Sheet 8 of 10 · Maths
Algebra
BODMAS, expressions, brackets, equations, sequences and function machines. 9 rules, each with a worked example.
Order and substitution
BODMAS
Brackets, Orders (powers), Division and Multiplication, Addition and Subtraction
- × and ÷ have equal rank: work left to right. The same goes for + and −
Example3 + 4 × 2 = 3 + 8 = 11 (not 14)Substitution
Replace each letter with its number
- 5a means 5 × a · a² means a × a
Examplea = 4, b = 3: 5a − 2b = 20 − 6 = 14Writing expressions
Turn the words into symbols
- n ÷ 4 is written n/4 · “n squared” is n²
Example“3 more than double n” → 2n + 3
Brackets
Multiplying out brackets
Multiply everything inside by the number outside
Example3(x + 4) = 3x + 12 · 2(5 − y) = 10 − 2yFactorising
Take out the common factor (the reverse of multiplying out)
Example6x + 9 = 3(2x + 3)
Equations
The balance method
Whatever you do to one side, do to the other
- Undo the + or − first, then the × or ÷
Examplex + 7 = 12 → x = 5 · 3x − 4 = 11 → 3x = 15 → x = 5Letters on both sides
Get the letters on one side and the numbers on the other
Example5x + 2 = 2x + 14 → 3x + 2 = 14 → 3x = 12 → x = 4
Sequences and function machines
Linear sequences
Goes up by d each time → nth term equals d × n + (adjustment)
- Term-to-term rule: how you get from one term to the next
- Check the nth term with n = 1
Example5, 8, 11, 14…: +3 each time, nth term = 3n + 2 (10th term = 32)Function machines
To go backwards, use inverses in reverse order: + ↔ −, × ↔ ÷
Example? → × 4 → − 3 → 25. Backwards: 25 + 3 = 28, 28 ÷ 4 = 7
Want the full explanation?
The study guide goes through each rule step by step, with more examples.