myF – 21

Mr. A.K. Abdul Haleem

Name:................................... juk;-09 NDT in Maths [ merit ]
Tel : 0754255545
rkdpypfs;

01. gpd;tUk; rkdpypapd; jPu;Tfis vz;Nfhl;by; Fwpj;Jf; fhl;Lf.

(i) 𝑥−7 <5 (ii) 2𝑥 + 3 > 7

(iii) 3𝑥 − 8 ≤ 4 (iv) 6𝑥 + 7 ≥ 25

02. gpd;tUk; rkdpypapid jPu;j;J mtw;wpd; epiwvz; jPu;Tj;njhilapid vOJf.

(i) 𝑥+3 >7 (ii) 𝑥−3<5

(iii) 8 + 𝑥 ≤ 12 (iv) 𝑥 − 5 ≥ −3

03. gpd;tUk; rkdpypfis jPu;f;f.

(i) 5𝑥 ≥ 15 (ii) 9𝑥 ≤ 18

(iii) 3𝑥 − 5 ≥ 10 (iv) −4𝑥 + 9 ≥ 13

𝑥 4𝑥
(v) ≥3 (vi) ≥8
2 3

−3𝑥 −8𝑥
(vii) +2≥5 (viii) + 3 ≤ 11
4 5

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~1~
04. 3𝑛 < 10 vDk; rkdpypapy; 𝑛 vLf;ff;$ba kpfg;ngupa KO vz; ahJ?

05. rpahk; 100 &gha; itj;jpUe;jhd;. mtd; &gha; 𝑎 tpiyAs;s mg;gps; xd;iwAk;
&gha; 40 ngWkjpAs;s Njhlk;gok; xd;iwAk; thq;fpdhd;. mtd; thq;fpa
goq;fspd; ngWkhdj;jij 𝑎 + 40 ≥ 100 vDk; rkdpyp %yk; fhl;lyhk;.
mr;rkdpypia jPu;j;J mg;gps; xd;wpd; Fiwe;jgl;r tpiyiaf; fhz;f.

06. g]; xd;wpy; 56 gazpfis Vw;wKbAk;. Kjyhk; ,lj;jpy; 𝑥 vz;zpf;ifahd gazpfSk;

,uz;lhk; ,lj;jpy; 24 gazpfSk; g];]py; Vwpdu; ,j;jftiy 𝑥 + 24 ≤ 56 vDk; rkdpyp
%yk; fhl;lyhk;.
(i) ,r;rkdpypiaj; jPu;j;J 𝑥 ,d; ngWkhdj;ijf; fhz;f.

(ii) Kjyhk; ,lj;jpy; g];]py; Vwf;$ba gazpfspd; vz;zpf;ifia fhl;Lk; jPu;Tj;

njhilia vz; Nfhl;by; Fwpj;Jf; fhl;Lf.

(iii) Kjyhk; jupg;gplj;jpy; Vw;wf;$ba gazpfspd; mjpfgl;r vz;zpf;if vt;tsT?

07. jd;dplk; ,Uf;Fk; gzk; rpahkplk; cs;s gzj;jpd; 5 klq;fpYk; 4 FiwT vd mg; uj;
$Wfpd;whd;. mg;uj;jplk; 101 &gha; cs;sJ. rpahkplk; cs;s gzk; 𝑥 vdpd;>

,j;jftiy 5𝑥 − 4 < 101 vDk; rkdpyp %yk; fhl;lyhk;.

(i) ,r;rkdpypia jPu;j;J rpahkplk; cs;s mjpfgl;r gzj;ijf; fhz;f.

(ii) rpahkplk; 5 &gha; ehzak; kl;LNk cs;sJ vdpd; rpahkplk; cs;s mjp$ba
gzj;ijf; fhz;f.

08. vz;Nfhl;bd; kPJ epow;wpa gFjpia

-3 -2 -1 0 1 2 3 rkdpyp %yk; fhl;Lf.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~2~
 myF - 22
Mr. A.K. Abdul Haleem
Name:................................... juk;-09 NDT in Maths [ merit ]
Tel : 0754255545
njhilfs;
01. gpd;tUk; njhilfs; KbTs;s njhilah? Kbtpypj;njhilah? vd vOJf.

(i) A = { ,ul;il vz;fs; } ……………………………

(ii) B = { ,yq;ifapYs;s khtl;lk; } ……………………………

(iii) C = { 50 ,Yk; Fiwe;j 5 ,d; klq;Ffs; } ……………………………

(iv) D = { 1 , 3 , 5 , 7…} ……………………………

(v) E = { RfNjfpahd xUtupd; ,jaj;Jbg;G tPjk; } ……………………………

(vi) F = { tPl;bYs;s mq;fj;jtu;fs; } ……………………………

(vii) G = {xU tl;lj;jpd; gupjp kPJs;s Gs;spfs; } ……………………………

02. gpd;tUk; njhilfspd; midj;J njhilg;gpupTfisAk; vOJf.

(i) A= { 2,5 } (ii) B= { a,b }

(iii) C= { 1,3,7 } (iv) D= { p,q,r }

03. njhil xd;wpd; cgnjhilfspd; vz;zpf;if 32 vdpd; mj;njhilapd; %yfq;fspd;

vz;zpf;ifiaf; fhz;f.

04. njhil xd;wpd; cgnjhilfspd; vz;zpf;if 256 vdpd; mj;njhilapd;

cgnjhilfspd; vz;zpf;ifiaf; fhz;f.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~3~
05. fPNo jug;gl;Ls;s ntd;tupg;glj;jpy; fhl;lg;gl;Ls;s njhilfis epow;Wf.
(i) 𝐴∩𝐵 (ii) 𝐴∪𝐵 (iii) (𝐴 ∩ 𝐵)′

A B

(iv) (𝐴 ∪ 𝐵)′ (v) 𝐴 ∩ 𝐵′ (vi) 𝐴′ ∩ 𝐵

(vii) 𝐴′ ∩ 𝐵′ (viii) 𝐴′ ∪ 𝐵′

06. fPNo jug;gLk; ntd;tupg;glj;jpy; fhl;lg;gl;Ls;s njhilfis epow;Wf.

