03
14
07
15
09
16
10
16
11
17
18
12 13 14
25
26
27
(Number System) midj;J
vz;fspd;
gz;GfisAk;
mbg;gilr;
nka;naz;fs; (Real Numbers): tpfpjKW
kw;Wk;
vz;fisNa
nka;naz;fs;
vd;gu;.
nray;ghLfisAk; ,g;gFjp tpsf;FfpwJ.
v.fh: “mwptpaypd; murp fzpjk;
tpfpjKwh √
√
,ay; vz;fs; (Natural Numbers):
fzpjj;jpd; murp vz;Kiwapdk;”
vd;W
vz;zf;
$ba
vz;fs;
,ay;
vz;fs;
vdg;gLk;.
vz;fspd; tifghL:vz;fs;
{
KOvz;fs; (Whole Numbers): g+r;rpaj;Jld;
nka; vz;fs;
}
fw;gid vz;fs;
,ay;
vz;fisr;
Nru;f;f
fpilg;gJ
KO
vz;fs;.
{
}
KOf;fs; (Intergers): tpfpjKW vz;fs;
tpfpjKwh vz;fs;
Fiwnaz;fs; kw;Wk; KO vz;fspd; njhFg;Ng KOf;fs; vdg;gLk;.
,ay; vz;fs;
{
kpifKOf;fs; KO vz;fs; KOf;fs; gpd;d vz;fs;
} {
} {
Fiw KOf;fs;
}
xw;iwg;gil vz;fs; (Odd Numbers): ,ay; vz;fspy; 2 My; tFglhj vz;fs;. v.fh: {
}
,U
,ul;ilg;gil vz;fs; (Even Numbers):
}
tpfpjKW
vz;
vdg;gLk;.
> NkYk;
v.fh: tpfpjKW vz;fspd; $l;ly; rkdp 0
gF vz;fs; (Composite Numbers):
tpfpjKW vz;fspd; ngUf;fy; rkdp 1
,uz;Lf;Fk; Nkw;gl;l tFj;jpfisf; nfhz;l vz;fs; vfh: 4> 6> 8> 9>…
tpfpjKwh vz;fs; (Irrational Numbers): KbTwh kw;Wk; Roy; jd;ikaw;w jrk tpuptpidf; nfhz;l
gfh vz;fs; (Prime Numbers): ,uz;L tFj;jpfis
tpfpjk;
tpfpjKW vz;zpd; tbtk;
,ay; vz;fspy; 2 My; tFglf;$ba vz;fs;. v.fh: {
KOf;fspd;
vz; tpfpj Kwh vz; vdg;gLk;.
kl;LNk nfhz;l vz;fs;.
v.fh 2> 3> 5> 7> 11…
tbtpy; vOj KbahJ v.fh: √ √
√
1 Kjy; 100 tiu 25 gfh vz;fs; cs;sd. mitfs; KiwNa>
(Divisibility)
{
}
1 vd;gJ gF vz;Zk; my;y> gfh vz;Zk; my;y.
2 My; tFgLk; jd;ik: Xu;
vz;fs; (C0-Prime Numbers):
,uz;L ,ay; vz;fspd;; kP.ngh.t 1 vdpy; me;j vz;fs; (15> 16)>
(2> 7)
tpfpjKW vz;fs; (Rational Numbers):
,yf;fk;
0>
2>
4>
6>
8
vd;w
4 My; tFgLk; jd;ik: Xu; vz;zpd; filrp ,uz;L ,yf;fq;fs; 4d; klq;fhf ,Ue;jhy; kl;Lk; me;j vz; 4 My; tFgLk;.
rhu;gfh vz;fs; vdg;gLk;. v.fh: (7> 9)>
filrp
vz;fshf ,Ue;jhy; kl;LNk 2 My; tFgLk;.
nkhj;j vz;fs; = gF vz;fs; + gfh vz;fs; + 1 rhu;gfh
vz;zpd;
8 My;
tFgLk; jd;ik:
Xu;
vz;zpd; filrp %d;W ,yf;fq;fs; 8d; klq;fhf
,Uf;Fk; vdpy; me;j vz; 8 My; tFgLk;.
