Detailed mind-maps covering each section of the Matric Mathematics syllabus.
The notes provide concise summaries on each section as well as easy to understand and precise overviews.
For both Paper 1 and Paper 2 Mathematics.
÷ ÷:÷ ÷:÷ ÷::÷i:::÷:"
÷: ÷ ÷: ÷
* find x AND sub x into f- (x) to → y
OF TANGENT PO l
GIVEN x - A f " (x) = 0 find x
gRAD1fNT→DERlVATJ
o
,
x find derivative
°
sub x into floc) to find y
f (x)
'
→
X SU b MT x y Into a sub x into f- (x)
xtc •
find y Moc t C
-
im
y
-
[ find C ]
:i÷¥:i:÷:::::::::::n
NB @ the
turning TO FIND EQUATION GIVEN 3C -
INT
in
f (x)
'
= 0
÷÷I÷oh①}"mwn¥÷I÷i
. -
OWEN Tp ( m X n)
,i÷÷÷÷÷÷÷siEet
POLYNOMIALS
NB DIFFERENCE OF CUB ft
x = -
l X =3 x = -
1
LIMITS
:÷÷÷÷÷:: ÷÷i÷÷÷÷÷÷
REMAINDER THEOREM
factor IIe
÷
I remainder
mYIh{!futn
x # =
x
DETERMINE GRADIENT / RATE OF CHANGE
× fc # f =
remainder
X remainder =
f- ( x ) with subbed in # -
h
find
m=imo""i'-
to A
# THE RATE of CHANGE AT x / DERIVATIVE
t:÷÷"÷÷÷÷÷÷÷÷÷: ÷ :
OF f- (x) / GRADIENT OF TANGENT
FACTOR THEOREM
si : : :"± 's:O.ie?a.....o
' "
.
:÷::÷:
OPTIMISATION
a C ) b ( ) C C ) of factor
RATE OF CHANGE
Y
AVE xz -
x ,
x = 8 X =
If at if a -
MODE TABLE ENTER f- ( x )
I W
i'"%"
AVERAGE GRADIENT U
mi :
"
"
aq"""P
IF THERE IS ONLY ONE TURNING POINT
( xiy )
y
JC z
-
X I
, 3
f- (x) =
ax tbx
2
tcxtd → I
f- C )
'
=3 ax
2
t 2b x t C → A
f
'
( x) 70
bax t 2b / f- ' ( x ) co
t.ch
"
f- ( x) = →
M
NEE , ,
i¥""/
f- Cx)
'
-
I
/
Mt
, m -
f- (a) 9 I feel d l
l " Cx)
l f-
I y
I m t
I r f Cx) M
"
\
O
f- " (x)
-
-
int
x
I
-
I
'
f-
"
Cock O
face, - F
,
l
TP derivative f
''
(x) > O
l T
i ,
TP f (x)
NB f ( x)
'
→ PARABOLA
f
'
( x) → GRADIENT OF f- (x)
GRAPH OF DERIVATIVE SECOND DERIVATIVE
f- (x) → Str line
"
•
f ( x)
'
> O (above x -
AXIS )
f- Cx)
"
.
f.(x) increases → 70
original graph increases f- Cx) Mt
above x -
axis
f ( x) so ( below x axis)
'
of (x) (x) co
' "
decreases → f
-
•
original graph decreases f-(x) m below x axis
- -
of ( x) (x) int
''
'
TP → f O → x
f (x) = O [ x Ints ]
' - -
• -
TPS of f- (x) are m - O
f '(x) → f (SC) = O
"
• TP of
POINT OF INFLECTION OF f-(x)
, FUNCTIONS
lfcxt-acx.p/
l#J.:i . : n:n....÷.
i i ai :oi
PARABOLA
'
or
:
! !!
TPC Fa if C- Fa ) ) x
-
-
,
y -
a -
"
Domain ' er
. .
RANGE
ma,nt V. YE Caio )
, p
÷:÷÷÷÷:
"" "
.
' I (x p ) tq
hors Ita Als y = -
p →
I:L:'T III. is: :P
"" "" " ' "
:
p)
2
y
= a (x -
ta
2x Ints and Op
✓
-
y
= a ( x -
sci ) (x -
xz )
ii. iinei.mn : ai
'
÷÷:÷÷÷÷
x -
P
a. b tq
y
=
at
TOP HEAVY ASYMPTOTE y q
-
-
b 71
STRAIGHT LINE
.
.
#
a -
o c b C l
M = 92-42
Xz - X l
( → VERTICAL SHIFT ( E)
( Oic) y -
int
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