Test 1

• Reciprocal


  Swap the numerator and the denominator, turn the fraction upside down
• A number x its reciprocal = 1
• Reciprocal examples


  • 2=3
  • 1/2
• Calculating reciprocals


  0.5 10.5
• The Multiplication Rule


  m^a x a^n = a^(m+n)
• The Division Rule


  a^m ÷ a^n = a^(m-n)
• The Power-on-Power Rule


  (a^m)^n = a^(m*n)
• The Zero Power Rule


  a^0 = 1
• The Negative Power Rule

  a^-m = 1/a^m
• Reciprocal examples


  • 5^3 = 1
  • 7^1 = 7
• Fractional Power Rule


  a^(1/n) = nth root of a
• Standard Form


  x x 10^n
• Standard Form examples


  • 5,000,000 = 5 x 10^6
• Bounds


  • Minimum and maximum values a measurement could represent
• Bounds examples


  • 3.55 <= 3.6 <= 3.65
  • 12.05 <= 12.1 <= 12.15
  • 2.725 <= 2.73 <= 2.735
  • 45 <= 50 <= 55
  • 168.5 <= 169 <= 169.5
• Whenever a quantity is measured, the measurement is never exact
• We can be precise about the lower and upper bounds for the measurement
• The lower bound is the minimum value the measurement could represent
• The upper bound is the maximum value the measurement could represent
• Calculating bounds for 80 golf balls

  • Lower bound = 152.05 x 80 = 12,164
  • Upper bound = 152.15 x 80 = 12,172
• Calculating bounds for a product

  LB(x*y) = LB(x) * LB(y)

  UB(x*y) = UB(x) * UB(y)
• Calculating bounds for a difference

  LB(x-y) = LB(x) - UB(y)

  UB(x-y) = UB(x) - LB(y)
• Significant figures


  The digits of a number used to express it to the required degree of accuracy, starting from the first non-zero digit
• This text will round numbers to three significant figures
• Factorising


  Expressing an expression in terms of its factors by putting brackets back and taking out a common factor
• Factorising examples


  • 7p-14g-7(p-2g)

  6p+9m-(2p+3m)

  12-7i-(1-7)

  6my+4py=2y(3m+2)