Xu; vz;zpd; xw;iw ,yf;fq;fspd; $LjYf;Fk; ,ul;il
5 My; tFgLk; jd;ik: Xu; vz;zpd; filrp ,yf;fk; 0 my;yJ 5 Mf ,Ue;jhy; kl;Lk; me;j vz; 5 My; tFgLk;.
vz;zpd; filrp ,yf;fk; 0 Mf ,Ue;jhy; kl;Lk;
me;j vz;
10 My;
vz;zpd;
,yf;fq;fspd;
$Ljy;
3d;
klq;fhf
(tFj;jp
(Division)
(Quotient)
+
kPjp (Remainder)
Xu; vz;iz kPjpapd;wp tFf;Fk; vz;fs; midj;Jk; me;j vz;zpd;
tFj;jpfs; vdg;gLk;.
v.fh: 6 d; tFj;jpfs; 1> 2> 3> 6
9 My; tFgLk; jd;ik: vz;zpd;
tFgLk; vz; =
tFj;jpfs; (Divisors):
,Ue;jhy; kl;Lk; me;j vz; 3 My; tFgLk;.
Xu;
11-d; klq;fhfNth ,Ue;jhy; me;j vz; 11 My; tFgLk;.
(Dividend)
tFgLk;.
3 My; tFgLk; jd;ik: Xu;
$LjYf;Fk; cs;s tpj;jpahrk; 0 my;;yJ
10 My; tFgLk; jd;ik: Xu;
,yf;fq;fspd;
,yf;fq;fspd;
$Ljy;
9d;
klq;fhf
,Uf;Fk; vdpy; me;j vz; 9 My; tFgLk;.
Xu; vz;zpd; tFj;jpfspy; 1 IAk;> me;j vz;izAk; jtpu kw;w
6 My; tFgLk; jd;ik:
tFj;jpfs;
midj;Jk;
me;j
vz;zpd;
fhuzpfs;
vdg;gLk;.
2 kw;Wk; 3 My; tFgLk; vz; 6 My; tFgLk;. 7 My; tFgLk; jd;ik: Xu; vz;zpd; filrp
fhuzpfs; (Factors):
,yf;fj;jpd; ,U klq;F kw;Wk;
v.fh: 6d; fhuzpfs; 2> 3 “vy;yhf; fhuzpfSk; tFj;jpfNs> tFj;jpfs; vy;yhk; fhuzpfs; my;y”
kw;w vz;fSf;F cs;s NtWghL 0 my;yJ 7d; klq;fhf ,Uf;Fkhapd; me;j vz; 7 My; tFgLk;. 11 My;
tFgLk; jd;ik:
(Arithmetic Sequence or Arithmetic Progression)
gpNghdhfp njhlu;tupir (Fibonacci Sequence):
$l;Lj; njhlu;tupirapd; nghJ tbtk;:
tJ cWg;G fhz: Kjy; cWg;G
nghJ tpj;jpahrk;
cWg;Gfspd; vz;zpf;if
,jd; cWg;Gfs; 1> 1> 2> 3> 5> 8> 13> 21>… rpwg;G njhlu;fs; (Special Series):
cWg;Gfspd; vz;zpf;if: $l;Lj; njhlu; tupirapd; Kjy;
I.
Kjy;
cWg;Gfspd; $Ljy;:
](nghJ tpj;jpahrk;
(filrp cWg;G
jug;gl;lhy;)
II.
Kjy;
,ay; vz;fspd; tu;f;fq;fspd; $Ljy;:
III.
vd;w njhlup;d; Kjy;
IV.
Kjy;
,ay; vz;fspd; fzq;fspd; $Ljy;: [
V.
tJ cWg;G fhz:
Kjy;
( nghJ tpfpjk;)
xU ngUf;F njhlu; tupirapd; Kjy;
cWg;Gfspd; $Ljy;:
VI.
xw;iwg;gil ,ay; vz;fspd; $Ljy;:
Kjy; cWg;G
Kbtpyp vz;zpf;ifapy; cWg;Gfs; ,Ug;gpd; $Ljy;:
xw;iwg;gil ,ay; vz;fspd; $Ljy; (filrp jug;gl;lhy;):
vdpy;)
]
cWg;Gfspd;
$Ljy;
(Geometric Sequence or Geometric Progression) ngUf;Fj; njhlu;tupirapd; nghJ tbtk;:
,ay; vz;fspd; $Ljy;:
jug;gl;lhy;)
vd;gjpypUe;J
ngwg;gLk; njhlu;tupir gpNghdhfp njhlu;tupir vdg;gLk;.
[
kw;Wk;
VII.
Kjy;
(
)
,ul;ilg;gil ,ay; vz;fspd; $Ljy;:
VIII.
Kjy;
xw;iwg;gil
,ay;
vz;fspd;
tu;f;fq;fspd;
$Ljy;: (
IX.
