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• VC2M10A10

  solve problems involving gradients of parallel and perpendicular lines

  Elaborations

  • solving problems using the fact that parallel lines have the same gradient and conversely that if 2 lines have the same gradient then they are parallel
  • solving problems using the fact that the product of the gradients of perpendicular lines is −1 and conversely that if the product of the gradients of 2 lines is −1 then they are perpendicular

  VC2M10A10 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M10A09

  solve simultaneous linear equations, using algebraic and graphical techniques including using digital tools

  Elaborations

  • investigating situations involving simultaneous linear equations in context (such as multiple quotes for a job, or profit and loss) and solving the equations graphically, giving solutions in everyday language (such as ‘break-even point’ or ‘point to change providers’ for the job)
  • describing the solution of simultaneous equations within the context of the situation
  • using the algebraic methods of substitution and elimination, with and without the use of digital tools, and identifying which technique is the most efficient for a given pair of equations
  • associating the solution of simultaneous equations with the coordinates of the intersection of their corresponding graphs
  • investigating the strategies inherent in Aboriginal and/or Torres Strait Islander children’s instructive games, for example, Weme from the Warlpiri Peoples of central Australia, and their connection to strategies to solve simultaneous linear equations in 2 variables

  VC2M10A09 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M10A02

  simplify algebraic products and quotients using exponent laws

  Elaborations

  • applying knowledge of exponent laws to algebraic terms, and simplifying algebraic expressions using both positive and negative integral indices

  VC2M10A02 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M10A13

  solve simple quadratic equations using a range of strategies, including null factor law

  Elaborations

  • using techniques to solve quadratic equations, including grouping like terms, completing the square, the quadratic formula and null factor law, and choosing 2 integers with the required product and sum
  • using digital tools to explore the conditions for solutions to exist
  • using digital tools to explore both graphically and algebraically the link between the value of the discriminant and the number of real solutions to a quadratic equation

  VC2M10A13 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M10A12

  solve linear equations involving simple algebraic fractions

  Elaborations

  • solving a wide range of linear equations, including those involving one or 2 simple algebraic fractions, and checking solutions by substitution
  • representing word problems, including those involving fractions, as equations and solving them to answer the question

  VC2M10A12 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M10A03

  apply the 4 operations to simple algebraic fractions with numerical or single variable denominators

  Elaborations

  • expressing the sum and difference of algebraic fractions with a common denominator
  • using the exponent laws to simplify products and quotients of algebraic fractions

  VC2M10A03 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M10A04

  expand binomial products and factorise monic quadratic expressions using a variety of strategies

  Elaborations

  • exploring the method of completing the square to factorise quadratic expressions and solve quadratic equations
  • identifying and using common factors, including binomial expressions, to factorise algebraic expressions using the technique of grouping in pairs
  • using the identities for perfect squares and the difference of squares to factorise quadratic expressions

  VC2M10A04 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M10M04

  use mathematical modelling to solve practical problems involving direct and inverse proportion and scaling of objects; formulate problems and interpret solutions in terms of the situation, including the impact of measurement errors on the accuracy of results; evaluate and modify models as necessary...

  Elaborations

  • exploring contexts where measurement errors may impact research results and how measurement data impacted by error can result in biased findings
  • using plans and elevation drawings to investigate making changes to building designs, employing appropriate scales and converting to actual measurements within the context to make decisions about changes
  • analysing and applying scale and ratios in situations such as production prototypes and 3D printing; for example, using a 3D printer to produce scaled versions of actual objects
  • estimating the scale of an object by measuring a linear dimension and using typical life-size dimensions to determine the scale factor; for example, measuring the dimensions of a toy car to determine a scale that can be used to estimate the dimensions of a life-size car
  • investigating compliance with building codes and standards in design and construction, such as for escalators in shopping centres

  VC2M10M04 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VC2M10M01

  solve problems involving the surface area and volume of composite objects using appropriate units

  Elaborations

  • determining the volumes and surface areas of composite solids, formed from a range of right prisms and cylinders, by considering the individual solids from which they are constructed
  • estimating the surface area and volume of composite objects in practical contexts
  • using mathematical modelling to provide solutions to problems involving surface area and volume; for example, ascertaining the rainfall that can be saved from a rooftop and the optimal shape and dimensions for rainwater storage based on where it will be located on a property, or determining whether to hire extra freezer space for the amount of ice cream required at a fundraising event for the school or community

  VC2M10M01 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VC2M10M03

  solve practical problems by applying Pythagoras’ theorem and trigonometry to right-angled triangles, including problems involving direction and angles of elevation and depression

