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7/31/2019 Maths Concept Map 8 CBSE
1/21
Vtngcjhe ) Nv*r [tm{etvner
Bmcbe{v Lg{r
Bhgrr YNN
Hncer ) Gcjher
Ghjedtgnb Ep{terrnmc
Gteg
Tgvnm R~ldmh
Tgvnm ) [tm{mtvnmc
[etbecvgje[tminv ) Hmrr
Rn h N v v
7/31/2019 Maths Concept Map 8 CBSE
2/21
Rn h N v v
G
BD
G
B
D W
[
T
p p
P
Q
9; 9;
^
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BD
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9;
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75;75
9; 75
T(nn.
DG
(nnn. (n.
RnfeGcjhe
1 GD DB BG1 DGB GDB DBGBhmref
butyelgfe u{ miv`tee hnce rejlecv#
Bhgrrninbgvnmc
Rbghece 1FCm vzm rnfer gte ewugh
Nrmrbeher 1
FVzm rnfer gte ewughdgre gcjher m{{mrnvevm ewugh rnfer gte ewugh
Ewunhgvetgh 1
F
Ghh rnfer gte ewughegb` gcjhe `gr legrute 9;
Yetvnber 1G D B
Gbuve gcjhe 1Fghh gcjher 1,jtegvet v`gc ;herr v`gc >;
Mdvure gcjhe 1
Fgc gcjhe 1,jtegvet v`gc >;herr v`gc 70;
Tnj`v gcjhef 1,Fgc gcjhe ewughr vm >;
[
W T
G
D BF
P
Q^
G
B
:; 0;
D
T
5;
W
75;
R
7;;
[
Epvetnmt gcjhe {tm{etv~ 1[TR < W[T / [WT
2;
Rul mi v`e hecjv` mi gc~ vzm rnfer mig vtngcjhe nr jtegvet v`gc v`e hecjv` miv`e v`ntf rnfe#2 bl / 5 bl 3 9 bl9 bl / 5 bl 3 2 bl9 bl / 2 bl 3 5 bl#
(n. (nn.(nnn.
2bl2bl
>;2;
(n. (nn. (nnn.
VTNGCJHE ) NV*R [TM[ETVNER
7/31/2019 Maths Concept Map 8 CBSE
3/21
Gbuve (; 8 8 >;.w
Bml{helecvgt~ gcjherVzm gcjher z`mreRul nr >;
Ru{{helecvgt~ gcjher
Vzm gcjher z`mrerul nr 70;
V~{er mi gcjherHnce
Tnj`v ( >;.w ; 8 8 70;.w
Rvtgnj v ( < 70;.w
Teihep (70; 8 70;.w 8
Bml{heve ( < 29;.w
hl
{ w
Hnce 1 `gye ncincnve hecjv`
[gtghheh hncer 1 ceyet ncvetrebvr
Ncvetrebvncj hncer
Rul mi ghh gcjher mcmce rnfe mi hnce nr 70;
6p
p 4p
5p
5p / 4p / p / 6p < 70;
2pp
4p
5p6p
Rul mi ghh gcjhegtmucf g {mncv nr 29;
p / 4p / 2p / 6p / 5p < 29;
7 4
62
9
0
5
:
Gcjher lgfed~ vtgcryetrgh
Bmtter{mcfncj gcjher(7 5. (4 9. (2 :. (6 0.
Ghvetcgve Ncv# gcjher(2 9. (6 5.
Bm#ncv# Gcjher(6 9. . (2 5.
