RECURRING DECIMALS
Rule
1
Count the digits from decimal to START
1 followed by those
repeating unit Multiply by
number of Zeros
f
0
11231
0
125
repeating
1
from decimal to END of
unit Multiply
those
1
by followed by
number of zeros
0 3165
eg
0 12561
3
Now
11000
10
0 3
2 Count the
digits
of
Subtract
10000
100000
both of these
Must simplify the final fraction
655
0.66666
START noDigits
2
END
START
0.66666
10K
6
1k
0.6666
92
6
2
1
93
2
3
6666
0
2
SUBTRACT
CONVERT RECURRING DECIMAL TO FRACTION
2 16
1
END 100
2
START 10
2
2.166666
END
100k
START
10K
216.6666
21.6666
90k
195 0
19811
2
163
SUBTRACT
END
2
gs USTART
1l00
IOR
2
E ND
START
1.25555
look
10K
125.5555
12 5555
90k
113
R
19
0
SUBTRACT
END 1000K
1.131T
START 10K
x
END
START
1 3414141
10002
1341.414141
10k
13.41 41 41
990 k
R
1328
132
0
664
990 495
n
49
SUB
END 1000002
081132157
START 100K
FRACTION
TO
0.1111
0.1
RECURRING DECIMAL
9
it
SURDS
SQUARE ROOTS
14
Simplify
in
18
19
ii 1180
Ig 136
2
59 12
15
125
5
536 55
655
352
sa
I ADD SUB ONLY SAME SURDS CAN
55
16
25
399
3
525 5 15
115
553
53554
BE ADD SUB
while adding subtracting the surdpart cannot change
i
352 752
1052
ii
1253
453
853
iii
258 552
21252
58
14
552
114
1255
355
IV
2511
7H
2
5452
452 552
952
252
1555
5511
egg
Iii
MULTIPLY
1
52
53
12
iii
352
553
15T
iii
552
4
2052
IMI
IV
DIVIDE
3
56
MATHS PEOPLE HATE HAVING
SURDS IN DENOMINATOR OF A
FRACTION
RATIONALIZATION Process to bringsends in numerators
lal
Ib
EYE
E
352
54
352
13
25
3Marks Must come in
Exam 2025,2026 2027
3
C
55
1
change middlesign
8 F.it
3
andthenmultiply
and divide
375 1
55
Thiswill come in algebratoo
55 1
1
3
3 15
2
5
a b
112
355
3
1
5
3
355
4
5
iii
2
F
2
57 2
5
F
5
2
55 21
57
2
557
5
2
557
7
2
10
2
2
10
4
557
3
10
atb _a
b
in
253
F
3
253
n
Is
s
257
F
3
2
13
653
2533
2133
2
9
11
653
2
533
353
x
533
IN
3
15
55
1
3
55
55 1
55 1
55 1
3
555 1
55 1
35
353
55
3
1512
1
525
355
55
1172
155
455
3
5
5
1
455
8
355
55
4
55
4
1
352
2
55
2
5
253 1
352
5
253
1
253
1
253
1
13 52
5
253 1
656 352
11
2
253
1
1053
5
cis
656
352 1053
12
656
5
1
352
11
1053
5
MENSURATION
FORMULAS
UNIT CONURT
FRUSTUM
Edited
i
Volume
SIMILARITY
fromtop
Volume of_Volume of
of frustum
Big come
small cone
TOTAL SURFACE AREA
Small civile
1114m
Bigcircle
art
state
ARL
AR
Stallone
are
ALGEBRA
FACTORIZE
a
23
622 1621
x
x2
x2
x
x 8
x
2 2
212
b
23
16
62
82
2
22
2
16
8
x
8
2
8
4
3
x
x
4
x
9 4
6
6
122
1121
22 32 42
x
2
80
8 2
REED
k
1 16
8 2
2
722
1161
4
12
40
3 4
3 4
2
3
x
3
x
1 12
2 6
3
3
7
7
EXPAND
FTZ
x
a
x2
x2
b
x
1
x
22
x
x
2
2
1
III
22 42
32
12
FRITZ
2355T
22 22
23 222
23
Rtx
12
2
12
12
112
12
2
1
2
1
1
22
c
2
x
x
1
3
3
32
2THII
2
2
3
3
3
422 6K
422 22
223
3
522
4
R
2R
3
62
22
3
3
CIRCLES
SEGMENT
ALTERNATE
THEOREM
by
You
w̅
P
55
a
46
55
QUADRATIC GRAPH
2
82
2m
Q Express
22
4
11
in
form
125 125
a
x
b
c
21
2EEF
2
k
2
2
8 7
11
EEE
Shafe
Turningpoint vertex
b
2,3
State the coordinates of
turning points
2
3
SIMULTANEOUS
EQUATIONS
ELIMINATION
SUBSTITUTION
Make subject in both
equations
and put them
24
4
32
7
2
12
2 24
5
equal
7
y
5
y 32 12
09
1
POINTS OF INTERSECTION
TWO
LINES
MEET
POINTS OF INTERSECTION
2
2
2
2
x
4242
3
k
42 3 12
15
2225k
b
x