  Elaborations

  • applying right-angled trigonometry to solve navigation problems involving bearings; for example, determining the bearing and estimating the distance of the final leg of an orienteering course
  • applying Pythagoras’ theorem and trigonometry to problems in surveying and design, where three-dimensional problems are decomposed into two-dimensional problems; for example, investigating the dimensions of the smallest box needed to package an object of a particular length
  • using a clinometer to measure angles of inclination, and applying trigonometry and proportional reasoning to determine the height of buildings in practical contexts
  • applying Pythagoras’ theorem and trigonometry and using dynamic geometry software to design three-dimensional models of practical situations involving angles of elevation and depression; for example, modelling a crime scene
  • exploring navigation, design of technologies or surveying by Aboriginal and Torres Strait Islander Peoples, investigating geometric and spatial reasoning and how these connect to trigonometry 

  VC2M10M03 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VC2M10M02

  interpret and use logarithmic scales in applied contexts involving small and large quantities and change 

  Elaborations

  • understanding that the logarithmic scale is calibrated in terms of order of magnitude, for example, doubling or powers of 10
  • identifying and interpreting data representations (charts and graphs) that use logarithmic scales (for example, graphs representing percentage change, a wide range of values or exponential growth) and discussing when it is appropriate to use this type of scale and when it is not appropriate
  • investigating and interpreting logarithmic scales used in real-world contexts (for example, Richter, decibel and sensitivity scales or growth in investments, timescales and the spread of microorganisms and disease) and describing reasons for choosing to use a logarithmic scale rather than a linear scale
  • investigating dating methods of geological sites to provide evidence of Aboriginal and Torres Strait Islander Peoples’ presence in Australia, including the Madjedbebe dig in the Northern Territory, that use logarithmic scales, scientific notation and measurement accuracy in the dating

  VC2M10M02 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VCMMG345

  Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes

  Elaborations

  • distinguishing between a practical demonstration and a proof (for example demonstrating triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent)
  • performing a sequence of steps to determine an unknown angle giving a justification in moving from one step to the next.
  • communicating a proof using a sequence of logically connected statements

  VCMMG345 | Mathematics | Level 10 | Measurement and Geometry | Geometric reasoning

• VCMMG344

  Formulate proofs involving congruent triangles and angle properties

  Elaborations

  • applying an understanding of relationships to deduce properties of geometric figures (for example the base angles of an isosceles triangle are equal)

  VCMMG344 | Mathematics | Level 10 | Measurement and Geometry | Geometric reasoning

• VCMMG346

  Solve right-angled triangle problems including those involving direction and angles of elevation and depression

  Elaborations

  • applying Pythagoras's Theorem and trigonometry to problems in surveying and design

  VCMMG346 | Mathematics | Level 10 | Measurement and Geometry | Pythagoras and trigonometry

• VCMMG343

  Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids

  Elaborations

  • investigating and determining the volumes and surface areas of composite solids by considering the individual solids from which they are constructed

  VCMMG343 | Mathematics | Level 10 | Measurement and Geometry | Using units of measurement

• VC2M10N01

  recognise the effect of using approximations of real numbers in repeated calculations and compare the results when using exact representations

  Elaborations

  • comparing and contrasting the effect of truncation or rounding on the final result of calculations when using approximations of real numbers rather than exact representations
  • investigating the impact of approximation on multiple calculations in contexts that involve the area of compound shapes involving circles, the surface area and volume of compound objects, and repeated calculations of simple interest where the solutions are not exact cents

  VC2M10N01 | Mathematics | Mathematics Version 2.0 | Level 10 | Number

• VCMNA328

  Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies

  Elaborations

  • working with authentic information, data and interest rates to calculate compound interest and solve related problems

  VCMNA328 | Mathematics | Level 10 | Number and Algebra | Money and financial mathematics

• VCMNA329

  Factorise algebraic expressions by taking out a common algebraic factor

  Elaborations

  • using the distributive law and the index laws to factorise algebraic expressions
  • understanding the relationship between factorisation and expansion

  VCMNA329 | Mathematics | Level 10 | Number and Algebra | Patterns and algebra

• VCMNA330

  Simplify algebraic products and quotients using index laws

  Elaborations

  • applying knowledge of index laws to algebraic terms, and simplifying algebraic expressions using both positive and negative integral indices

  VCMNA330 | Mathematics | Level 10 | Number and Algebra | Patterns and algebra

• VCMNA333

  Substitute values into formulas to determine an unknown and re-arrange formulas to solve for a particular term

  Elaborations

  • solving simple equations arising from formulas
  • re-arranging expressions to make a specified variable the subject such as calculating the radius of a sphere to produce a given volume

  VCMNA333 | Mathematics | Level 10 | Number and Algebra | Patterns and algebra