[
{
̅̅̅̅ }
)
Vinculum (or) Bar
Kjy;
xw;iwg;gil
,ay;
vz;fspd;
fzq;fspd;
Circular Bracket
$Ljy;:
Curly Bracket
X.
vd;w
njhlupd;
Kjy;
Square Bracket
cWg;Gfspd;
Brackets I ePf;fk; nra;Ak; tupirahdJ>
$Ljy;:
[
]
Simplification RUf;Fjy; Kiwapy; gad;gLj;jg;gLk; tpjpKiwfs;:
{ } [ ]
O vd;gJ Of (,y;> ,d;> klq;F> gq;F) D vd;gJ Division (tFj;jy;)
I.
M vd;gJ Multipication (ngUf;fy;)
II. III.
A vd;gJ Addition ($l;ly;)
IV.
S vd;gJ Subtraction (fopj;jy;) II.mLf;F tpjpfs; (Surds and Indices):
I.VBODMAS Rule: xU
]
tpupj;jiy
RUf;Ftjw;F
tpjpapd;
RUf;Ffpd;w tupir: V – vd;gJ Vinculum (Nkw;Nfhl;L milg;G “ ̅ ”) B – vd;gJ Brackets
mbg;gilapy;
I. II. III. IV. V.
(ngUf;fy; tpjp) (tFj;jy; tpjp) (mLf;F tpjp)
VI.
(Nru;f;if tpjp)
VII. VIII.
9.
( ) ( )
IV.tu;f;f%yk; kw;Wk; fd%yk; (Square Root and Cube Root):
( )
IX. X.
√
XI.
√
XII.
√
√
√
√
XIV.
√√
√
XV.
(√ )
√
( )
d; fd%yk;
√
d; tu;f;f%yk; √
3) √
√
√
( ) ( )
v.fh: √
III.,aw;fzpj Kw;nwhUikfs; (Basic Algebra Formulae): ,q;F
1. 2. 3. 4. 5. 6. 7.
d; tu;f;fk;
2) √ √ √
NkYk; rpy Kf;fpa tpjpfs;:
2. ( )
d; fdk;
1) √ √ √
(√ )
( )
√
XIII.
1. ( )
8.
4) √
√
√
√
√
v.fh: √
√
√
,q;F
tu;f;f vz;fs; kw;Wk; fd vz;fs;(Square and Cube Numbers): vz;fs;
vz;fspd; tu;f;fk;
Vz;fspd; fdk;
1
1
1
2
4
8
3
9
27
4
16
64
5
25
125
14
196
2744
15
225
3375
16
256
4096
17
289
4913
18
324
5832
19
361
6859
20
400
8000
(LCM & HCF) I.
gpd;dq;fspd; kP.rp.k kw;Wk; kP.ngh.t: gpd;dq;fspd; kP.rp.k
6
36
216
7
49
343
8
64
512
9
81
729
10
100
1000
11
121
1331
12
144
1728
kP.ngh.t:
13
169
2197
Fiwe;j
gpd;dq;fspd;kP.ngh.t II.
ததொகுதிஎண்களின்மீ சி ம பகுதிஎண்களின்மீ தபொ வ
ததொகுதிஎண்களின்மீ தபொ வ பகுதிஎண்களின்மீ சி ம
mLf;Ffis cila vz;fspd; kP.rp.k kw;Wk; kP.ngh.t:
kP.rp.k: mjpf mLf;Ffis cila nghJ kw;Wk; nghJ my;yhj vz;fspd; ngUf;fw;gyd;.
mLf;Ffis
ngUf;fw;gyd;.
cila
nghJthd
vz;fspd;
III.
,U vz;fspd; ngUf;fw;gyd; = me;j vz;fspd; kP.rp.k
kP.ngh.t
(Percentage) rjtPjk; vd;gJ Percentum vd;w yj;jPd; nkhop thu;j;ijapd; RUf;fk;. E}w;Wf;F vd;gJ ,jd; nghUs; rjtPjk; vd;gJ gFjpapy; 100 I cila xU gpd;dk; ,jd;
FwpaPL
.
cjhuzkhf
vd;gjid
vd
vOjyhk; vspa topKiwfs;: Xu; vz;zpd; Xu; vz;zpd; Xu; vz;zpd; Xu; vz;zpd; Xu; vz;zpd; Xu; vz;zpd; rjtPjk; (Percentage)
அந்தஎண் அந்தஎண் அந்தஎண் அந்தஎண் அந்தஎண் அந்தஎண்
gpd;dk; (Fraction)
vd;gJ (
I tpl )
vd;gJ (
vd;gJ
I tpl
FiwT vdpy;
vd;gJ
I tpl
FiwT. I tpl
)
mjpfk; vdpy;
mjpfk;.
