• 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 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.

  • Units of Measurement and Applications 16 concepts

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

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

    3. Use formulae to calculate the percentage error

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

    5. Solve problems involving repeated percentage change

    6. Divide a quantity in a given ratio

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

    8. Convert between metric units of volume and capacity

    9. Convert between metric units of area

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

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

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

    13. Apply the unitary method to ratio problems

    14. Use the unitary method to solve problems involving percentages

    15. Decrease a quantity by a percentage

    16. Increase a quantity by a percentage

  • Application of perimeter, area and volume 11 concepts

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

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

    3. Construct a notebook entry from a field diagram

    4. Construct a field diagram from a notebook entry

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

    6. Find the perimeter of sectors including quadrants and semicircles

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

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

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

    10. Find the areas of quadrants, semicircles and sectors

    11. Calculate the area of an annulus

  • 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 volume of a shape

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

    4. Surface areas of spheres

    5. Calculate the volume of of right pyramids

    6. Calculate the volume of a cone

    7. Calculate the volume of an annular cylinder

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

    9. Find the surface areas of triangular prisms

    10. Find the surface area of a cylinder

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

    12. Find the surface area of rectangular prisms

    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. Use a scale factor to find unknown sides

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

  • Applications of Trigonometry 17 concepts

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

    2. Conduct a plane table survey

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

    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. Solve worded problems involving bearings using SOH CAH TOA

    7. Calculate the perimeter of a plane table survey

    8. Calculate the area of a plane table survey

    9. Calculate the perimeter of a radial survey

    10. Calculate the area of a radial survey

    11. Conduct a radial survey

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

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

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

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

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

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

  • Spherical Geometry 14 concepts

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

    2. Convert angular distance to nautical miles

    3. 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

    4. Convert nautical miles to kilometres

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

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

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

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

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

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

    11. Solve problems involving international time zones

    12. Calculate the distance between two coordinates on the Earth

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

    14. Terminology associated with the Earth

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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