Ghvetcgv Epv# gcjhe(7 0. (4 :. Ni hncer gte xxeh v`ec
Bmtter{mctfncjgcjher gte ewugh
Ghvetcgvegcjher gte ewugh
p
~
p / ~
bmllmc gtl
Yetvnbghh~ m{{# gcjher
7
4
2
6
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M
G
D
B m{{#gtlBmllmc yetvep
7 < 2 ? 6 < 4
2;75;
[ W
T
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Hncegt {gnt
vzm gfagbecv gcjherz`mre rul nr 70;
Rul mi Bm# Ncv#gcjher nr 70;
[
l
h
74
7gcf 4 gtegfagbecv gcjher
HNCER GCF GCJHER
7/31/2019 Maths Concept Map 8 CBSE
4/21
Uchnoe vetlr1
Fniietecv ghjedtgnb igbvmtr
2p ~ < 2 p p ~4
2p~ < 2 p ~ ~4
Rgle ghjedtgnb igbvmtr
9pgd < 9 p g d
,2gdp < ,2 g d p
gffnvnmc
Rudvtgbvnmc
>gd / 5gd < (> / 5. gd < 76gd
>gd 6gd < (> 6.gd < 5gd
Yghue mi Ep{terrnmc
gv p < g _{uv p < g\
ej 1 yghue mi p ,5p4
gv p < ,7
(,7. ,5(,7. #######2c#######
V~{er mi GhjedtgnbEp{tnrrnmc
Lmcmlngh Mce vetl 1 ej 1 2p ,4v ? 2
Dncmlngh Vzm vetlr 1 ej 1 2p ,4v ? 2R/4
Vtncmlngh V`tee vetlr 1 ej 1 2p / 4~ , 5
Wugftncmlnghr Imut vetlr 1 ej gd / 4{w / 2tr / v
p / 2~ ? p / 24
Rvgcfetf imtl4p / 2~ p / 2p , 5p / 9
4 4 4
(n. 2p~ / 5p , 5p / 94 4
(nn. 9 , 5p / 5p /2p~4 4
Lgv`elgvnbgh M{etgvnmc
BmcrvgcvrYgtngdher
(p ~ qg dv######.
Nvr yghue nr cmv inpef
_ / , \
(4 2 ,6 7;;#########.
Nv `gr inpef yghue
Ep{terrnmc 1 >p , 2~p / 7;4
Vetlr >p4
,2~p 7;
p p ,2 ~
Igbvmtr Igbvmtr
Culetnbghbmeiinbnecv (,2.
Nc ,2p ~4
Bmeiinbnecv mi
p ~4
,2p4 p ,2~
nrnr nr nr
,2 : ,2p~ p4
Eyec cm# p
GHJEDTGNB EP[TERRNMC
7/31/2019 Maths Concept Map 8 CBSE
5/21
T`mldur 1
Vtg{eqnulWugftnhgvetgh 1Rwugte
[gtghhehmjtglBntbheVtngcjhe
Tebvgcjhe
`7
`4
G
F
B
D
f
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g
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g
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g ucnv
`7
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f
g ucnv
t
T
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D
G
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G
Bg ucnv
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D
G
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74
g `7
6ucnv 4ucnv
0 ucnv
4ucnv
0/4/4[
W
TR
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4
6/4/4
ej#
Gteg mi [gv` -yetgcfg`< Gt# [WTR , Gt#GDBF
h ucnv
f
Gteg < g ` < d < b Rw# ucn vr7 4 2
G < ` (g /d. rw# ucnvr
Gteg < fngjmcgh rul mi miirevr< f _` / ` \ rw# ucnvr7 4
Gteg < g ` rw# ucnvr < f f rw# ucnvr7 4
Gteg < g ` rw# ucnv < d ` rw# ucnvr
dgre < Gteg bmtter{mcfncj ghvnvufeghvnvufe < Gteg bmtter{mcfncj dgre
7 4
Gteg mi r`gfef tejnmc < (5. , (2.{ {4 4
(g. [gncvncj - z`nve zgr`ncj(d. heyehhncj
(b. [hmuj`ncj(f. jtgqncj - zgvetncj
T < 2 / 4 bl < 5t < 2 bl
Z`ec vm bghbuhgve Gteg 1
G < g g rw# ucnvRnfe < gteg ucnvf < 4 g
Gteg < h d rw# ucnvrhecjv` < (Gteg dtegfv`. ucnvdtegfv` < (Gteg hecjv`. ucnvf < h / d
4 4
dgre < 4Gteg ghvnvufeghvnvufe < 4Gteg dgre
74
74
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ej#
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< 4 24 4
< 6 > < 29
Ep{terr 624 gr {tmfubv mi{mzetr mi {t nle cm#
7
22
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4:2
564
7;04
47946244
< 4 4 4 4 2 2 2 < 4 26 2
[tnle igbvmtnrgvnmc
ej 1 4 / 2 / 6 < 7 / 7 / 7 < 2
ej 1 (n. 2 < 07 < 2 2 2 2 < 2 p < 5#> 7;5>; < 5#> 7;5>;; < 5#> 7;
7
4
2
ej 1 7;;;< 7; 7;; < 7; 7; 7;< (45.(45.(45.