xU
nghUspd;
tpiy
mjpfupf;fg;gl;lhNyh>
Fiwf;fg;gl;L
gpd;G
ntw;wp ngWfpwhu; vdpy;
my;yJ
Fiwf;fg;gl;L
my;yJ
nkhj;j thf;Ffs; vz;zpf;if
mjpfupf;fg;gl;lhNyh Kbtpy; Fiwg;G(m) mjpfupg;G rjtPjk;
Njhytpailfpwhu; vdpy;
nkhj;j thf;Ffs; vz;zpf;if
xU nghUspd; tpiy
mjpfupj;j gpd;G kWgbAk;
xU efupd; kf;fs;
(Profit and Loss & Discount)
( )
Fiwe;jhy; e\;lrjtPjk;
njhifahdJ xt;nthU Mz;Lk;
mjpfkhdhNyh my;yJ Fiwe;jhNyh
yhgk;
= tpw;wtpiy – mlf;ftpiy
e\;lk;
= mlf;ftpiy – tpw;wtpiy
yhg rjtPjk;
=
லொபம் அடக்கவிலல
e\;l rjtPjk;
=
நஷ்டம் அடக்கவிலல
mlf;ftpiy
=
mlf;ftpiy
=
)
tpw;wtpiy
=
லொப
khztu;fs;
tpw;wtpiy
=
நஷ்ட
(
tUlq;fSf;F gpwF kf;fs; njhif
tUlq;fSf;F Kd;G kf;fs; njhif
xU efupd; kf;fs; njhifahdJ %d;W
tUlq;fSf;F
mjpfupg;G
kf;fs;
(
) )
vd;f. NkYk; Kjy;
njhif
FiwT
rjtPjkhdJ
my;yJ
vdpy;
3
tUlq;fSf;F gpwF kf;fs; njhif ( xU
Nju;tpy;
ghlg;gpuptpy;
)(
nkhj;j
)(
khztu;fspy;
Njhy;tpailfpd;wdu;;.
ghlg;gpuptpy;
khztu;fs;
Njhy;tpailfpd;wdu;
,Ughlg;gpupTfspYk;
kw;Wk;
khztu;fs; Njhy;tpailfpd;wdu;
,Utu;f;F
,ilNa
nkhj;j thf;Ffspy;
egu;
,U
tpw;Fk;NghJ nghUSf;F
நஷ்ட
nghUl;fis
xU
nghUSf;F
ngw;W
xU
Nju;jypy;
xUtu;
e\;lj;ijAk;
thf;Ffs; tpj;jpahrj;jpy;
(
விற்றவிலல அடக்கவிலல அடக்கவிலல xNu
yhgj;ijAk;>
]
elj;jg;gl;l
விற்றவிலல
jdpj;jdpNa
ngWfpwhu;.
tpahghuj;jpy; mile;j e\;l rjtPjk;
vdpy; ,Ughlg;gpupTfspYk; Nju;r;rp ngw;w khztu;fs; [
xU
லொப
)
tpiyf;F kw;nwhU
vdpy;
mtu;
nghUl;fspd;
mlf;ftpiyahdJ
nghUl;fspd;
2. ngUf;Fr; ruhrup: (Geometric Mean)
tpw;wtpiyf;F rkk; vdpy;
yhg
e\;l
xUtu; &.
√ 3. ,irr;ruhrup: (Harmonic Mean)
nghUl;fis &
tpiyf;F thq;fp
tpiyf;F tpw;why; yhg (
nghUl;fis
(m) e\;l rjtPjk;
)
Fwpj;jtpiy
mlf;f tpiy + $l;lg;gl;l kjpg;G
js;Sgb
Fwpj;jtpiy – tpw;wtpiy
js;Sgb
குறித்தவிலல
nghUspd;
6. Kjy;
லொப தள்ளுபடி
kPJ
vdpy;>
5. ,U vz;fspd; $Ljy;:
தள்ளுபடி
Fwpj;j tpiy xU
4. ,U vz;fspd; ,irr; ruhrup:
js;Sgbf;F
njhlu;
gpwF
இலசச்சரொசரி
,ay; vz;fspd; ruhrup:
அடக்கவிலல
nfhLf;fg;gLk;
(தபருக்குச்சரொசரி)
js;Sgbfs;
me;jg;
7. Kjy;
,ay; vz;fspd; tu;f;fq;fspd; ruhrup:
nghUspd;
tpw;wtpiyகுறித்தவிலல 8. Kjy;
xw;iwg;gil ,ay; vz;fspd; ruhrup:
(Average) சரொசரி
தகொடுக்கப்பட்டஎண்களின்கூடுதல்
9. Kjy;
10.