(i) 𝑃∩𝑄 (ii) 𝑃∪𝑄 (iii) 𝑃′ ∩ 𝑄 (iv) 𝑃 ∪ 𝑄′

Q P

07.
 jug;gl;l ntd;tupg;glj;ij gad;gLj;jp
9 gpd;tUtdtw;wpd; %yfq;fis vOjp mjd;
1 Kjypikia vOJf.
4 8
P 3 Q
6
10
5
B 7

(i) 𝑃 = (i) ∩ (𝑃) =

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~4~
 (ii) 𝑄 = (ii) ∩ (𝑄) =

(iii) 𝑃′ = (iii) ∩ (𝑃′) =

(iv) 𝑄′ = (iv) ∩ (𝑄′) =

(v) 𝑃 ∩ 𝑄 = (v) ∩ (𝑃 ∩ 𝑄) =

(vi) 𝑃 ∪ 𝑄 = (vi) ∩ (𝑃 ∪ 𝑄) =

(vii) 𝑃′ ∩ 𝑄 = (vii) ∩ (𝑃 ′ ∩ 𝑄) =

(viii) 𝑃 ∩ 𝑄′ = (viii) ∩ (𝑃 ∩ 𝑄′ ) =

(ix) (𝑃 ∪ 𝑄)′ = (ix) ∩ (𝑃 ∪ 𝑄)′ =

(x) (𝑃′ ∩ 𝑄)′ = (x) ∩ (𝑃′ ∩ 𝑄)′ =

(xi) ∈ = (xi) ∩ (∈) =

08. 
1 jug;gl;l ntd;tupg;glj;ij gad;gLj;jp
9
3 2 gpd;tUtdtw;wpd; %yfq;fisAk;
6 KjypikiaAk; vOJf.
B
4 A
5 8
1 7

(i) 𝐴= (i) ∩ (𝐴) =

(ii) 𝐵 = (ii) ∩ (𝐵) =

(iii) 𝐴 ∩ 𝐵 = (iii) ∩ (𝐴 ∩ 𝐵) =

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~5~
 (iv) 𝐴 ∪ 𝐵 = (iv) ∩ (𝐴 ∪ 𝐵) =

(v) 𝐴′ = (v) ∩ (𝐴′) =

(vi) 𝐵′ = (vi) ∩ (𝐵′) =

(vii) ∈ = (vii) ∩ (∈) =

(viii) 𝐴 ∩ 𝐵′ = (viii) ∩ (𝐴 ∩ 𝐵′ ) =

09.  = { 10 ,Yk; Fiwe;j vz;Zk; vz;fs; }

A = { 10 ,Yk; Fiwe;j ,ul;il vz;fs; }

B = { 10 ,Yk; Fiwe;j Kjd;ik vz;fs; }

(i) NkNy jug;gl;l njhilfis %yfq;fSld; vOJf.

(ii) NkNy jug;gl;l jfty;fis nghUj;jkhd ntd;cUtpy; Fwpf;f.

(iii) 𝐴 ∩ 𝐵 I vOJf.

(iv) ∩ (𝐴 ∪ 𝐵) ahJ?

(v) njhil A ,w;F vj;jid njhil gpupTfs; cz;L? mtw;Ws; 5 ,id vOJf.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~6~
10. ntd;cUtpy; jug;gl;l juTfSf;Nfw;g gpd;tUtdtw;iw fhz;f.
 (i) 𝑃 ∩ 𝑄
3
P 2
Q (ii) 𝑃 ∪ 𝑄
4 6

(iii) 𝑄′ ∩ 𝑃


(iv) 𝑃′ = {5 , 7 , 8 } vdpd; ∈11,d; %yfq;fis vOJf.
11. ntd;cUtpd; juTfSf;Nfw;g>
3
(i) 𝑁 … … . 𝑀 vd;gjpy; ntw;wplj;jpw;F nghUj;jkhd 1 2
M
FwpaPl;il milg;gpypUe;J njupf.(∈ , ∉ , ⊂ , ⊄) 4 6 N
5 7
9

(ii) 𝑀 ∩ 𝑁′ I fhz;f.

(ii) ∩ (𝑀 ∪ 𝑁) I vOJf.

(iii) (𝑀 ∩ 𝑁)′ gpuNjrj;ij epow;wpf; fhl;Lf.

(iv) 𝑁 ,w;F cs;s cgnjhilfspd; vz;zpf;ifia fhz;f.

13.  = { 1 – 18 tiuahd vz;Zk; vz;fs; }

A = { 12 ,d; fhuzpfs;; }

B = { 18 ,d; fhuzpfs;; } Mfpa njhilfis tif Fwpf;Fk; G+uzkw;w ntd;tupg;glk;

fPNo jug;gl;Ls;sJ. 10 13
12 1
(i) ntd;tupg;glj;jpy; vy;y
; h gpuNjrq;fSf;F upa P
18 Q
cupa %yfq;fis vOjp G+uzg;gLj;Jf.
5

(ii) ntd;tupg;glj;jpy; 12 ,dJk; 18 ,dJk; nghJf;fhuzpfisf; nfhz;l njhilia

njhilf;Fwpg;gPl;il gad;gLj;jp vOJf.

(iii) (𝑃 ∪ 𝑄)′ njhilia %yfq;fSld; vOjpf;fhl;Lf.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~7~
 myF - 23
Mr. A.K. Abdul Haleem
Name:................................... juk;-09 NDT in Maths [ merit ]
Tel : 0754255545
gug;gsT
01. gpd;tUk; cUtq;fspd; gug;gsitf; fhz;f.
C S P
(i) (ii) (iii)

24𝑐𝑚 9𝑐𝑚 15𝑐𝑚

12𝑐𝑚 8𝑐𝑚 10𝑐𝑚

A B P 6𝑐𝑚 Q 20𝑐𝑚 R Q R
14𝑐𝑚 12𝑐𝑚

02. jug;gl;l cUtpy; ∆PQR ,y; cs;s juTfSf;fika> P

(i) ∆PQR ,d; gug;gsitf; fhz;f.

