Algebraic Notation (Edexcel IGCSE Maths)

Spec point — 1.3A

Algebraic notation

What is algebra?

• Algebra is a topic in mathematics that uses letters to represent general (or unknown) numbers

  • x and y are two unknown numbers

    • More information is needed to find their values

• Letters are also called variables

How do I write calculations in algebra?

• Writing mathematical ideas in letters is called using algebraic notation

• You can use + and – to mean add and subtract

  • a + b c + d – e

• However no symbol is used for multiplication

  • ab (means a × b) 3ab (means 3 × a × b)

• Fractions are used for division

  • $\frac{a}{b}$ (means a ÷ b)

• You can combine the ideas above

  • $ab+\frac{c}{3}$ (means a×b + c÷3)

  • The order of operations for numbers still works

    • work out a×b and c÷3 before adding them together

• Powers (indices) and roots are the same as with numbers

  • a² means a × a 4a² means 4 × a²

    • With the order of operations, a² happens before multiplying by 4

  • $\sqrt{a}$ means the square root of $a$

• Brackets work in the same way as they do with numbers

  • $3(a+b)$ means $3\times(a+b)$

    • Add the a and b first, then multiply the result by 3

Worked Example Raheem is playing a game and starts with q points. He then earns a further 6 points.

(a) Use algebra to write down the total number of points that Raheem has.

Answer:

Final answer: Raheem has q + 6 points

The game then decides to doubles his total number of points.

(b) Use algebra to write down the number of points that Raheem now has.

Answer:

Final answer: Raheem has 2(q + 6) points

You can also write:

Final answer: Raheem has (2q + 12) points