தகொடுக்கப்பட்டஎண்களின்எண்ணிக்லக
1. $l;Lr;ruhrup: (Arithmetic Mean)
d; ruhrup:
11.
̅
,ul;ilg;gil ,ay; vz;fspd; ruhrup:
d; ruhrup:
12. Xu; vz;zpd; n klq;Ffspd; ruhrup:
(Ratio and Proportion)
எண்
tpfpjk; (Ratio):
13. mLj;jLj;j vz;fspd; ruhrup: முதல்எண் கலடசிஎண்
14.
egu;fspd;
ruhrupahdJ
>
egu;fspd;
vd;w ,U msTfspd; tpfpjk;
vd;gij
vdyhk;
ruhrupahdJ tpfpjrkk; (Proportion):
vdpy; nkhj;j egu;fspd; ruhrup:
,U
tpfpjq;fspd;
vspa
tbtk;
rkkhf
,Uf;Fk;
vdpy;
mt;tpfpjq;fs; tpfpjrkk; MFk;. 15. xU
Fwpg;gpl;l
kPz;Lk;
mNj
J}uj;ij
Ntfj;jpy;
,lj;jpw;F
nrd;wile;J
Ntfj;jpy; jpUk;gpdhy;
gpd;
Mfpad tpfpjrkj;jpy; mikAk; vdpy;>
ruhrup
Ntfk;:
fil cWg;Gfspd; ngUf;fy;= ,il cWg;Gfspd; ngUf;fy;
16. xU egu; 3 rkJ}uq;fis
vd;w Ntfq;fspy;
flf;fpwhu;> vdpy; ,e;j gazj;jpy; ,tuJ rurup Ntfk;:
17. xU
egu;
Ntfj;jpYk;>
J}uj;ij J}uj;ij
mikAk;. Ntfj;jpYk;> Ntfj;jpYk;
nkhj;j gazj;jpy; ,tuJ ruhrup Ntfk;:
,t;thW ,Ue;jhy; kl;LNk ,U tpfpjq;fs; tpfpj rkj;jpy;
J}uj;ij 3tJ tpfpjrkd; (3rd Proportional):
flf;fpwhu;>vdpy;
,q;F
vd;gJ
f;F 3 tJ tpfpj rkd;.
4tJ tpfpjrkd; (4th Proportional):
,q;F
vd;gJ
(Simple Interest):
f;F 4tJ tpfpj rkd;.
,iltpfpjrkd; (Mean Proportion):
(
√
,q;F
vd;gJ
kw;Wk;
f;F
jdptl;b> mry;> fhyk;> tl;btPjk;
,q;F
,ilNaAs;s
,iltpfpjrkd;.
,jid ruhrup tpfpjrkd; vdTk; miog;gu;.
) njhif
xU njhifapy; jdptlb mriyg; Nghy;
gq;F> NkYk;
fhyKk; tl;btPjKk; rkk; vdpy;> $l;L tpfpjk; (Compound Ratio):
fhyk;
vd;w 3 tpfpjq;fspd; $l;L tpfpjk;:
xU Fwpg;gpl;l njhif
,Ugb tpfpjk; (Duplicate Ratio):
d; ,Ugb tpfpjk;
d; Jiz ,Ugb tpfpjk;
√
d; Kg;gb tpfpjk;
d; Jiz Kg;gb tpfpjk;
√
Kk;klq;fhf khWk; vdpy;
4 klq;fhf khWk; vdpy;
√
tl;btPjj;jpy;
,Uklq;fhf khWk; vdpy;
MfpwJ. vdpy;
klq;fhf khw
tUlq;fs;
klq;fhf khw> tUlq;fs; MFk;.
(Compound Interest)
Kg;gb tpfpjk; kw;Wk; Jiz Kg;gb tpfpjk;:
tUlq;fspy;
xU njhif jdptl;b tPjj;jpy;
Jiz ,Ugb tpfpjk; (Sub-Duplicate Ratio):
√
tl;btPjk;
xU tUl tl;b fhz
√
njhif
[
]
miu tUl tl;b fhz
njhif
[
]
fhy; tUl tl;b fhz
njhif
[
]
jiyfPo; tpfpjk; (Inverse Ratio):
d; jiyfPo; tpfpjk;
Mz;Lfs;>
njhlu;itg;Gj; njhif (Recurring Deposit):
khjq;fs; $l;Ltl;b fhz njhif
) (
[(
)]
tl;b tPjk; &.