T
8𝑐𝑚
(ii) PR ,d; ePsk; ahJ?
R 20𝑐𝑚 Q S

03. gpd;tUk; ,izfuq;fs; xt;nthd;wpdJk; gug;gsitf; fhz;f.

(i) (ii) ≫

6𝑐𝑚 8𝑐𝑚 10𝑐𝑚

≫
20𝑐𝑚 14𝑐𝑚

04. ,izfuj;jpd; gug;gsTfs; jug;gl;Ls;sJ. njupahf;fzpaj;jpd; ngWkhdj;ijf; fhz;f.

(i) ≫ (ii)

𝑎
ℎ

≫
16𝑐𝑚

𝐴 = 80𝑐𝑚 2 𝐴 = 175𝑐𝑚 2

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~8~
 R R
05. ≫
cUtpYs;s juTfspd; gb>
20𝑐𝑚 ℎ
(i) ,izfuj;jpd; gug;gsitf; fhz;f.
≫
R 24𝑐𝑚 R R

(ii) ℎ If; fhz;f.

D C
06. 05. ≫
cUtpYs; s juTfisf; nfhz;L ℎ If; fhz;f.
35𝑐𝑚
15𝑐𝑚 ℎ

≫
A 21𝑐𝑚 B

07. gpd;tUk; cUtpd; gug;gsitf; fhz;f.

8𝑐𝑚 12𝑐𝑚
(i) > (ii) >
9𝑐𝑚 24𝑐𝑚
10𝑐𝑚

> >
19𝑐𝑚
14𝑐𝑚

08. cUtpy; epow;wg;gl;l gFjpapd; gug;gsitf; fhz;f.

20𝑐𝑚

4𝑐𝑚

6𝑐𝑚

14𝑐𝑚

09. cUtpYs;s ehw;gf;fypd; gug;gsT 140𝑐𝑚2 vdpd; 𝑎 ,d; ngWkhdj;ijf; fhz;f.

12𝑐𝑚
>

>
16𝑐𝑚

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~9~
10. ruptfj;jpd; gug;gsT 240𝑐𝑚2 vdpd; 𝑦 ,d; ngWkhdj;ijf; fhz;f.
15𝑐𝑚

12𝑐𝑚

11. gpd;tUk; msTfis cila tl;l tbtpyhd mlupd; gug;gsitf; fhz;f.

(i) Miu 21𝑐𝑚 (ii) tpl;lk; 28𝑐𝑚

(iii) Miu 10.5𝑐𝑚 (iv) tpl;lk; 63𝑐𝑚

12. gpd;tUk; gug;gsTila tl;l mlu;fspd; Miuiaf; fhz;f.

(i) 616𝑐𝑚2 (ii) 346.5𝑐𝑚2

13. juk; 9 khztu;fs; 0.7m MiuAila tl;ltbthd G+e;Njhl;lk; xd;iw mikj;J mjid
rkkhd 6 Miur;rpiwfis gpupj;Jf; nfhz;ldu;.
(i) G+e;Njhl;lj;jpd; tpl;lj;jpid cm ,y; jUf.

(ii) G+e;Njhl;lj;jpd; Rw;wsitf; fhz;f.

(iii) G+e;Njhl;lj;jpd; gug;gsit 𝑐𝑚2 ,y; jUf.

(iv) G+e;Njhl;lj;ij Rw;wpAk;> cl;Gwj;ij Miur;rpiwfshf gpupg;gjw;F xd;wpd; ePsk;

130𝑐𝑚 MfTs;s mYkpdpaj;jfLfs; gad;gLj;jg;gLfpd;wJ. vdpd; Njitahd

mYkpdpaj; jfLfs; vj;jid vdf; fhz;f.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 10 ~
14. jpUkz kz;lgk; xd;wpd; fpilg;glk; fPNo jug;gl;Ls;sJ. miutl;l gFjp NkilahfTk;>
nrt;tfg;gFjp ghu;itahsUf;Fk; xJf;fg;gl;Ls;sJ.
(i) Nkilg;gFjpapd; Miuiaf; fhz;f.

21𝑚
(ii) Nkilapd; Rw;wsitf; fhz;f.

120𝑚

(iii) Nkilapd; gug;gsitf; fhz;f.

(iv) ghu;itahsUf;F xJf;fg;gl;l ,lj;jpd; gug;gsitf; fhz;f.

(v) kz;lgj;jpd; nkhj;jg; gug;gsitf; fhz;f.

15. nrt;tf tbthd fhzp xd;wpy; miutl;lf;Fsk; xd;W fhl;lg;gl;Ls;sJ.

(i) nrt;tfj;jpd; mfyj;ij fhz;f.

(ii) Fsj;jpd; Rw;wsitf; fhz;f.

(iii) nrt;tf tbt epyj;jpd; gug;gsT ahJ? 14𝑚

(iv) epow;wg;gl;l gFjpapd; gug;gsT ahJ?

3
(v) epow;wg;gl;l gFjpapd; gug;gsT miutl;l Fsg;gFjpapd; gug;gstpd; gq;F
11
vdf;fhl;Lf.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 11 ~
16. jug;gl;l cUtpYs;s juTfis gad;gLj;jp gpd;tUk; tpdhf;fSf;F tpilaspf;Ff.
(i) AD ,d; ePsj;ijf; fhz;f. E

8𝑚 6𝑚

(ii) AB ,d; ePsk; ahJ?

A D
(iii) nrt;tfk; ABCD ,d; gug;gsT ahJ?

B C
(iv) miutl;l gFjpapd; gug;gsT ahJ?

(v) epow;wpa gFjpapd; gug;gsT ahJ?

17. jug;gl;l cUthdJ Xu; Xl;l ikjhdj;jpd; khjpupg;glkhFk;.

(i) miutl;lg;gFjpapd; Miuiaf; fhz;f.

28𝑚
(ii) ikjhdj;jpd; miutl;l tpy;ypd; ePsk; ahJ?

56𝑚

(iii) ikjhdj;jpd; Rw;wsT ahJ?

(iv) ikjhdj;jpd; xU miutl;l gFjpapd; gug;gsT ahJ?

