Maths 1 types of numbers.docx

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Section One — Number1

Types of Number and BODMAS

Ah, the glorious world of GCSE Maths. Get stuck into this section and you’ll be an expert in no time. Here are some handy definitions of different types of number, and a bit about what order to do things in.

IntegersAn integer is another name for a whole number — either a positive or negative number, or zero.Examples:Integers: -365, 0, 1, 17, 989, 1 234 567 890Not integers: 0.5, ⅗, √7, 13/3, -1000.1, 6.66, π

Square and Cube Numbers

1. When you multiply a whole number by itself, you get a square number:1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, … , 15^2 = 225

2. When you multiply a whole number by itself, then by itself again, you get a cube number:1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125, 10^3 = 1000

3. You should know these basic squares and cubes by heart — they could come up on a non-calculator paper, so it’ll save you time if you already know what they are.

BODMASBrackets, Other, Division, Multiplication, Addition, Subtraction

BODMAS tells you the ORDER in which these operations should be done:Work out Brackets first, then Other things like squaring, then Divide / Multiply groups of numbers before Adding or Subtracting them.

EXAMPLEFind the reciprocal of √4 + 6 x (12 - 2).

• √4 + 6 x (12 - 2) = √4 + 6 x 10

• = √4 + 60

• = √64

• = 8The reciprocal of 8 is ⅛.

Brackets, Other, Division, Multiplication, Addition, SubtractionIt’s really important to check your working on BODMAS questions. You might be certain you did it right, but it’s surprisingly easy to make a slip. Try this Exam Practice Question and see how you do:Q1 Without using a