$l;Ltl;b fhz vspaKiw:
2 3 4 5 6
tUlq;fs; tUlq;fs; tUlq;fs; tUlq;fs; tUlq;fs;
vdpy; vdpy; vdpy; vdpy; vdpy;
2 3 4 5 6
I
,q;F
1 3 6 10 15
f;F khje;NjhWk; nrYj;Jk; mry; njhif khjq;fSf;F nrYj;jpdhy; tl;b
njhlu; itg;G fhyk;
1 4 10 20
1 5 15
]
தமொத்தத்ததொலக தமொத்தமொதங்கள்
khjj; jtid
1 6
[
1
(Time and Work) xt;nthU tUlKk; tl;btPjk;
vd khWfpwJ
vdpy;:
[
][
][
1)
xU
)
3 tUlq;fSf;F vdpy;
(
) (
Fwpg;gpl;l
njhif
klq;fhfpwJ vdpy;
$l;L
tl;bapy;
klq;fhf khw
2 tUlq;fspy; 9 klq;F
3 tUlq;fspy; 8 klq;F
4 tUlq;fspy; 256 klq;F
vd;gtu;
ehl;fspYk;>
vd;gtu;
)
MFk; ehl;fs;
3)
tUlq;fspy;
Ak;
Ak;
Kbf;fpwhu;fs;.
tUlq;fs; MFk;.
Kbj;jhy;
Nru;e;J
xU
Ntiyia
kl;Lk; mt;Ntiyia jdpahf
ehl;fspy; ehl;fspy;
kl;Lk; jdpahf mt;Ntiyia Kbf;f MFk;
ehl;fs;
vspaKiw:
Ntiyia
நவலல பணம்
ehl;fspYk; Kbj;jhy; ,UtUk; Nru;e;J mt;Ntiyia Kbf;f
jdp tl;bf;Fk; $l;Ltl;bf;Fk; ,ilNaAs;s tpj;jpahrk; (
ஆட்கள் நொட்கள் மணிநநரம்
நவலல பணம்
2) xU
]
2 tUlq;fSf;F vdpy;
ஆட்கள் நொட்கள் மணிநநரம்
4)
vd;w
%tUk;
xU
Ntiyia
jdpj;jdpahf
ehl;fspy; Kbj;jhy; %d;W egu;fSk; Nru;e;J mt;Ntiyia Kbf;f MFk; ehl;fs;
5)
Ak;
Ak; Nru;e;J xU Ntiyia
Nru;e;J
mt;Ntiyia
mt;Ntiyia
ehl;fspYk;
ehl;fspYk;>
ehl;fspyk;
Ak;
Kbj;jhy;
Ak;
Ak;
Ak;
Nru;e;J
%tUk;
Nru;e;J
4) xU
Foha;
vd;gtu;
I tpl
Foha;
kzp
xU
Foha;
kzp
Neuj;jpYk;
J}uk;
KO
Neuj;jpYk;> ,uz;Lk;
kw;nwhU
vspa
fhyp
nra;Ak;.
%d;Wk;
kzp xNu
Ntfk;
தூரம்
நநரம் தூரம்
நவகம்
Kiw:
S = D/T,
T = D/S D
Foha;
kw;nwhU
D=S T
Nru;e;J
njhl;bia epug;g MFk; fhyk;
2) xU njhl;bia xU Foha;
njhl;biaAk;
Neuk;
Ntfk;
epug;gpdhy;
Neuj;jpYk;>
(Time, Distance and Speed)
klq;F jpwikahdtu; vdpy;
vdpy; jpwd; tpfpjk;
njhl;bia
kzp
Neuj;jpy; jpwf;fg;gl;lhy; njhl;b epuk;g MFk; fhyk;
(Pipes and Cisterns) Neuk; 1) xU
Foha;
7) ehs; tpfpjk;
xU
kzp Neuj;jpYk; epug;Gk;. %d;whtJ Foha;
Neuj;jpy;
mt;Ntiyia Kbf;f Njitg;gLk; ehl;fs;
6)
njhl;bia
kzp Neuj;jpy; epug;Gk;. kw;nwhU
S
kzpNeuj;jpy; njhl;bia fhyp nra;Ak; ,uz;Lk;
T
xNu Neuj;jpy; jpwf;fg;gl;lhy; njhl;b epuk;g MFk; fhyk;
,uz;L
,uapy;fspd;
Ntfq;fspd;
tpfpjk;
rkJ}uj;ij flf;Fk;NghJ Neuq;fspd; tpfpjk; 3) xU
njhl;bia
Foha;
xU
Foha;
kzpNeuj;jpYk;>
kzp
Neuj;jpYk;>
%d;whtJ
Foha;
kw;nwhU kzp
Neuj;jpYk; epug;gpdhy; %d;Wk; Nru;e;J epug;g MFk; fhyk;
vdpy;
I.