(v) ikjhdj;jpd; miutl;l gFjpfSf;F khj;jpuk; Gy; el jPu;khdpf;fg;gl;Ls;sJ.

nryT 1𝑚2 ,e;F 100 vdpd; Vw;gLk; nkhj;j nryitf; fhz;f.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 12 ~
18. 21cm ePsKk; 14cm mfyKk; nfhz;l nrt;tf tbthd xU jfl;bypUe;J rkkhd ,U
miutl;lq;fis cila ,yl;riz xd;W ntl;b vLf;fg;gLfpd;wJ.
(i) ntl;lg;gl;l ,yl;rizapd; miutl;lg;gFjpapd; 21𝑐𝑚

Miuiaf; fhz;f.

14𝑚 14𝑚
(ii) ,yl;rizapd; Rw;wsT 58cm vdf; fhl;Lf.

−
14𝑐𝑚

−
(iii) ,yl;riz ntl;b vLf;fKd; jfl;bd; gug;gsT ahJ?

(iv) ,yl;rizapd; gug;gsT ahJ?

(v) epow;wg;gl;l gFjpapd; gug;gsT ahJ?

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 13 ~
 myF - 24
Mr. A.K. Abdul Haleem
Name:................................... juk;-09 NDT in Maths [ merit ]
Tel : 0754255545
epfo;jfT

01. gpd;tUk; epfo;jfTfSf;Fupa khjpupntspia vOJf.

(i) ehzak; xd;iw NkNy Rz;Ljy;

(ii) 1 – 6 tiu ,yf;fkplg;gl;l Nfhlhj rJuKfp jhaf;fl;il xd;iw cUl;Ljy;

(iii) 1 – 4 tiu ,yf;fkplg;gl;l xOq;fhd ehd;Kfp jhaf;fl;ilia cUl;Ljy;

(iv) ig xd;wpYs;s 5 nts;is> 2 fUg;G epw khgps;;fs; cs;sd. mtw;wpy; xd;iw

vOkhwhf vLj;jy;

(v) 6 khk;goq;fis nfhz;l ngl;bapy; 4 gOj;jit 2 gOf;fhjit mtw;wpy;

xd;iw vOkhwhf ntspNa vLj;jy;.

02. tFg;giw xd;wpYs;s 160 khztu;fs; cs;sdu;. mtu;fspy; xUtiu njupT nra; jhy;
2
mtu; Mzhf ,Ug;gjw;fhd epfo;jfT vdpd; tFg;giwapy; cs;s ngz;fspd;
5
vz;zpf;if ahJ?

03. 6 rptg;G 2 fWg;G epw khgpisf; nfhz;l ig xd;wpypUe;J xU khgps; vOkhwhf

vLf;fg;gLk; NghJ mJ fWg;G epwkhf ,Ug;gjw;fhd epfo;jfitf; fhz;f.

04. 1 > 1 > 2 > 2 > 3> 3 vd ,yf;fkplg;gl;l Nfhlhj rJuKfp jhaf;fl;ilia cUl;Lk;
NghJ NkypUf;Fk; vz;iz Fwpf;Fk; gupNrhjidapy;>
(i) ngwf;$ba vy;yh NgWfisAk; cs;slf;fpa khjpup ntspia (𝑆) vOJf.

(ii) 𝑛(𝑠) ,d; ngWkhdj;ijf; fhz;f.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 14 ~
 (iii) Kjd;ik vz; tpOk; epfo;r;rp 𝐴 vdpd; 𝐴 ,d; %yfq;fis vOjp 𝑛(𝐴) If;
fhz;f.

(iv) 𝑃(𝐴) ,idf; fhz;f.

05. 4 ePy epw khgps;fSk;> 3 fWg;G epw khgps;fSk; mlq;fpa ig xd;wpypUe;J vOkhwhf
xU khgpis vLj;J epwk; Fwpf;Fk; gupNrhjidapy;
(i) khjpupntspia vOJf.

(ii) mJ xU ePy epwkhf ,Ug;gjw;fhd epfo;jfitf; fhz;f.

(iii) mJ xU fWg;G epwkhf ,Ug;gjw;fhd epfo;jfitf; fhz;f.

06. ngl;b xd;wpy; 5 kQ;rs; epw ml;ilfSk;> 4 nts;is epw ml;ilfSk;> 3 fWg;G epw
ml;ilfSk; cs;sd. vOkhwhf xU ml;il ntspNa vLf;fg;gLfpd;wJ.
(i) epfo;r;rpf;fhd khjpupntspia vOJf.

(ii) vLf;fg;gl;l ml;il fWg;G epwkhf ,Ug;gjw;fhd epfo;jfitf; fhz;f.

(iii) vLf;fg;gl;l ml;il nts;is my;yJ kQ;rs; ,Ug;gjw;fhd epfo;jfitf; fhz;f.

(iv) vLf;fg;gl;l ml;il kQ;rs; epwkhf ,y;yhjpUg;gjw;fhd epfo;jfitf; fhz;f.

07. AKKARAIPATTU vd;w nrhy;ypYs;s vOj;Jf;fs;

(i) njhilia %yfkhf vOJf.

(ii) ,j;njhilapd; %yfq;fs; vOjg;gl;l ml;il xU igapy; ,Ue;jd. mjpypUe;J

vOkhwhf vLf;Fk; ml;il xd;wpy; vOj;J A ,Ug;gjw;fhd epfo;jfit vOJf.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 15 ~
08. tpQ;Qhd tpdhg;gj;jpuj;jpy; gFjp xd;wpYs;s tpdh xd;wpf;F jug;gl;l 4 tpilfspy; 1
tpil khj;jpuk; rupahdjhFk;. rupahd tpil njupahj xU khztd; vOkhwhf xU
tpilapid Nju;e;njLj;jhd;. mtdJ tpil
(i) gpioahd ,Ug;gjw;fhd epfo;jfit vOJf.

(ii) rupahf ,Ug;gjw;fhd epfo;jfit vOJf.

09. 60 khk;goq;fs; ngl;b xd;wpDs; cs;sd mtw;wpy; xd;iw njupe;njLj;jhy; mJ

7
gOj;jjhf ,Ug;gjw;fhd epfo;jfT MFk;.
12

(i) gOf;fhjitahf ,Ug;gjw;fhd epfo;jfitf; fhz;f.

