Maths - Algebra

Maths - Algebra

1. Algebra Formulae

   • Formulae is a calculation for specific reasons
   • Always true

2. Substitution

   • Putting numbers in place of letters
   • Use BIDMAS
     • 1 - Brackets
     • 2 - Indices
     • 3 - Division
     • 4 - Multiplication
     • 5 - Addition
     • 6 - Subtraction

3. Creating Formulae

   • EXAMPLE
     • 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.
       • A job to take 2 hours would look like T= 40+18h x 2 (40+36) = £76
         • BIDMAS is used to do the multiplication before addition
     • The total cost (which would be symbolised as 'T') would be equal to the call out charge
       • Plus the £18 for the hourly charge (would be symbolised as 'h')
   • SECOND EXAMPLE
     • On a given day the plumber charges £130. How long did the plumber work for?
       • Total cost doesn't need calculating - the hours do
         • 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

4. Changing Subject of a Formula

   • 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.
     • 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.
       • The subject is the thing that is being worked out
       • 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.
         • 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.
   • EXAMPLE
     • Rearrange the formula v = u + at to make u the subject of the formula.
       • Answer this question by finding the letter Equation: u in the formula.
         • 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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