Ep{gcf imtl 1 6:597< 6 7; / : 7; / 9 7; / 7 7;
6 2 4 ;
< 4 52 2
7/31/2019 Maths Concept Map 8 CBSE
12/21
Bmcjtuecv Inj
Ewugh R`g{e gcf Ewugh Rnqe
Btnvetng imt Bmcjtuecbe mi
Vtngcjhe Nc [WT v`ec d~ b#{#b#v#
WT < HL < 5bl [ < C
T < H < 0; T[ < HC
WT[ LHC W[ < LC
F
F F
gcf HLC
W < L < 2 ;
F
d~ G# R# G# [tm{etv~2;
T
[W D
l [WT < l GDB
[WT GDB
Nc tv# gcjhe vtngcjhe*r
V`e `~{mvecure < (bmrtter{mcfncj.gcf mce rnfe `~{mve cure
mi g vt ngcjhe gcf mce rnfe mimv`et vtngcjhe
B
G
D Ni G D < GB
D < B
[G
Nc GMD gcf WM[GM < MW
GMD < WM[MD < M[
F F
ej 1
D B
d b
g
G
0bl W T
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p
~9; 6;
0;q
Jn yec 1 G DB [WTvm Incf 1 p~q g db#
Rm (n. GD < [W (ny. G < [9bl < q g < 0;
(nn. DB < WT (y. D < W0bl < ~ d < 9;
(nnn. GB < [T (yn. B < T:bl < p b < 6;
F F
9bl 6bl
NcGD < P^ < 2bl v`ec d~ b#{#b#v#
DB < PQ < 9bl G < ^
GB < ^Q < 6bl D < P
GDB ^PQ B < Q
F F
#
GDB ) P^Q
_ \
F F
d~ R R#R {tm{etv~
L C
2;
TW
2; 0;
D B
G
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P
2 rnfer mi g < Bmtter{mcfncj v`teevtngcjhe rnfer mi mv et vtngcjhe
[ H
0;
(Bmtter{mcfncj.
[ G
4 rnfer gcf v`e ncbhufefgcjhe mi g vtngcjhe
(bmtter{mcfncj.< 4 rnfer gcf v`e ncbhufef
gcjhe mi mv`et vtngcjhe
D B
9;
TW
9;
Nc [WT[W < DB < 5bl
[ < D < 9;
_ \
F gcf GDBWT < GB
T < G
[T < GD < 6bl W < B
[WT DBG
F
F F d~ R#G#R {tm{et ~v
^
P
Q
>;6bl
5bl
>;L C
H
Nc v# P Q gcf v HLC
^ < C < >;`~{# PQ < `~{# HL < 5bl^Q < HC < 6bl
^QP CHL
t t #F F
F Fd~ T#@#R# {tm{et~#
V`ec d~ b#{#b#v
P < L
Q < HP^ < LC
2;
B
G
T D B
G
F F[WT GDB
Bmtter{mcfncj yetvep 1 G [ ? D W ? T BBmtter{mcfncj rnfer 1 GD < [W ? DB < WT ? GB < [T
Bmtter{mcfncj gcjher 1 G [ ? D W ? B T
GMD WM[
d~ R#G#R# {tm{etv~
F F
Nc GBW gcf GDW
B < D < >;`~{ WG < ` { WG
BW < DWGBW GDW
d~ T#@#R# {tm{etv~
F F
F
F
# ~ #
W
G
D
B
W
[
M
WD
7/31/2019 Maths Concept Map 8 CBSE
13/21
Ncvejetr_Ghh cgvutgh culdetr / ; / cejgvnye
mi bmucvncj culdetr\
, , , , , , , , , , , , 6 2 4 7 ; 7 4 2 6 , , , , , , , , ,
Cejgvnye ncvejetr [mrnvnye ncvejetrCenv`et {mrnvnye
Cmt cejgvnye
(nn. ,4: , (,2. < , 4: / 2 < 46
(nnn. 4: (,2. < 4: / 2 < 2;
(ny. 2 (,4:. < ,2 / 4: < 46
(y. 4: (2. < 4:2 < 2;
Z`ec v`e fnynfecf gcf fnynrmtgte mi uchnoe rnjcr v`e wumvnecv nr cejgvnyemv`et znre {mrnvnye Ni g gcf d gte ( / y .v`ec
(,g. d < (g d.(
9. 2 . (7:.\ < 2 _49\ < 2 / 49 < 42
(nnn. Grrmbngvnye {tm{etv~(g. (g / d. / b < g / (d/b.
