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IGCSE/GCSE Mathematics - Counting, Accuracy, Powers and Surds

Counting, Accuracy, Powers and Surds

· Reciprocals,Surds,Rationalising,Accuracy,GCSE Mathematics

Reciprocals

  • Flip the fraction to get the reciprocal.
    5 = ⁵⁄1 ; ⁵⁄1 ⟶ ⅕
     
  • For the negative reciprocal, switch the sign and flip the fraction.
    -½ ⟶ ²⁄1 ; ²⁄6 ⟶ -⁶⁄2

Surds

  • √a x √b = √ab
  • C√a x D√b = CD√ab
  • √a ÷ √b = √a⁄b
  • C√a ÷ D√b = C⁄D√a⁄b
  • √a/√b = √a⁄b
  • When adding, treat it like algebra, you can only add together the same surd, so change the √’s to like terms.
  • Do this by leaving the same irrational number.

Simplifying Surds

  • Find 2 numbers that are factors, one must be a square number.
  • Simplify ⟶ Root of square number goes outside, other number goes inside.

Expanding surds

  • Square a — ²a
  • Multiply a² x b
  • √a² x √b = √a²b

Simplifying Surd x Surd

  • Times outside numbers together
  • Times irrational numbers together
  • Simplify further, want biggest possible number outside.
  • Recognise square factors, root then multiply them to the outside number.

Rationalising

  • Getting rid of surd from the denominator.
  •  For normal rationalising, just multiply the surd by itself.
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  • For rationalising when there is more than just the surd as the denominator, multiply by the opposite.
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Limits of Accuracy

  • Degree of rounding
  • E.g. 1100 = 2 s.f.
  • Find the values that would round to 1100 for 2sf
  • 1050 ≤ 1100 < 1150
  • Max speed = greatest distance/shortest time
  • Population density = total population/total area
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That's the end of the topic!

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Drafted by Bonnie (Mathematics)

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