(ii) gOj;j khk;goq;fspd; vz;zpf;if ahJ?

(iii) gOf;fhj khk;goq;fspd; vz;zpf;if ahJ?

10. 1 – 20 tiuahd vz;fs; ,lg;gl;l ml;il ngl;bapypUe;J vOkhw;whf xU ml;il

ntspNa vLf;fg;gLk; NghJ gpd;tUtdtw;Wf;fhd epfo;jfTfis fhz;f.
(i) xw;iw vz;zhf ,Uf;Fk;

(ii) Kjd;ik vz;zhf ,Uf;Fk;

(iii) 4 ,d; klq;fhf ,Uf;Fk;

(iv) Kf;Nfhz vz;zhf ,Uf;Fk;

(v) rJu vz;zhf ,Uf;Fk;

(vi) 5 My; kPjpapd;wp tFglf;$bajhf ,Uf;Fk;

(vii) 12 ,d; fhuzpfshf ,Uf;Fk;

11. xNu mstpyhd 𝑥 vz;zpf;ifahd rptg;G ew gY}d;fSk; 𝑦 vz;zpf;ifapyhd kQ;rs;

epw khgps;fSk; cs;sd. rptg;G epwk; fpilg;gjw;fhd epfo;jfT kQ;rs; epwk;
fpilg;gjw;fhd epfo;jftpYk; mjpfkhFk;
(i) 𝑥, 𝑦 ,ilapyhd njhlu;ig rkdpyp %yk; Fwpf;f.

(ii) rptg;G epwk; fpilg;gjw;fhd epfo;jfitf; fhz;f.

(iii) kQ;rs; epwk; fpilg;gjw;fhd epfo;jfitf; fhz;f.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 16 ~
 myF - 25
Mr. A.K. Abdul Haleem
Name:................................... juk;-09 NDT in Maths [ merit ]
Tel : 0754255545
gy;Nfhzpapd; Nfhzq;fs;
01. gpd;tUk; gy;Nfhzpfspy; mff;Nfhzq;fspd; gUkidf; fhz;f.
(i) mWNfhzp (ii) etNfhzp (iii) 13 gf;fk; nfhz;l gy;Nfhzp

02. fPNo jug;gl;Ls;s cUtq;fspy; 𝑥 ,d; ngWkhdj;ijf; fhz;f.

(i) (ii)
950 1050
1100 1200
1300 1000

𝑥 1000 1650 𝑥

(iii) 800 (iv)

1400 𝑥
850
𝑥 1300
0
55

1200 𝑥
𝑥 750

03. Xu; xOq;fhd jrNfhzpapd; mff;Nfhzk; xd;wpd; gUkd; ahJ?

04. Xu; xOq;fhd gy;Nfhzpapd; xd;wpd; mff;Nfhzk; 1560 vdpd;

(i) Gwf;Nfhzj;jpd; gUkidf; fhz;f.

(ii) gy;Nfhzpapd; gf;fq;fs; vz;zpf;if?

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 17 ~
05. Xu; xOq;fhd gy;Nfhzpapd; xd;wpd; mff;Nfhzk; 1440 vdpd;
(i) Gwf;Nfhzj;jpd; gUkidf; fhz;f.

(ii) gy;Nfhzpapd; gf;fq;fs; vz;zpf;if?

06. Xu; xOq;fhd gy;Nfhzpapd; xd;wpd; mff;Nfhzk; 1600 vdpd;

(i) gy;Nfhzpapd; gf;fq;fs; vz;zpf;if?

(ii) Gwf;Nfhzj;jpd; gUkidf; fhz;f.

07. mWNfhzp xd;wpd; Gwf;Nfhzk; 1 ∶ 2 ∶ 2 ∶ 3 ∶ 4 ∶ 6 vdpd; xt;nthU Gwf;Nfhzq;fspd;

gUkidAk; jdpj;jdpNa fhz;f.

08. Xu; xOq;fhd gy;Nfhzpapd; xd;wpd; mff;Nfhzk;> Gwf;Nfhzj;jpd; %d;W klq;F vdpd;
mg;gy;Nfhzpapd; gf;fq;fspd; vz;zpf;ifiaf; fhz;f.

09. cUtpy; PQRST xOq;fhd Iq;Nfhzp

MFk;. 𝑄𝑅𝑉 , 𝑃𝑄𝑈 vd;gd Neu;NfhLfshFk;.
(i) nrt;tfj;jpd; mfyj;ij fhz;f. S V
̂ ̂ 𝑈 = 900
𝑄U𝑉 = 𝑆V MFk;. jug;gl;l juTfis
gad;gLj;jp>
T
̂ 𝑉t,d;
(ii) (i) nrt;
𝑃Q f tbt epyj;jpd;
ngWkhdk; gug;gsT ahJ?
ahJ? R

̂ Uw,d;
(iii)(ii) epow;
𝑄V g;gl;lngWkhdk;
gFjpapd; ahJ?
gug;gsT ahJ?
−

P Q U

̂ R ,d; ngWkhdk; ahJ?

(iii) 𝑆V

(iv) 𝑇ŜV ,d; ngWkhdk; ahJ?

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 18 ~
10. PQRST Xu; xOq;fhd gy;Nfhzp MFk;.

(i) ,g;;gy;Nfhzpapd; rpwg;Gg; ngau; vd;d? P

(ii) ,g;;gy;Nfhzpapd; mff;Nfhzq;fspd; T Q

$l;Lj;njhif ahJ?

(iii) ̂ R ,d; gUkd; ahJ?

𝑃Q
S R

(iv) ̂R gf;fk; rhu;ghf vt;tifahd Kf;Nfhzp?

∆𝑃Q

(v) ̂ 𝑄 ,d; gUkd; ahJ?

𝑃R

(vi) ̂ 𝑆 ,d; gUkd; ahJ?

𝑃R

(vii) 𝑇Ŝ𝑅 + 𝑃R
̂ 𝑆 ,d; gUkd; ahJ?

(viii) 𝑇𝑆 , 𝑃𝑅 vDk; Neu;NfhLfSf;fpilapyhd rpwg;Gj;njhlu;G ahJ? fhuzk; jUf.

