Maths - Algebra

Algebra Formulae
1. Formulae is a calculation for specific reasons
2. Always true
Substitution
1. Putting numbers in place of letters
2. Use BIDMAS
  1. 1 - Brackets
  2. 2 - Indices
  3. 3 - Division
  4. 4 - Multiplication
  5. 5 - Addition
  6. 6 - Subtraction
Creating Formulae
1. EXAMPLE
  1. A plumber has a call out fee of £40, plus an hourly rate of £18. Write a formula to calculate the cost of any job and calculate the cost of a job estimated to take 2 hours.
    1. A job to take 2 hours would look like T= 40+18h x 2 (40+36) = £76
      1. BIDMAS is used to do the multiplication before addition
  2. The total cost (which would be symbolised as 'T') would be equal to the call out charge
    1. Plus the £18 for the hourly charge (would be symbolised as 'h')
2. SECOND EXAMPLE
  1. On a given day the plumber charges £130. How long did the plumber work for?
    1. Total cost doesn't need calculating - the hours do
      1. FORMULAE = T= 40+18h
        130= 40 + 18h
        FIRST - Take 40 from both sides (130 AND 40)
        90 = 18h
        SECOND - Divide both sides by 18
        5 = h
        NUMBER OF HOURS WORKED = 5
Changing Subject of a Formula
1. The subject of a formula is the variable that is being worked out. It can be recognised as the letter on its own on one side of the equation.
  1. For example, in the formula for the area of a rectangle Equation: A = bh (Equation: text{area} = text{base} times text{height}), the subject of the formula is Equation: A.
    1. The subject is the thing that is being worked out
    2. If the area and height of a rectangle was known and the base of the rectangle was required instead, the formula Equation: A = bh wouldn't help as it is Equation: b that now needs to be calculated.
      1. A = bh means A = b times h. To make b the subject of the formula,b needs to be isolated. In the formula above, the letter b is multiplied by h. The inverse of multiplying by h is dividing by h, so divide both sides by h to isolate b.
2. EXAMPLE
  1. Rearrange the formula v = u + at to make u the subject of the formula.
    1. Answer this question by finding the letter Equation: u in the formula.
      1. Isolate this letter by inversing any other items on this side of the equation. Next to the u, there is also a + at. The inverse of adding at is subtracting at, so subtract at from both sides.

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