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let'sstart withtheintegers
im naturalnumbers
I integers
3 2 1 0 1 2 3 wholenumbers denoted as 2 Q rational numbers
From this we construct therational numbers which are ratio's of integers
anynumber r can be expressed as
r where mand n are integers denoted as m nÉÉj
however rememberthedivision of zero is ruledout as any number divided
by zero is
undefined
undefined
There aresomereal numbersthatcannot be expressed
as a ratio of integers
and these are called irrational numbers
e
g E or M
Real numbers aredenoted
by R
Tables ofintervals
round bracket ab
meansexcluded
ab
a a d
a
mi in can
c o bl 8
infinity.fr
included ob
1 0,0 real numbers
R
Inequalities
rules for inequalities
1 if acb then ate Cbtc addanynumber to bothsides
2 If acb and cad then ate abtd 12 inequalitiescan beadded
3 If acb and so thenacabe if c is positive wecanmultiply bothsides
4 If acb and eco then as be HOWEVER if c is negative thenwereverse thenedi.pe
gigaitf
5 If ocacb then hasto if wetakethereciprocals we reversedirectionofinequality
, What is an absolutevalue
the magnitude ofa number ofthesign
regardless
lal the absolute value of a is thedistancebetween a ando on a number line
the distance is always positive if I walktothe Neelsie from
Krotoa or from Kroton to the Neelsiethedistancewillbepositiv
it m
1
inany question get ridof the
absolutevalue
e
121 2 1 21 2
g
5 jo
Properties let a beR and neN
111 Ii b last in
3 Ian lain
Helpful statements
1 bet c iff x c
j I
2 In ca iff a cocca a
Ia I
3 In a iff a c a versa c
la j i s
, Trigonometry
Anglesaremeasured in degrees or
Esta go
22h xo
1rad
E
rola a ro
are
Tength subtended
by rad
ia.CM
cosse
unit circle
SpelialTriangles
2 1 A
no no 0
no
a a
B
I
Trigonometric functions
19 coso
ma
tano
51
50 iii
y
i
inx sink it s
is cos
an sin
fiction
an rini
i
T.tn
iion
T
F
f
Fa
f
MATHSO
D
cap
c
114 m
m.mn
X
É
ÉIm
7
D
T
t
x
B 7
I
A
, absolutevalues B realnumbers
titi mn
ireaiiii i
let'sstart withtheintegers
im naturalnumbers
I integers
3 2 1 0 1 2 3 wholenumbers denoted as 2 Q rational numbers
From this we construct therational numbers which are ratio's of integers
anynumber r can be expressed as
r where mand n are integers denoted as m nÉÉj
however rememberthedivision of zero is ruledout as any number divided
by zero is
undefined
undefined
There aresomereal numbersthatcannot be expressed
as a ratio of integers
and these are called irrational numbers
e
g E or M
Real numbers aredenoted
by R
Tables ofintervals
round bracket ab
meansexcluded
ab
a a d
a
mi in can
c o bl 8
infinity.fr
included ob
1 0,0 real numbers
R
Inequalities
rules for inequalities
1 if acb then ate Cbtc addanynumber to bothsides
2 If acb and cad then ate abtd 12 inequalitiescan beadded
3 If acb and so thenacabe if c is positive wecanmultiply bothsides
4 If acb and eco then as be HOWEVER if c is negative thenwereverse thenedi.pe
gigaitf
5 If ocacb then hasto if wetakethereciprocals we reversedirectionofinequality
, What is an absolutevalue
the magnitude ofa number ofthesign
regardless
lal the absolute value of a is thedistancebetween a ando on a number line
the distance is always positive if I walktothe Neelsie from
Krotoa or from Kroton to the Neelsiethedistancewillbepositiv
it m
1
inany question get ridof the
absolutevalue
e
121 2 1 21 2
g
5 jo
Properties let a beR and neN
111 Ii b last in
3 Ian lain
Helpful statements
1 bet c iff x c
j I
2 In ca iff a cocca a
Ia I
3 In a iff a c a versa c
la j i s
, Trigonometry
Anglesaremeasured in degrees or
Esta go
22h xo
1rad
E
rola a ro
are
Tength subtended
by rad
ia.CM
cosse
unit circle
SpelialTriangles
2 1 A
no no 0
no
a a
B
I
Trigonometric functions
19 coso
ma
tano
51
50 iii
y
i
inx sink it s
is cos
an sin
fiction
an rini
i
T.tn
iion