Quadratic formula
Jb
0
0
4
11 5,242415
212
5
x
x
2
5
x
1.76
4
42 12
Wrong
5 545 4
correct
2
1.76
1 76,4 96
4.26 29.04
1.76
12
4 4.96
51,545
5 545 4
4.26
29.04
4.26 29.04
145
1154
k
4 414.26 12 4 4 1.76
4ac
2A
15
4.26
4 42 12
2
4.96
FUNCTIONS
flat
6k
flat 2
6 2
7
2
7
6K
12
7
6N
5
fin
6N
7
4
6
7
Y 7
62
x
4
fix
flu
GRAPHS
7
6
7
2
6
62 7
ga
goes
f 22
2
6 22
2
3
3
125
125
7
53
125 3
1
R
3
5
3 4
13 4
glx
Y
2
5
24
5
Y 5
2 R
x
Y
g a
5
2
25
7
5
2
41
n
4
x
4
2
x
4
222
3
20
2
3
2
202
822
2
gf
3
3
11
x
gf
gf 2
a
2
x
8
52
2
12
80
SR
212
4
22
8
22
3
2
20
2
5
5
3
1
h x
9712
3
1
32
30
x
0
80
4 23 1
1
y
m
2
351
f a
3T
1 112
2
11
3
2K
1
34
52
1
52
1
1
1
0
2
2
0
0
71
gg
gg
a
x
3
2
3
92
6
9
8
2
2
comma
hfla
I
12
ghin
1
hfla
x
f int
gin 25
t
t
3 2
2 2 2x 1
1
11
x
2x
6k
3
4k
2x
1
x
at
2
ghk
2n't
1121
3
Yx
5k
K
22
3
1
matte
x
hla
2n
in
Jin
Jy
Jae
3101 1
11 5 4
0 5 0 4
20
girl Y
Y
y
2
3
3
22
4
a
23
g
gh 2
gh
1
3
4214
2
2
43
3
64
3
128
3
3
2x
2
3
2
125
gx
g 2x
att
1
2142
a
a
2n
3
g
3
4
2x
7
9122
3
7
42
10
42
girl
2K
3
g
x2
g
2
24
x
2
2
3
gg
3
222
2
3
2
ggcal
42 9
42
429
1
429
1
16
16
42
4
1
1
b 16
3
42 6 3
11
Lets suppose
a
2 2
a
ggins
gin
h
2.5
I
x
a
16 h a
9
3
2
1
29
2A
3
A
1.5
h 16
1.5
3
32 1
2 5
1
k
32 1
4
x
4
5
R2
59
4
3
20
20
2
323
323
3x
60k
3 2
R
3 3
ar
22
x
20
R
20
422
for
592
bn
C R
d
20
20
11 3
2
245
3
243
3
35
5
iii
3 263
3 81
3 27
3 9
3
fin
7
f 7
x
37
K
2189
2
FUNCTIONS
1
Graphs Sketching
2
Domain
3
Asymptotes
Range
SHAPE
SKETCH
y intercept x 0
x intercept 4
0
symmetry if any
SKETCH
1
4
12
30
Intercept
grad
3
1275
4
Font
grad
s
s
2.15
x intercept
y o
0
2
2K
5
x
52
5
2.5
Quadratic
stap
11.1.14
u
9
Turningpoint 1,61
6
x
y intercept
Y
0
3 0 172 6
31 172 6
6
341
9
4
Y
1 n
2
7
E F
Tupied 1217
y intercept x 0
Y 10 272 7
Y
Y
1 212 7
11
11
1
5
2
Y
x
shafeo
A
y int
2
3
25
3
25
TP 3,25
0
25
7
2 0 35 25
21 372 25
219 25
18
25
7
Y
x
Tymptotes
70
Y
asymptotes
1 x axis 4 0
2
y axis x 0
asymptote
Y
y int x 0 y
Asymptotes
NIn
31 axis
y o
y axis
x
1
Asymptote
0
3
y3
11
Y
3
2
yintercept
Asymptote x axis
Y o
43
y
y int n o
5
Y 5 2
5
1
5
7
x axis
Asymptote
5
y
Asymptote
2
y
2
14 01
7
7 5 29 7
7
12
Tun
1 5 2
8
iiÉ.ttit
D
R 0
3 20
5
4134518
0
8
5
5
45
0
write down equation of asymptotes
3
5
y
y 52
1
40
boxes
4 523
4 3
Asymptote
y
Asymptote
3
y
3
72
4
y 4
7
y
3
7
y 72
I
y
3
k 70
y 12 3
4 3
3
1 0
Asymptotes
Y
2
Vertical y axis
Horizontal 17 31
270
2 0
y 0
to
Asymptotes
x
4
Horizontal
y
2
Vertical
x
0
2
y
5
5m
5
4 5
4
x
y
Asymptotes
Horizontal y
5
x
0
Vertical
DOMAIN
RANGE
AND
implet values
output values
values of x
values of y
GRAPHS ARE VERY
USEFUL TO CHECK
O
RANGE OF A FUNCTION
Domain
flat
Q1
D iñ in
write
Input
1
k
3
1
12
2
15
3271
3
12
down range of
fix
is
1
15
3
1
36 1
1
3
1
2
f3
f 12
3 3
1
9
1
10
3 12 1
36 1
37
f 15
3 15
1
4871
46
flat
ft 1
Range
1
2
output
10
37
46
I t.ie
SI
GoldenRule Never tell
range without looking at graph if
domain is in
inequality form
included
Y3
6
1
Range
OUTPUTS
RANGE Yande
4
f 1a
16
Eluded
intended
not
155B
Q
Find
ay.fi
3hts
range of
fix
4
y 3 5
included
Range
17
5
Funded
fin
17
fin
Q
314 tt
Smiley
Find
range of fin
2cxco
fin
30 212 5
3 212 5
17
ten
17
Range
5
5
5
flat
17
y
17