Graphs ①
nY
Y
= mo + C
③ MY
y=
+
q
-
①
straight line graph
?
E 7
y
'
=
mec + c
V vV
parabola
② ax + 1
y
=
②
: ② NY ⑪ aY k b" +
hyperbola
<
y
:
+ ,
q
.
y N a
y
= ax- c
& >s < >s
①
y
= k b" .
+
q exponential
~ ~
②
Parabolas y ax +c
a(x-root) (x-root)
y
= =
,
·
·
...
as
happy :
positive as I sad
negative Solving with and
point suby into then sub in point
yout
a s c,
Domain all values , ER and (x-root) Caroot) then sub
x-ints a
point y : a in
point
=
-
both
Range --> all the
y
values ,
y-4 yElR ,
I random
points
: sub into
yeas to
then solve
simultaneously
= q
③
Hyperbolas ,
y
+
N &
Lines
of symmetry =
y
=
x+
q ,
y
= -
x +
q
acO
>
978 &
y
V
Domain scElR
easymtote
=
,
Range =
y asymtote yelR
= ,
①
Exponential Graphs s
y
= Kb+
.
q
g asymptote
Reflected over the
y-axis
=
values will change
k sub
point equation
=
into
-x(y (5)"
>
3
y y 3
=
=
=
<
·,
T (3 :
. 6)
: 0
10 : 10 1)
:
·
1) E
Reflectedvalues willthe
over cc axis
y change
Reflected over the sc axis
values will
y drange
-
·
10 : -1) 10 : -1)
⑳
-6)
13
:
-( -
3: -
6) ·
(y (j)
~ "
3
-
y
=
INEQUALITES
= -
z
Y
=.
M
Reflected the
yaxis Fractions
multiply out by LCM
over
values -
change
Whole Numbers : ... No
0, 1 2 3 00o
Lincluding C not
including infinity
,
I
,
,
Natural Numbers: 1, ,
2 3 IN 00000
inequality
...
-
io"23hg notation - 3 x4 ; xER
Z
Integers : -3 -1
, , 0, 1,3 ...
; interval notation - xE(-3 ; 4]
number IR 234]
⑳
Real numbers
any o
-
, Algebraic Expressions AlgebraicFractions
Only cancelIdentical brackets
Sum divide
Difference Between L Cubes Invert
multiply to
·
+
Sum-first bracket-bedsube
second bracket- (first term& (first term)(secondterm (second term Laws
of Exponents
E
g
.
. = a3 + b3 only when
you
have one term
1 am
first bracket
x an amen
(a + b)
.
=
=
second bracket (a2 -ab + b2) a xas al
eg
: =
=
.. (a + b)(a2 -
ab + b)
am
2
am = an =
an
=
am -
Difference-first bracket-tube - be
e /2x = 2x3 bat
g:
.
=
second bracket =
(first term (first term)(second term + (second term)
E a3- b3
3
am " = am
.
n
g
.
. =
first bracket = (a b) -
.
e
g
: (as)3 =
a
second bracket = (a 2 ab + b2)
.. (ab)(a2 ab + b) "(ab) ambm
"
=(am ae ,
e
:: 3
g
Patterns +
Sequences sa an
difference
-n =
#n = Common
2 == t
Eig 3 8 13 18 eg
:
:
, , ,
Common difference = S
: Tn =
En I ? ⑥ "m = e
244 4 42
difference from
I In a number .
e = = 16
g
=
= :
5 -
x = 3
x =
- 2
: Tn = 5n-2
Creating Equation an
Example
1 200 =
people - concert .
Adults R45 Children R2I
=
,
=
Total amount RSOHO how children ?
spent on tickets many
=
,
Let no
of Child . = x
Price Amount Paid 2(x + 45(200 x) - = 8048
Children sc 21 21x 2(x + 9000 45x -
= 8040
Adults 200- x 45 45(200 x)
- -
24x -
=
960
Total 200 8040 x= 40 .... 40 children
nY
Y
= mo + C
③ MY
y=
+
q
-
①
straight line graph
?
