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Indices and surds – advanced

This lesson comprises two (2) master classes focusing on:

  • Index laws
  • The zero index and power of a power
  • Negative indices
  • Fractional indices and surds
  • Operations with surds

Content:

MA5-IND-P-01


Apply index laws to algebraic expressions involving negative-integer indices

  • Apply index notation, patterns and index laws to establish a1=1a, a2=1a2, a3=1a3 and an=1an
  • Represent expressions involving negative-integer indices as expressions involving positive-integer indices and vice versa
  • Apply the index laws to simplify algebraic products and quotients involving negative-integer indices
  • Describe and use x1 as the reciprocal of x and generalise this relationship to expressions of the form  (ab)1
  • Use knowledge of the reciprocal to simplify expressions of the form  (ab)n

 

MA5-IND-P-02


Describe surds

  • Describe a real number as a number that can be represented by a point on the number line
  • Examine the differences between rational and irrational numbers and recognise that all rational and irrational numbers are real
  • Convert between recurring decimals and their fractional form using digital tools
  • Describe the term surd as referring to irrational expressions of the form (nx) where x is a rational number and n is an integer such that n2, and x>0 when n is even
  • Recognise that a surd is an exact value that can be approximated by a rounded decimal
  • 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: (x)2=x=x2,  xy=x×y and  xy=xy
  • Apply the 4 operations to simplify expressions 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=na and amn=nam=(na)m
  • Translate expressions in surd form to expressions in index form and vice versa
  • Evaluate numerical expressions involving fractional indices, including using digital tools