(ix) ehw;gf;fy; 𝑃𝑇𝑆𝑅 ,d; rpwg;Gg; ngau; ahJ?

11. cUtpy; ABCDEF Xu; xOq;fhd mWNfhzp MFk;.

(i) mWNfhzpapd; mff;Nfhzq;fspd;

$l;Lj;njhif ahJ?
B C
(ii) ̂ 𝐹 ,d; gUkd; ahJ?
𝐵A

(iii) ̂ 𝐹 ,d; gUkd; ahJ?

𝐴B
A D
(iv) 𝐵F̂𝐸 ,d; gUkd; ahJ?

F E

(v) mWNfhzpapd Rw;wsT 60𝑐𝑚 vdpd; 𝐴𝐵 ,d; ePsj;ijf; fhz;f.

(vi) 𝐵𝐹 = 8𝑐𝑚 vdpd;; 𝐵𝐸 ,d; ePsj;ijf; fhz;f.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 19 ~
 myF - 26
Mr. A.K. Abdul Haleem
Name:................................... juk;-09 NDT in Maths [ merit ]
Tel : 0754255545
ml;rufzpjg;gpd;dk;
01. gpd;tUk; ml;ru fzpjf; Nfhitfis RUf;Ff.
(i) 4𝑥 − 5 + 2𝑥 + 9 (ii) 6𝑎 − 2 − 5𝑎

(iii) 6(𝑥 + 4) − 3(𝑥 − 2) (iv) 2(5𝑎 − 7) − 3(2𝑎 + 3)

02. rkdhd gFjp vz;iz cila ml;ru fzpjg; gpd;dq;fis RUf;Ff.

𝑥 𝑥 5𝑥 3𝑥
(i) + (ii) +
3 3 4 4

2𝑥−1 3𝑥−5 3𝑥−6 2𝑥+7

(iii) + (iv) +
4 4 5 5

5𝑥 4𝑥 5𝑎 2𝑎
(v) − (vi) −
9 9 3 3

5𝑥−4 3𝑥+2 4𝑥−3 3𝑥+2

(vii) − (viii) −
6 6 7 7

2𝑥−1 5𝑥−2 8𝑥+7 4𝑎−5 3𝑎+10 2𝑎−9

(ix) − + (x) + −
3 3 3 16 16 16

03. gpd;tUk; rkdw;w gFjp vz;izAila ml;rufzpjg; gpd;dq;fis RUf;Ff.

𝑥 𝑥 5𝑎 2𝑎
(i) + (ii) +
2 3 4 3

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 20 ~
 5𝑎 2𝑎 2𝑏 𝑏
(iii) − (iv) −
4 3 5 4

𝑎+1 5𝑎+1 𝑥−3 𝑥+4

(v) + (vi) +
2 4 4 3

5𝑥−1 2𝑥−3 4𝑚−𝑛 3𝑚+𝑛

(vii) − (viii) −
6 5 9 12

𝑥 2𝑥 5𝑥 3𝑥+4 𝑥+5 2𝑥−1

(ix) + − (x) − +
2 3 6 4 6 12

04. gpd;tUk; gFjpapy; rkdhd ml;ru fzpj cWg;ig nfhz;l gpd;dq;fis RUf;Ff.
1 3 8 2
(i) + (ii) −
𝑥 𝑥 𝑎 𝑎

5𝑥 7𝑥−1 15𝑎 9𝑎−2

(iii) + (iv) −
𝑎+3 𝑎+3 𝑏+5 𝑏+5

9 11 15 15 8 3
(v) + − (vi) − +
2𝑚+5 2𝑚+5 2𝑚+5 7𝑥−2 7𝑥−2 7𝑥−2

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 21 ~
05. gpd;tUk; ml;ru fzpj Nfhitfis nfhz;l gpd;dq;fis RUf;Ff.
2𝑥 𝑥 2𝑎 𝑎
(i) + (ii) −
𝑥−3 𝑥−3 𝑎−5 𝑎−5

3𝑎+1 2𝑎−5 𝑎+𝑏 𝑏−𝑎

(iii) + (iv) −
𝑡−4 𝑡−4 𝑎−𝑏 𝑎−𝑏

2𝑥−1 𝑥−3 𝑥+𝑦 𝑦

(v) − (vi) −
𝑎−𝑏 𝑎−𝑏 (𝑥−𝑦) (𝑥−𝑦)

𝑥 𝑥−𝑦 5−𝑎 2𝑎+1

(vii) − (viii) −
𝑥+𝑦 𝑥+𝑦 𝑥+3 𝑥+3

𝑎+𝑏 𝑎 𝑎−2𝑏 𝑝−3 𝑝+1 2𝑝

(ix) − + (x) − +
𝑎−𝑏 𝑎−𝑏 𝑎−𝑏 𝑝−2 𝑝−2 𝑝−2

𝑥 3𝑥 2 3
(xi) + (xii) −
𝑥+2 2(𝑥+2) 𝑥−5 4(𝑥−5)

4𝑎 3𝑎 3 3
(xiii) − (xiv) −
𝑎−2 3(𝑎−2) 𝑝−5 2(𝑝−5)

2𝑥 𝑥+𝑦 𝑝+𝑞 𝑞
(xv) − (xvi) −
𝑥−𝑦 2(𝑥−𝑦) 𝑝−𝑞 3(𝑝−𝑞)

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 22 ~
 myF - 27
Mr. A.K. Abdul Haleem
Name:................................... juk;-09 NDT in Maths [ merit ]
Tel : 0754255545
mstpilg;glk;
01. jug;gl;l cUtpy; N
(i) A ,ypUe;J B ,d; jpirNfhisf; fhz;f.
1100 N
(ii) B ,ypUe;J A ,d; jpirNfhisf; fhz;f. A

B
02. 𝑁 600 𝐸 60𝑚 vDk; ,lj;jpw;Fwpa jpirNfhis vOJf.

03. gpd;tUk; jpirNfhis tupg;glk; %yk; fhl;Lf.

