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• Mathematics: Level 10 achievement standards

  Number and Algebra

  Students recognise the connection between simple and compound interest. They solve problems involving linear equations and inequalities, quadratic equations and pairs of simultaneous linear equations and related graphs, with and without the use of digital technology. Students...

  Level description | Mathematics | Level 10

• Mathematics: Level 10 description

  In Level 10, students extend their use of mathematical models to a wide range of familiar and unfamiliar contexts, involving the use of all types of real numbers. They recognise the role of logical argument and proof in establishing mathematical propositions. Students apply mental, written or...

  Level description | Mathematics

• 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

• 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

• VCMNA332

  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

  VCMNA332 | Mathematics | Level 10 | Number and Algebra | Patterns and algebra

• VCMNA331

  Apply the four operations to simple algebraic fractions with numerical denominators

  Elaborations

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

  VCMNA331 | Mathematics | Level 10 | Number and Algebra | Patterns and algebra

• 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

• 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

• VCMNA342

  Solve equations using systematic guess-check-and-refine with digital technology

  Elaborations

  • refining intervals on graphs and/or in tables of values to determine with increasing accuracy when the values of two functions are approximately equal

  VCMNA342 | Mathematics | Level 10 | Number and Algebra | Linear and non-linear relationships