E 7
y
'
=
mec + c
V vV
parabola
② ax + 1
y
=
②
: ② NY ⑪ aY k b" +
hyperbola
<
y
:
+ ,
q
.
y N a
y
= ax- c
& >s < >s
①
y
= k b" .
+
q exponential
~ ~
②
Parabolas y ax +c
a(x-root) (x-root)
y
= =
,
·
·
...
as
happy :
positive as I sad
negative Solving with and
point suby into then sub in point
yout
a s c,
Domain all values , ER and (x-root) Caroot) then sub
x-ints a
point y : a in
point
=
-
both
Range --> all the
y
values ,
y-4 yElR ,
I random
points
: sub into
yeas to
then solve
simultaneously
= q
③
Hyperbolas ,
y
+
N &
Lines
of symmetry =
y
=
x+
q ,
y
= -
x +
q
acO
>
978 &
y
V
Domain scElR
easymtote
=
,
Range =
y asymtote yelR
= ,
①
Exponential Graphs s
y
= Kb+
.
q
g asymptote
Reflected over the
y-axis
=
values will change
k sub
point equation
=
into
-x(y (5)"
>
3
y y 3
=
=
=
<
·,
T (3 :
. 6)
: 0
10 : 10 1)
:
·
1) E
Reflectedvalues willthe
over cc axis
y change
Reflected over the sc axis
values will
y drange
-
·
10 : -1) 10 : -1)
⑳
-6)
13
:
-( -
3: -
6) ·
(y (j)
~ "
3
-
y
=
INEQUALITES
= -
z
Y
=.
M
Reflected the
yaxis Fractions
multiply out by LCM
over
values -
change
Whole Numbers : ... No
0, 1 2 3 00o
Lincluding C not
including infinity
,
I
,
,
Natural Numbers: 1, ,
2 3 IN 00000
inequality
...
-
io"23hg notation - 3 x4 ; xER
Z
Integers : -3 -1
, , 0, 1,3 ...
; interval notation - xE(-3 ; 4]
number IR 234]
⑳
Real numbers
any o
-
, Algebraic Expressions AlgebraicFractions
Only cancelIdentical brackets
Sum divide
Difference Between L Cubes Invert
multiply to
·
+
Sum-first bracket-bedsube
second bracket- (first term& (first term)(secondterm (second term Laws
of Exponents
E
g
.
. = a3 + b3 only when
you
have one term
1 am
first bracket
x an amen
(a + b)
.
=
=
second bracket (a2 -ab + b2) a xas al
eg
: =
=
.. (a + b)(a2 -
ab + b)
am
2
am = an =
an
=
am -
Difference-first bracket-tube - be
e /2x = 2x3 bat
g:
.
=
second bracket =
(first term (first term)(second term + (second term)
E a3- b3
3
am " = am
.
n
g
.
. =
first bracket = (a b) -
.
e
g
: (as)3 =
a
second bracket = (a 2 ab + b2)
.. (ab)(a2 ab + b) "(ab) ambm
"
=(am ae ,
e
:: 3
g
Patterns +
Sequences sa an
difference
-n =
#n = Common
2 == t
Eig 3 8 13 18 eg
:
:
, , ,
Common difference = S
: Tn =
En I ? ⑥ "m = e
244 4 42
difference from
I In a number .
e = = 16
g
=
= :
5 -
x = 3
x =
- 2
: Tn = 5n-2
Creating Equation an
Example
1 200 =
people - concert .
Adults R45 Children R2I
=
,
=
Total amount RSOHO how children ?
spent on tickets many
=
,
Let no
of Child . = x
Price Amount Paid 2(x + 45(200 x) - = 8048
Children sc 21 21x 2(x + 9000 45x -
= 8040
Adults 200- x 45 45(200 x)
- -
24x -
=
960
Total 200 8040 x= 40 .... 40 children