ej 1_(2. / (>.\ / 7: < (74. / 7: < 5(2. / _(>. / 7:\ < (2. / 0 < 5
(ny. Gffnvnye nfecvnv~
g / ;
7/31/2019 Maths Concept Map 8 CBSE
14/21
Fnynrnmc
ITGBVNMC
6
77
6
5'
6
7
/
6
7
7mi4
7
4
77
4
7'%
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7'%
744
7'%
7mi4
7
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7
%%
%%
' 5
6
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nr!
79
6
Tr# 29
Bml{gte culetgvmt
Fecmlncgvmt rgle
Culetgvmt rgle
Bml{gte fecmlncgvmt
Incf H#B#L# mi fecmlncgvmtrH#B#L# mi (25. < 75
75
9
25
24?
75
5
52
57'
%
%'
%
%
:
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2
5
6
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5
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71ej 7
7/31/2019 Maths Concept Map 8 CBSE
15/21
Bml{gtncj Febnlghr
ej 1 Gttgcje nc grbgcfncj mtfet4#;7 7#> ;#>5 2#4 gcf 4#:50
N B`gcje vm hnoe febnlghr4#;7; 7#>;;;#>5; 2#4;; 2#4;; 4#:50
NN ztnve bmtter{mcfncj culdetr
4;7; 7>;; >5;24;;4:50NNN Cmz gte gcjhe>5; 7>;; 4;7; 4:52 24;;
NY ;#>5 7#> 4#;7 4#:5; 2#4
Fnynrnmc#
Febnlghr
Febnlghr itgbvnmcr
e
gtez`mre fecmlncgvmtr gte7;7;;7;; #v#b#ej 1 42 # ;;5
z`mhe culdet Febnlgh {gtv{gtv
hnoe febnlghr uchnoe febnlghr
rgle febnlgh {hgbe5#45 9#0>
fniietecv febnlgh {hgbe5#45 9#0>2
Luhvn{hnbgvnmc
febnlgh d~ febnlgh
lmye febnlgh {mncv nc v`e culdet vmv`e tnj`v d~ gr lgc~ {hgber gr v`etegte qetmr# myet 7ej ;#52 7; < 5#2
;#52 7;; < 52;#52 7;;; < 52;
(n. Intrv luhvn{h~ gr z`mhe cm
(nn. Bmucv v`e cm# mi fnjnvr vm v`etnj`v mi v`e febnlgh {mncv
(ny. [uv febnlgh {mncv nc v`e {tmfubv d~bmucvncj v`e fnjnvr itml v`e tnj`v lmrv {hgbe
(nnn. Gff v`e cm# mi fnjnvr bmucvef
ej 1 459# : ;#;;5 7;; < ;# 2;> _4 {hgbe vm v`e heiv\
d~ z`mhe culdet
7#5:5 25 < _75:5 25\7;;;
7
< _65\ < ;#;657;;;
7
d~ febnlgh cm#;#795 d~ 7#5
7 ;
7 5
7 ; ;
7 9 5,'
\7 57 9 5_7 ; ;
7,'
7 7#;7 ; ;
7 7 ''
(n. febnlgh ncvm itgbvnmc
ej 1 2#:5
(nn. itgbvnmc ncvm febnlgh
6
7 5
7 ; ;
2 : 5''
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45>
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%
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Rudvtgbv 1 0#>9 itml 45#7
b`gcje vm
76#79
>9#0
7;#45
) hnoe febnlghr v`ecrudvtgbv hnoe z`mhe cm#
Gffnvnmc
ej 1 Gff 2#;7 4#50 gcf 9#>
6>#74
>#9
50#4
;7#2 Oee{ febnlgh {mncvr ucfet egb` mv`et
Ztnve fnjvr nc v`e bmttebv {hgbe yghue bmhulcr
Gff hnoe z`mhe culdetr#
Bmcyetv
7/31/2019 Maths Concept Map 8 CBSE
16/21
Tgvnmcgh Culdetr
G culdet v`gv bgc de ep{terref nc v`e imtlw
{ ncvejet
ncvejetduv w m-
Gffnvnmc
Bmcyetv egb` mi v`el ncvm culdet znv`g {mrnvnye fecmlncgvmt#
_z`ec fecmlncgvmtgte rgle\
b
dg
b
