11. Calculate the area of an annulus

What you'll get

Learning Content

  • A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
  • All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

  • We match you to a private, expert tutor who is right for your needs and goals
  • Our tutors are talented, tested, top ATAR achievers and subject experts
  • During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Measurement

Reporting

  • Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
  • You and your parents receive a comprehensive feedback report after every session
  • Every session is recorded and available for you to watch at any time, allowing you to review what was covered

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