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• VCMNA308

  Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software

  Elaborations

  • investigating graphical and algebraic techniques for finding distance between two points
  • using Pythagoras' theorem to calculate distance between two points

  VCMNA308 | Mathematics | Level 9 | Number and Algebra | Linear and non-linear relationships

• VCMNA283

  Plot linear relationships on the Cartesian plane with and without the use of digital technologies

  Elaborations

  • completing a table of values, plotting the resulting points and determining whether the relationship is linear
  • finding the rule for a linear relationship

  VCMNA283 | Mathematics | Level 8 | Number and Algebra | Linear and non-linear relationships

• VCMNA335

  Solve problems involving linear equations, including those derived from formulas

  Elaborations

  • representing word problems with simple linear equations and solving them to answer questions

  VCMNA335 | Mathematics | Level 10 | Number and Algebra | Linear and non-linear relationships

• VCMNA362

  Factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts

  Elaborations

  • writing quadratic equations that represent practical problems

  VCMNA362 | Mathematics | Level 10A | Number and Algebra | Linear and non-linear relationships

• VCMNA338

  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 two 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 two lines is –1 then they are perpendicular

  VCMNA338 | Mathematics | Level 10 | Number and Algebra | Linear and non-linear relationships

• VCMNA341

  Solve simple quadratic equations using a range of strategies

  Elaborations

  • using a variety of techniques to solve quadratic equations, including grouping, completing the square, the quadratic formula, and choosing two integers with the required product and sum

  VCMNA341 | Mathematics | Level 10 | Number and Algebra | Linear and non-linear relationships

• VCMNA340

  Solve linear equations involving simple algebraic fractions

  Elaborations

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

  VCMNA340 | Mathematics | Level 10 | Number and Algebra | Linear and non-linear relationships

• VCMNA339

  Explore the connection between algebraic and graphical representations of relations such as simple quadratic, reciprocal, circle and exponential, using digital technology as appropriate

  Elaborations

  • sketching graphs of parabolas, and circles
  • applying translations, reflections and stretches to parabolas and circles
  • sketching the graphs of exponential functions using transformations
  • plotting graphs of families of relations where the product of two variable is equal to a fixed constant

  VCMNA339 | Mathematics | Level 10 | Number and Algebra | Linear and non-linear relationships

• VCMNA336

  Solve linear inequalities and graph their solutions on a number line

  Elaborations

  • representing word problems with simple linear inequalities and solving them to answer questions

  VCMNA336 | Mathematics | Level 10 | Number and Algebra | Linear and non-linear relationships

• VCMNA337

  Solve simultaneous linear equations, using algebraic and graphical techniques including using digital technology

  Elaborations

  • associating the solution of simultaneous equations with the coordinates of the intersection of their corresponding graphs

  VCMNA337 | Mathematics | Level 10 | Number and Algebra | Linear and non-linear relationships

• VCMNA281

  Simplify algebraic expressions involving the four operations

  Elaborations

  • understanding that the laws used with numbers can also be used with algebra

  VCMNA281 | Mathematics | Level 8 | Number and Algebra | Patterns and algebra

• VCMNA306

  Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate

  Elaborations

  • understanding that the distributive law can be applied to algebraic expressions as well as numbers
  • understanding the relationship between expansion and factorisation and identifying algebraic factors in algebraic expressions

  VCMNA306 | Mathematics | Level 9 | Number and Algebra | Patterns and algebra

• VCMNA275

  Investigate the concept of irrational numbers, including π

  Elaborations

  • understanding that the real number system includes irrational numbers

  VCMNA275 | Mathematics | Level 8 | Number and Algebra | Real numbers

• VCMNA303

  Express numbers in scientific notation

  Elaborations

  • representing extremely large and small numbers in scientific notation, and numbers expressed in scientific notation as whole numbers or decimals

  VCMNA303 | Mathematics | Level 9 | Number and Algebra | Real numbers

• VCMNA277

  Solve a range of problems involving rates and ratios, including distance-time problems for travel at a constant speed, with and without digital technologies

  Elaborations

  • understanding that rate and ratio problems can be solved using fractions or percentages and choosing the most efficient form to solve a particular problem
  • calculating population growth rates in Australia and Asia and explaining their difference
  • finding one of distance travelled, time taken or average speed given the other two quantities

  VCMNA277 | Mathematics | Level 8 | Number and Algebra | Real numbers

• VCMNA304

  Solve problems involving simple interest

  Elaborations

  • understanding that financial decisions can be assisted by mathematical calculations

  VCMNA304 | Mathematics | Level 9 | Number and Algebra | Money and financial mathematics

• VCMNA305

  Extend and apply the index laws to variables, using positive integer indices and the zero index

  Elaborations

  • understanding that index laws apply to variables as well as numbers

  VCMNA305 | Mathematics | Level 9 | Number and Algebra | Patterns and algebra

• VCMNA301

  Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems

  Elaborations

  • identifying direct proportion in real-life contexts

  VCMNA301 | Mathematics | Level 9 | Number and Algebra | Real numbers

• VCMNA280

  Factorise algebraic expressions by identifying numerical factors

  Elaborations

  • recognising the relationship between factorising and expanding
  • identifying the greatest common divisor (highest common factor) of numeric and algebraic expressions and using a range of strategies to factorise algebraic expressions

  VCMNA280 | Mathematics | Level 8 | Number and Algebra | Patterns and algebra

• VCMNA278

  Solve problems involving profit and loss, with and without digital technologies

  Elaborations

  • expressing profit and loss as a percentage of cost or selling price, comparing the difference
  • investigating the methods used in retail stores to express discounts

  VCMNA278 | Mathematics | Level 8 | Number and Algebra | Money and financial mathematics