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g.n(
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ej 1 Gffnvnye ncyetre mi
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5
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[tmfubv mi Tgvnmcgh Cm#
gvmtrlncfecmmi{tmfubv
culetgvmtrmi{tmfubv'
4 0
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Luhvn{hnbgvnye ncyetre mi
;w{z`ete{
wnr
w
{-
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5nr
5
2mibn{tmbghTe1ej
Rnl{herv (Hmzerv. mt rvgcfgtf imtl
Ni fecmlncgvmt nr g {mrnvnye ncvejet gcf
fecmlncgvmt gcf culetgvmt `gyecm bmllmc igbvmt mv`et v`ec 7
ej 1 Rvgcfgtf imtl mi 5
4
.2(75
.2(9
nr75
9 )
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fnynfe d~ @#B#I mi 9 gcf 75
Ewunyghecv Tgvnmcgh cm#
70
7;
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54
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ewunyghecv
Tgvnmcgh cm#
ewunyghecv
Tgvnmcgh cm#
Bml{gtnrmc
!Vzm {mrnvnye tgvnmcgh culdetr
bgc de bml{gtef gr itgbvnmcr
!(n. Bml{gte v`e tgvnmcgh cm#r njcmtncjv`ent cejgvnye rnjcr
(nn. V`ec teyetre v`e mtfet
2
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5
:
2
5
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:1ej
);
)&7
4
7
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! G cejgvnye tgvnmcgh cm# nr ghzg~r herrv`ec {mrnvnye tgvnmcgh cm#
:
7:
; G [
7:;
fnynfe ncvm :ewugh {gtvr
6
>.nn(
)
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Tgvnmcgh culdet mc culdet hnce
(n. Vm te{terecv:
7 :.n(
22p?.2(
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p
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%'%'%)')
! Cgvutgh culdetr / z mhe culdetr /ncvejetr / itgbvnmcr gte tgvnmcgh cm#r
#b#v#e7;;;
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7
;
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)
! G itgbvnmc nr g tgvnmcgh culdet duv g tgvnmcgh culdet lg~ mt lg~ cmv de g itgbvnmc
ej 1, tgvnmcgh cm# / itgbvnmc ? tgvnmcgh cm duv cmv g itgbvnmc5
2
5
2)
! V`ete gte ncincnve tgvnmcgh cm*r devzeec vzm tgvnmcgh cm*r 1
75
5
75
9
75
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7/31/2019 Maths Concept Map 8 CBSE
17/21
V`ete nr ewugh ucbetvencv~mi egb` muvbmle mi gc ep{etlecv
[tmdgdnhnv~ mi gc eyecv G < [ (G.muvbmler{mrrndhemiculdetVmvgh
GmiigymutncmuvbmlermiCuldet'
; [ (G. 78 8[tmdgdnhnv~ mi jevvncj gculdet jtegvet v`gc :
[tmdgdnhnv~ mi jevvncjVuerfg~ givet Lmcfg~
RuteB`gcbe
JmmfB`gcbe
EyecB`gcbe
[mmtB`gcbeCm B`gcbe
;7-6
7-42-6
[tmdgdnhnv~
Ewughh~ hnoeh~ muvbmler
Ep{etnlecv
Rgl{he R{gbe
MuvbmleFeghr znv` v`e legrutelecv
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