xU
,uapy; tz;b
gpd;G
apypUe;J
apypUe;J
f;F
f;;F
Ntfj;jpYk; Ntfj;jpYk;
fPo;epiyapy; glfpd; Ntfk; (Speed of Boat in Low Stream)
II.
gazk;
vjpu;ePr;சிy; glfpd; Ntfk; (Speed of Boat in Up Stream)
mile;jhy; ruhrup Ntfk; III.
epiyahd ePupy; glfpd; Ntfk;
(fPo;epiy + vjpu; ePr;R)
(Speed of Boat in Still Water)
,uz;L
,uapy;fs;
xNu
jpirapy;
nrd;W
nfhz;bUe;jhy;
IV.
mjd; ruhrup Ntfk;
,uz;L
(Speed of Stream)
,uapy;fs; ntt;NtW jpirapy;
I. II.
,uapy;
xU
kzpjiuNah>
kuj;ijNah>
kpd;rhu
fk;gj;jpidNah fle;jhy;
elg;G taJ taJfs;
vd;why;
tpfpjk;
,Utupd;
jw;Nghija
uapy; tz;b xU ghyj;jpid fle;J nrd;why;
uapy; tz;b eilghijia fle;J nrd;why; J}uk; = uapypd; ePsk; + eilghijapd; ePsk;
xU
vd;why;
uapy; tz;b kw;nwhU uapy; tz;bia fle;J nrd;why;
taJ
vdy;
glfpd; Ntfk;
>
KiwNa
tpfpjk;
.
vdpy;
IV.
,Utupd;
jw;Nghija
taJ
Xilapd; Ntfk;
tpfpjk;
tUlq;fSf;F gpd;G taJ tpfpjkhdJ.
J}uk; = Kjy; uapypd; ePsk; + ,uz;lhtJ uapypd; ePsk;
ePupy;
taJfs;
tUlq;fSf;F Kd;G taJ tpfpjkhdJ.
J}uk; = uapypd; ePsk; + ghyj;jpd; ePsk;
xU
klq;F taJ
kw;Wk; III.
J}uk; = ,uapypd; ePsk;
xU
(Problems on Age)
(vjpu; vjpu; jpirapy;)
gazpj;jhy; mjd; ruhrup Ntfk;
xU
(fPo;epiy – vjpu;ePr;R)
Xilapd; Ntfk;
vdpy;
(Mensuration)
t.vz;
tbtk; (Figure)
tisgug;G(Curved Surface Area)
cUis - Cylinder
1
$k;G - Cone
2 rhAAuk;
√
nkhj;jgug;G(Total surface area)
fd msT(Volume)
Nfhsk; - Sphere
3
______
miuf;Nfhsk; -HemiSphere
4
cs;sPlw;w cUis –Hollow Cylinder
5
cs;sPlw;w Nfhsk; - Hollow Sphere
6
______
cs;sPlw;w miuf;Nfhsk; - Hollow Hemi Sphere
7
tl;lNfhzg;gFjp (Sector):
(i)
tl;l Nfhzg;gFjpapd; tpy;ypd; ePsk;:
(ii)
tl;l Nfhzg;gFjpapd; gug;G:
(iii)
tl;l Nfhzg;gFjpapd; gug;GsT: r.m
(iv)
tl;l Nfhzg;gFjpapd; Rw;wsT: myFfs;
(Probability) 1.
III.
சொதொரண நிகழ்ச்சிகளின் எண்ணிக்லக
epfo;jfT
தமொத்த நிகழ்ச்சிகளின் எண்ணிக்லக
3 ehzaq;fs; Rz;lg;gLk; NghJ: {
}
IV.
ehzaq;fs; Rz;lg;gLk; NghJ:
2. 3. cWjpahd epfo;r;rpapy; epfo;jfT
4. elf;f ,ayhj epfo;r;rpapd; epfo;jfT
5.
vd;w
epfo;r;rp
eilngwhky;
̅
gfil cUl;lg;gLk; epfo;T: I.
,Ug;gjw;fhd
epfo;jfT II.
$l;ly; tpjp:
Ak;
Ak;
}
2 gfilfs; cUl;lg;gLk; NghJ:
III.
}
3 gfilfs; cUl;LNghJ:
Ak; xd;iwnahd;W tpyf;Fk; epfo;r;rpfs; vdpy;> IV.
