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NSW Curriculum
NSW Education Standards Authority

K–10Mathematics K–10 Syllabus

Record of changes
Implementation for K–2 from 2023 and 3–10 from 2024
Expand for detailed implementation advice

Content

Stage 5

Indices C (Path)

Stn (Standard), Adv (Advanced) and Ext (Extension) have been used to suggest paths for related Stage 6 courses.

Describe surds
  • Describe a real number as a number that can be represented by a point on the Loading 

  • Examine the differences between Loading  and Loading  and recognise that all rational and irrational numbers are real

  • Convert between Loading  and their Loading  form using digital tools

  • Describe the term surd as referring to irrational expressions of the form xn where x is a rational number and n is an integer such that n2, and x>0 when n is even

  • Recognise that a Loading  is an exact value that can be Loading  by a Loading  Loading 

  • Demonstrate that x is undefined for x<0 and that x=0 when x=0 using digital tools

  • Describe x as the positive square root of x for x>0 and 0=0

Apply knowledge of surds to solve problems
  • Establish and apply the following results for x>0 and y>0: x2=x=x2, xy=x×y and xy=xy

  • Apply the 4 Loading  to simplify Loading  involving surds

  • Expand and simplify expressions involving surds

  • Rationalise the denominators of surds of the form abcd

Describe and use fractional indices
  • Apply index laws to describe fractional indices as: a1n=an  and amn=amn=anm

  • Translate expressions in surd form to expressions in Loading  form and vice versa

  • Evaluate numerical expressions involving fractional Loading  including using digital tools

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