VIII – Maths – III Term

js;Sgb vd;gJ Fwpj;jtpiy my;yJ gl;baypy; cs;s tpiyiatplf; Fiwj;Jf; nfhLg;gjhFk;.

thpfs; Neh;Kf thp> kiwKf thp vd ,Utifg;gLk;

Neh;Kf thp – tUkhd thp> nrhj;J thp> njhopy; thp> jz;zPh; thp (kf;fshy; Neubahf nrYj;jg;gLgit)

kiwKf thp – fyhy; thp> gzp thp> tUkhd thp fyhy; thp - cw;gj;jp nra;ag;gLk; nghUs;fspd; kPJ tpjpf;fg;gLtJ.

gzp thp (service tax) – czT tpLjp> jpiuauq;F> njhiyNgrpf; fl;lzk; Nghd;wit.

tpw;gid thp – xU filf;fhuh; xU nghUis tpw;Fk; NghJ tpjpf;fg;gLk; thp.

jdptl;b , $l;Ltl;bmrYf;F kl;Lk; tl;b fhZjiy jdptl;b vd;fpNwhk;.

xt;nthU Kiw ngw;w tl;biaAk; mrYld; Nrh;j;J tl;b fhZjiy $l;L tl;b vd;fpNwhk;.

$l;Ltl;b fzf;fpLjy; : Mz;Lf;nfhUKiwxt;nthU Mz;L ,WjpapYk; tl;b mrYld; Nrh;f;fg;gLfpwJ.

$l;Ltl;b fzf;fpLjy; : miuahz;Lf;nfhUKiwMW khjj;jpw;nfhUKiw tl;b mrYld; Nrh;f;fg;gLk;

miuahz;L tl;btPjk; r/2

$l;Ltl;b fzf;fpLjy; : fhyhz;Lf;nfhUKiw

fhyhz;Lf;nfhUKiw (3khjk;) tl;b mrYld; Nrh;f;fg;gLfpwJ. fhyhz;L tl;b tPjk; r/4

jdptl;bf;Fk; $l;Ltl;bf;Fk; cs;s tpj;jpahrk;.

kjpg;G $LjYk; FiwjYk;

$Ljy;

Fiwjy;

gzj;ijr; Nrkpf;f

epue;ju itg;Gj;jpl;lk; (Fixed Deposit)

xU njhifia Fwpg;gpl;l fhyj;jpw;F KjyPL nra;jy;

njhlh;itg;Gj; jpl;lk; (Recurring Deposit)

xt;nthU khjKk; xU Fwpg;gpl;l njhifia Fwpg;gpl;l Mz;LfSf;F nrYj;jp tUjy;.

thliff; nfhs;Kjy; kw;Wk; jtiz Kiw

thliff; nfhs;Kjy; jpl;lk;

,j;jpl;lj;jpd; fPo;> nghUs; thq;FNthUf;F xU Fwpg;gpl;l fhyj;jpw;F nrhe;jkhfhJ. nghUspd; tpiyia tl;bAld; fl;ba gpwNf nrhe;jkhFk;.

jtiz Kiwj; jpl;lk;

nghUspd; tpiy> tl;b> ,ju nryTfs; Nrh;j;J nkhj;j njhifahfpwJ. Fwpg;gpl;l fhyf;nfLTf;Fs; cs;s khjq;fspd; vz;zpf;ifahy; tFj;Jg;ngWth;.

Neh;khwy;

njhlh;Gila ,U msTfSs; xd;W mjpfkhFk; NghJ kw;nwhd;W mjpfhpj;jhNyh my;yJ xd;W FiwAk; NghJ kw;nwhd;W Fiwe;jhNyh mit Neh;khwypy; cs;sd vd;W nghUs;.