{
Ak; xd;iwnahd;W tpyf;fhj epfo;r;rpfs; vdpy;>
{
̅
NkYk;
xU gfil cUl;Lk;NghJ:
gfilfs; cUl;Lk; NghJ:
ehzak; Rz;lg;gLk; epfo;T: I.
{
} ,q;F
vd;gJ jiy
II.
rPl;Lfs; (Cards):
xU ehzak; Rz;lg;gLk; NghJ: vd;gJ g+
I.
xU rPl;Lf;fl;by; 52 rPl;Lfs; cs;sd.
II.
Clubs (or) Clover, Spades, Tiles (or) Diamonds, Hearts ,itfs; xt;nthd;wpYk; 13 fhu;Lfs; cs;sd.
2 ehzaq;fs; Rz;lg;gLk; NghJ:
{
}
III.
rPl;Lfl;by; 4 Ace , 4 Jack, 4 Queen, 4 King fhu;Lfs; cs;sd.
fpoikfs; (Days):
IV.
Face Cards vz;zpf;if = 12 (King, Queen, Jack)
V.
Black Cards vz;zpf;if = 26
VI.
Red Cards vz;zpf;if = 26
rpy vspaKiw: I.
Spade Mf ,Uf;f epfo;jfT Heart Mf ,Uf;f epfo;jfT
epfo;r;rpfs;
I.
yPg;
rhjhuz
Mz;L
Mz;L
53 nts;spf;fpoikfs; ,Uf;f epfo;jfT(ve;jfpoikfs;Nfl;lhYk;) 52 nts;spf;fpoikfs; ,Uf;f
II.
epfo;jfT (ve;j fpoikfs; Nfl;lhYk;)
Clover Mf ,Uf;f epfo;jfT
(Statistics)
Dimond Mf ,Uf;f epfo;jfT
1. $l;Lr;ruhrup (Arithmetic Mean): II.
Red cards Mf ,Uf;f epfo;jfT Black Cards Mf ,Uf;f epfo;jfT
III.
King Mf ,Uf;f epfo;jfT
̅
2. ,ilepiy (Median):
Queen Mf ,Uf;f epfo;jfT
nfhLf;fgl;Ls;s
tptuq;fis
VW
(m) ,wq;F
tupirapy;
vOJk; NghJ eLepiyahf ,Uf;Fk; cWg;G. IV.
Black Queen Mf ,Uf;f epfo;jfT Black King Mf ,Uf;f epfo;jfT
3. KfL (Mode):
Red King Mf ,Uf;f epfo;jfT Red Queen Mf ,Uf;f epfo;jfT
V.
Face Cards Mf ,Uf;f epfo;jfT
Gs;sp
tptuj;jpYs;s
cWg;Gfspy;
ngw;Ws;s cWg;gpd; kjpg;Ng KfL vdg;gLk; 4. KfL
= 3(,ilepiy) – 2(ruhrup)
5. tPr;R
= ngupa vz; - rpwpa vz;
6.
=
tPr;Rf;nfO
mjpf
Kiw
,lk;
7. jpl;l tpyf;fk; (Standard Deviation):
√
(i)
∑
(Algebra)
̅
√
(or)
(ii)
∑
√
̅
cWg;Gfspd; jpl;ltpyf;fk;:
> 0 = 0
√
< 0 8. khWghl;Lf;; nfO (Coefficient of Variation):
̅
α, β α + β =
̅
jpl;ltpyf;fk;
$l;Lr;ruhrup
9. tpyf;f tu;f;fr; ruhrup
திட்டவிலக்கம்
3.α β
10. fhy;khd tpyf;fk; (Fourth Quartile):
11. fhy;khd tpyf;ff; nfO (Fourth Quartile Variation):
( ;
=0
,aw;fzpj Kw;nwhUikfs; (Algebra Formulae):
1.
மீ .ப ொ.வ மற்றும் மீ .சி.ம ஆகியவற்றுக்கு இடையயயுள்ள ப ொைர்பு: இரு
2.
ல்லுறுப்புக்யகொடவகளின்
ப ருக்கற் லன்
அவற்றின்
மீ .ப ொ.வ
மற்றும் மீ .சி.ம ஆகியவற்றின் ப ருக்கற் லனுக்குச் சமமொகும்.
3.
f(x)×g(x)={ LCM (f(x) , g(x))} × { HCF (f(x) , g(x))}
4.
5. 6. 7. 8. 9. 10. (
)2 =
+ 2(
)
11. 3
12. 13.
3a
14. 15. 16. 17. 18. 19.
( If
f(x), g(x) என்பன
இரு
ல்லுறுப்புக்யகொடவகள்