(i) A ,ypUe;J B jpirNfhs; 0400 (ii) M ,ypUe;J N jpirNfhs; 0950

(iii) P ,ypUe;J Q jpirNfhs; 1700 (iv) S ,ypUe;J T jpirNfhs; 2100

04. gpd;tUk; xt;nthU re;ju;g;gj;jpYk; A ,ypUe;J B ,d; jpirNfhisAk; B ,ypUe;J A

,d; jpir NfhisAk; fhz;f.
N
(i) N (ii)
A→B= A→B=
B

500 B→A= A B→A=

0
50
B
A

N N
(iii) (iv)
B
A→B= A→B=
0
160
A 250
B→A= B→A=

A
B

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 23 ~
05. gpd;tUk; jpirNfhis tupg;glk; %yk; fhl;Lf.
N N
(i) P ,ypUe;J Q jpirNfhs;
1400 1500 R
P

(ii) Q ,ypUe;J P jpirNfhs; N

(iii) Q ,ypUe;J R jpirNfhs; Q

(iv) R ,ypUe;J Q jpirNfhs;

06. khYkp JiwKfk; A ,ypUe;j Gwg;gl;L 0300 jpirNfhspy; 100𝑚 J}uk; nrd;W JiwKfk;
B I milfpwhu;. gpd; B ,ypUe;J 2700 jpir NfhspYk; 80𝑚 J}uj;jpYk; A ,w;F tlf;Nf
cs;s JiwKfk; C ,id milfpd;whu;.

(i) Nkw;gb jftiy gUkl;lhd glk; %yk; fhl;Lf.

(ii) igjfurpd; Njw;wj;ij gad;gLj;jp AC ,d; ePsj;ij fhz;f.

07. mstpilg;glk; xd;wpy; 5𝑐𝑚 ,dhy; 2.5𝑘𝑚 Fwpf;fg;gLkhapd; mjd; mstpil tpfpjj;ij
fhz;f.

08. 1 ∶ 1 000 vDk; mstpilf;F tiuag;gl;l mstpilg;glj;jpy; 8𝑐𝑚 ,dhy; Fwpf;fg;gLk;

cz;ik ePsj;ijf; fhz;f.

09. 1 ∶ 25 000 vDk; mstpilf;F tiuag;gl;l mstpilg;glj;jpy; 4𝑐𝑚 ePsj;jpdhy;

Fwpf;fg;gLk; cz;ik ePsj;ij 𝑘𝑚 ,y; jUf.

10. 1 ∶ 50 000 vDk; mstpilf;F tiuag;gl;l ,yq;if tiuglj;jpy; ,U

efuq;fSf;fpilapyhd cz;ikj; J}uk; 5𝑘𝑚 vdpd; mjd; mstpil ePsj;ij 𝑐𝑚 ,y;
jUf.

11. 1 ∶ 2 000 vDk; mstpilf;F tiuag;gl;l tiuglj;jpy; cz;ik ePsj;ij 1𝑘𝑚 ,dhy;
Fwpf;fg;gLk; mstpil ePsj;ij 𝑐𝑚 ,y; jUf.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 24 ~
12. fpilj;jsk; xd;wpy; mike;Js;s P, Q ,R vDk; 3 Gs;spfspd; gUkl;lhd mikTfis
Fwpf;Fk; xU glk; fPNo jug;gl;Ls;sJ.
N
(i) Q ,ypUe;J P ,d; jpirNfhis vOJf.
N
R
800
(ii) Q ,ypUe;J P ,d; mikit tptupf;f. P
300
200 N
(iii) R ,ypUe;J P ,d; jpirNfhis vOJf.
Q

13. fpilj;jiuapy; 200𝑚 J}uj;jpy; mike;Js;s Gs;sp P , Q ,y; KiwNa 150𝑚 , 100𝑚
cauKs;s epiyf;Fj;J NfhGuq;fs; 2 mike;Js;sd.
(i) nghUj;jkhd mstpilfis gad;gLj;jp Nkw;Fwpj;j jfty; cs;slf;fpa
mstpilg;glk; xd;iw tiuf.
(ii) P ,d; cr;rpapypUe;J Q ,d; cr;rpapd; jpirNfhis mse;J vOJf. ,jpypUe;J Q
,ypUe;J P ,d; jpirNfhis fzpf;f.

14. tlf;F njw;fhf nry;Yk; xU Neu; ghijapy; mike;Js;s Gs;sp R ,ypUe;J ,lJ
gf;fj;jpy; itj;jparhiy 2300 jpir Nfhspy; cs;sJ. R ,ypUe;J ghij topNa 140𝑚
njw;F Nehf;fp te;J Gs;sp S ,ypUe;J itj;jparhiyia mtjhdpj;j NghJ 3000 jpir
Nfhspy; ,Ue;jJ.
(i) Nkw;Fwpj;j jfty;fis cs;slf;fpa gUkl;lhd glk; xd;iw tiuf.

(ii) nghUj;jkhd mstpilapy; Xu; mstpilg;glj;ij tiue;J mjpypUe;J

itj;jparhiyapypUe;J S , R vd;gtw;Wf;fpilapyhd J}uj;ijf; fhz;f.
(iii) itj;jparhiyapypUe;J Gs;sp R ,w;Fs;s cz;ikj; J}uk; vt;tsT?

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 25 ~
 myF - 28
Mr. A.K. Abdul Haleem
Name:................................... juk;-09 NDT in Maths [ merit ]
Tel : 0754255545
juTfis tifFwpj;jYk; tpsf;fkspj;jYk;

01. 5 – 11 > 12 – 18 > 19 – 25 tFg;ghapilia nfhz;l vz; guk;gy; xd;wpd; 12 – 18

tFg;ghapilapd; fPo; vy;iyiaAk; Nky; vy;iyiaAk; vOJf.

02. tpahghup xUtu; &gha; 50 cila 3 khk;goq;fisAk; &gha; 60 cila 7

khk;goq;fisAk; tpw;whu;. vdpd; khk;gok; xd;wpd; ,il tpiyia fhz;f.

03. 4 khztu;fspd; epiwfspd; ,il 80𝑘𝑔 MFk;. ,tu;fSld; 60𝑘𝑔 epiwAila xU

khztd; ,ize;jhy; 5 khzttu;fspdJk; ,ilepiwiaf; fhz;f.

