Cambridge International Mathematics

Assumed Knowledge

(Number)

Contents:

A Number types [1.1]

B Operations and brackets [1.2]

C HCF and LCM [1.3]

D Fractions

E Powers and roots [1.4]

F Ratio and proportion [1.5]

G Number equivalents [1.7]

H Rounding numbers [1.11]

I Time [1.12]

The set ofnaturalorcountingnumbers is N =f 0 , 1 , 2 , 3 , 4 , 5 , 6 , ......g.

The set of natural numbers is endless, so we call it aninfinite set.

The set ofintegersor whole numbers is Z=f::::,¡ 4 ,¡ 3 ,¡ 2 ,¡ 1 , 0 , 1 , 2 , 3 , 4 , ......g:

The setZincludesN as well as all negative whole numbers.

For example: 0 , 127 ,¡ 15 ,10 000 and ¡34 618 are all members ofZ:

The set ofrationalnumbers, denotedQ, is the set of all numbers of the form

a

b

whereaandbare

integers and b 6 =0.

For example: ²^13 ,^1532 ,¡ 45 are all rational ²¡ 214 is rational as ¡ 214 =¡ 49

² 5 is rational as 5=^51 or^204 ² 0 : 431 is rational as 0 :431 = 1000431

² 0 : 8 is rational as 0 :8=^89

All decimal numbers that terminate or recur are rational numbers.

The set ofrealnumbers, denotedR, includes all numbers which can be located on a number line.

2

0 and

p

¡ 5 cannot be placed on a number, and so are not real.

A NUMBER TYPES [1.1]

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