v.fh. fhyk; - njhiyTmry; - tl;b

vjph;khwy;

njhlh;Gila ,U msTfSs; xd;W mjpfkhFk; NghJ kw;nwhd;W Fiwe;jhNyh my;yJ xd;W FiwAk; NghJ kw;nwhd;W mjpfhpj;jhNyh mit vjph;khwypy; cs;sd vd;W nghUs;.v.fh. fhyk; - Ntfk;

kf;fs; njhif - ,Ug;gpYs;s czTfhyk; kw;Wk; Ntiy

Kf;Nfhzj;jpd; xU Gs;sptopf; NfhLfs;

xU jsj;jpy; %d;W my;yJ mjw;F Nkw;gl;l NfhLfs; xU Gs;sp topNa nrd;why; mit xU Gs;sptopf; NfhLfs; vd;W ngah;. mtw;wpd; nghJg;Gs;sp re;jpf;Fk; Gs;sp vdg;gLk;.

xU Kf;Nfhzj;jpd; Xh; cr;rpapypUe;J mjd; vjph;g;gf;fj;jpd; eLg;Gs;spia ,izf;Fk; NfhL eLf;NfhL vdg;gLk;.

xU Kf;Nfhzj;jpd; eLf;NfhLfs; re;jpf;Fk; Gs;spahdJ> mk;Kf;Nfhzj;jpd; eLf;Nfhl;L ikak; (G) vdg;gLk;.

eLf;Nfhl;L ikak;> eLf;NfhLfis 2:1 vd;w tpfpjj;jpy; gphpf;Fk;.

eLf;Nfhl;L ikak; mk;Kf;Nfhzj;jpd; GtpaPh;g;G ikak; MFk;.

xU Kf;Nfhzj;jpd; cr;rpapypUe;J mjd; vjph;g;gf;fj;jpw;F nrq;Fj;jhf tiuag;gLk; NfhL nrq;NfhL (Fj;Jf;NfhL) MFk;.

xU Kf;Nfhzj;jpd; %d;W Fj;Jf;NfhLfs; re;jpf;Fk; Gs;sp mjd; nrq;Nfhl;L ikak;(H) vdg;gLk;.

xU Kf;Nfhzj;jpd; xU Nfhzj;jpd; ,Urkntl;b vd;gJ mf;Nfhzj;ij ,Urkf;$wpLk; Nfhl;Lj;Jz;lhFk;.

xU Kf;Nfhzj;jpd; %d;W Nfhzq;fspd; ,Urkntl;bfs; re;jpf;Fk; Gs;sp mjd; cs;tl;l ikak;(I) vdg;gLk;.

xU Kf;Nfhzj;jpd; gf;fj;jpd; ikaf;Fj;Jf;NfhL vd;gJ mg;gf;fj;jpw;Fr; nrq;Fj;jhfTk; mNjrkak; mg;gf;fj;ij ,Urk ghfq;fshfTk; gphpf;Fk; NfhL.

xU Kf;Nfhzj;jpd; %d;W ikaf;Fj;Jf; NfhLfSk; re;jpf;Fk; Gs;sp Rw;W tl;l ikak;(O) vdg;gLk;.

Rw;Wtl;l ikak;> eLf;Nfhl;L ikak;> nrq;Nfhl;L ikak; Mfpad xNu Neh;Nfhl;by; mike;jhy; mJ Ma;yh; NfhL vdg;gLfpwJ.

rkgf;f Kf;Nfhzj;jpy; Rw;Wtl;l ikak;> eLf;Nfhl;L ikak;> nrq;Nfhl;L ikak;> cs;tl;l ikak; Mfpad xNu Gs;spapy; mikAk;.

gpjhfu]; Njw;wk;:gpjhfu]; xU fpNuf;f fzpj Nkij. nrq;Nfhz Kf;Nfhzj;jpd; gf;fq;fSf;fpilNaAs;s njhlh;ig ,j;Njw;wk; tpsf;FfpwJ.

