Test 3

• Subtract


  To take away one number from another
• Squares and square roots


  • Squares are a number multiplied by itself
  • Square roots are the inverse operation, finding the number that when multiplied by itself gives the original number
• Squares and square roots examples

  • v1 = 1
  • v9 = 3
  • v100 = 10
  • v121 = 11
  • v144 = 12
  • v196 = 14
  • v225 = 15
  • v366 = √366
  • v648 = √648
• 120² = 14,400
• 0.52 = 25 x 100 = 2,500
• 0.015² = 0.225
• (1)² = 1
• Direct proportion


  The relationship between two variable quantities; as one quantity increases then the other increases at the same rate
• Solving direct proportion problems

  1. Given information

  2. Set up equation

  3. Solve for unknown
• An electric fire uses 9 units of electricity in 6 hours
• Solving direct proportion problems - example 1

  1. Given: 9 units in 6 hours

  2. Find units in 4 hours

  3. Units = (4/6) * 9 = 6 units
• Solving direct proportion problems - example 2

  1. Given: 9 units in 6 hours

  2. Find hours for 12 units

  3. Hours = (12/9) * 6 = 8 hours
• Cost per unit mass

  A better deal will have a lower cost per unit mass
• Mass per unit cost

  A better deal will have a higher mass per unit cost
• Direct proportion


  As one quantity increases, the other increases at the same rate
• Inverse proportion


  As one quantity increases, the other decreases at the same rate
• Mixed proportion


  Involves both direct and inverse proportion
• A car travels 240 miles in 4 hours. How far will it travel in 7 hours?
• The distance between two cities is 52 kilometres on a map with a scale of 1:200,000
• A map measures 5.5cm between two cities. The actual distance is 11km.
• Equation


  An expression with an equal sign, containing one unknown variable
• Solving equations


  1. Multiply out fractions/brackets

  2. Group everything (variables + numbers)

  3. Move variable to one side and simplify
• Factorising quadratics


  • Finding two factors that multiply to give the original expression
  • e.g. x^2 + 7x + 12 = (x+3)(x+4)
• To make the subject of a formula, isolate the variable on one side of the equation