“xU nrq;Nfhz Kf;Nfhzj;jpy; fh;zj;jpd; th;f;fkhdJ kw;w ,U gf;fq;fspd; th;f;fq;fspd; $LjYf;Fr; rkk;”nrq;Nfhz ΔABC –y;> C=900 >gf;fq;fs; BC=a> CA=b, fh;zk; AB=c vdpy;gpjhfu]; Njw;wg;gb a2+b2=c2

gpjhfu]; Njw;wj;ij epiwT nra;Ak; vz;fSf;F gpjhfu]pd; %d;wd; njhFjp vd;W ngah;.

tl;lq;fs;:tl;lk; vd;gJ xU jsj;jpy; cs;s epiyahd Gs;spapypUe;J rknjhiytpy; efUk; Gs;spapd; epakg; ghij MFk;. epiyahd Gs;sp – tl;likak; rknjhiyT – Muk;. xU tl;lj;jpy; cs;s Muq;fs; - rk ePsKilait. tl;lj;jpd; kPJs;s ,U Gs;spfis ,izf;Fk;

Nfhl;Lj;Jz;L ehz;. tl;l ikaj;jpd; topNa nry;Yk; ehz; tpl;lk;. tl;lj;jpy; tiuag;gLk; kpfg;nghpa ehz; tpl;lk;. tpl;lk; = 2X Muk; my;yJ Muk; =tpl;lk;/2 xt;nthU tpl;lj;jpd; ikaKk; tl;l ikakhFk;. tl;lj;jpy; tiuag;gLk; midj;J tpl;lq;fSk; xU

Gs;sptopf; NfhLfshFk;. mit tl;likaj;jpy; re;jpf;fpd;wd.

tl;lj;jpd; ,U Gs;spfis ntl;bf;nfhz;L nry;Yk; NfhL ntl;Lf;NfhL.

tl;lj;jpid xUGs;spapy; kl;Lk; njhl;Lr;nry;Yk; NfhL njhLNfhL. mg;Gs;sp njhLGs;sp.

xU tl;lj;ij ehz; ,U gFjpfshf gphpf;fpwJ. xt;nthU gFjpAk; tl;lg;gFjp MFk;.

,uz;L Muq;fshYk; tl;l tpy;yhYk; milgLk; gFjp tl;lf;Nfhzg;gFjpahFk;.

tptuq;fisf; ifahSjy;

njhlh;r;rpahd epfo;ntz; gutiy ,Ughpkhz tiuglj;jpy; Fwpg;gJ epfo;Tnrt;tfkhFk;(Histogram)

epfo;T nrt;tfq;fspd; Nkw;gf;fq;fspd; ikag;Gs;spfis Neh;Nfhl;Lj;Jz;Lfs; %yk; ,izj;jhy; fpilf;Fk; gyNfhzk; epfo;T gyNfhzk; (Frequency Polygon) vdg;gLfpwJ.

tl;ltpsf;fg;glk; (Pie Chart)tl;ltpsf;fg;glk; mjd; KOikf;Fk; xt;nthU gFjpf;Fk; cs;s njhlh;it tpsf;FfpwJ.

$l;Lr;ruhrhp (Arithmetic Mean - AM)fz;lwpe;j kjpg;Gfspd; $LjYf;Fk;> kjpg;Gfspd; vz;zpf;iff;Fk; cs;s tpfpjk;.

$l;Lr;ruhrhpia vd;W Fwpg;gh;.$l;Lr;ruhrhp ruhrhp (average) my;yJ kj;jpkk; (mean) vdTk; miof;fg;gLfpwJ.

,ilepiy (Median)

xU epfo;ntz; gl;baypy; FtpT epfo;ntz; vd;gJ me;jg;gphpT ,ilntsptiu cs;s epfo;ntz;fspd; $LjyhFk;.,ilepiy msTf;F fPo; vj;jid tptuq;fs; cs;sdNth mNj vz;zpf;ifapyhd tptuq;fs; mjw;F Nky; ,Uf;Fk;.

KfL (Mode)xU gutypy; kpFjpahf tUfpd;w kjpg;G KfL MFk;.

nghJika tl;lq;fs;xU jsj;jpy; nghJthd ikaj;ijf; nfhz;L ntt;NtW Muq;fspy; tiuag;gLk; tl;lq;fs; nghJika tl;lq;fs; vdg;gLk;.

,uz;L nghJika tl;lq;fSf;F ,ilNaAs;s gug;G tl;ltyak; MFk;.

tl;ltyaj;jpd; mfyk; w = R – r (R>r)(w = ntsptl;l Muk; – cs;tl;l Muk;)