04. 7 Njq;fha;fspd; tpiyf;fhd ,il 50 NkYk; 3 Njq;fha;fspd; tpilf;fhd ,il 60

MFk; vdpd; 10 Njq;fha;fspdJk; ,il tpiyiaf; fhz;f.

05. 50 khztu;fspd; ,il fpl;ba 𝑘𝑔 ,y; jug;gl;Ls;sJ.

jpzpT (𝑘𝑔) 31 32 33 34 35 36 37 38
khzttu;
vz;zpf;if 3 13 7 6 6 8 5 2
(i) khztu;fspd; jpzptpd; tPr;R ahJ?

(ii) khztu;fspd; jpzptpd; Mfhuk; ahJ?

(iii) khztu;fspd; jpzptpd; ,ilak; ahJ?

(iv) xU khztdpd; ,ilj;jpzpitf; fpl;ba 𝑘𝑔 ,y; fhz;f.

(v) vOkhwhf xU khztid njupT nra;jhy; mtd; 35𝑘𝑔 jpzpit tpl mjpf
jpzpTilatdhf ,Ug;gjw;fhd epfo;jfitf; fhz;f.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 26 ~
06. E}yfk; xd;wpy; jpde;NjhUk; vLj;Jr;nry;yg;gl;l Gj;jfq;fspd; vz;zpf;if njhlu;ghd
jftiyf; nfhz;L cUthf;fg;gl;l ml;ltiz fPNo jug;gl;Ls;sJ.

Gj;jfq;fspd; ehl;fspd;
eLg;ngWkhdk; 𝑓𝑥
vz;zpf;if vz;zpf;if (𝑓)

0 – 10 5
10 – 20 11
20 – 30 25 21
30 – 40 13
40 – 50 8
50 – 60 2

𝑓 = 𝑓𝑥
=

(i) Mfhu tFg;G ahJ?

(ii) 𝑥 , 𝑓𝑥 epuy;fis G+uzg;gLj;Jf.

(iii) E}yfj;jpy; ehs; xd;Wf;F tpepNahfpf;fg;Lk; Gj;jfj;jpd; vz;zpf;ifapd; ,ilia

KO vz;zpy; fhz;f.

07. khztu;FO xd;W fzzpia gad;gLj;Jtjw;F vLj;j Neuk; njhlu;ghd tpguk; fPNo
ml;ltizapy; jug;gl;Ls;sJ.
vLj;j Neuk; khztu; eLg;ngWkhdk; 𝑓𝑥
vz;zpf;if 𝑥
0 – 5 2
5 – 10 5
10 – 15 6
15 – 20 8
20 – 25 5
25 – 30 4
(i) Mfhu tFg;G ahJ?

(ii) 𝑥 , 𝑓𝑥 epuy;fis G+uzg;gLj;Jf.

(iii) G+uzg;gLj;jpa jfty;fisf; nfhz;L khztd; xUtDf;F fzzpia

gad;gLj;Jtjw;F vLj;j Neuj;jpd; ,iliaf; fhz;f.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 27 ~
08. fil xd;wpy; tpw;fg;gl;l muprpapd; jpzpT (kg) gw;wpa tpguk; fPNo ml;ltizapy;
jug;gl;Ls;sJ.

jpzpT (𝑘𝑔) eLg;ngWkhdk; (𝑥) kPbwd; (𝑓) 𝑓𝑥

1 – 15 7
16 – 30 23 5
31 – 45 8
46 – 60 53 5
61 – 75 3
76 – 90 2

𝑓 = 𝑓𝑥 =
(i) 1 – 15 vDk; tFg;ghapilapd; fPo; vy;iy Nky; vy;iy vd;gtw;iw vOJf.

(ii) Mfhu tFg;G ahJ?

(iii) 𝑥 , 𝑓𝑥 epuy;fis G+uzg;gLj;Jf.

(iv) xU ehspy; tpw;fg;gl;l muprpapd; jpzpit fpl;ba 𝑘𝑔 ,y; fhz;f.

(v) vOkhwhf xU ehis njupT nra;Ak; NghJ me;ehspy; 60𝑘𝑔 ,Yk; $Ljyhd
muprpia tpw;wpUg;gjw;fhd epfo;jfT ahJ?

09. 30 khztu;fspd; fzpj ghlj;jpy; ngw;w Gs;spfs; njhlu;ghd jfty;fs; fPNo

jug;gl;Ls;sJ. ,g;guPl;irapy; gs;spahdJ 50 ,w;F toq;fg;gl;lJ.

eLg;ngWkhdk;
jpzpT (𝑘𝑔) kPbwd; (𝑓) 𝑓𝑥
(𝑥)
0 – 10 2 5
11 – 20 6 15.5
21 – 30 10
31 – 40 8
41 – 50 4 45.5
𝑓 = 𝑓𝑥
=

(i) Mfhu tFg;G ahJ?

(ii) ml;ltizia G+uzg;gLj;Jf.

(iii) khztu; xUtu; ngw;w Gs;spia fpl;ba KO vz;zpy; fhz;f.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 28 ~
 %d;whk; jtiz khjpupg;guPl;ir
Mr. A.K. Abdul Haleem
Name:................................... juk;-09 NDT in Maths [ merit ]
Tel : 0754255545
fzpjk;

gFjp – 1
vy;yh tpdhf;fSf;Fk; ,j;jhspNyNa tpil vOJf.

01. 44 , 41 , 38 , … vd;w vz; njhlupd; mLj;J tUk; ,U cWg;Gf;fis vOJf.

……………………………………………………………………………………………………………

02. 27 I Jtpj vz;zhf khw;Wf.

……………………………………………………………………………………………………………

03. 5𝑥 2 + 10𝑥 I fhuzpg;gLj;Jf.

……………………………………………………………………………………………………………

04. −3𝑥 −2 I Neu;Rl;bahf jUf.

……………………………………………………………………………………………………………

05. 𝑥 ,d; ngWkhdj;ijf; fhz;f.

300
……………………………………………………… 𝑥 2𝑥
06. &gh 500 ,wF nfhs;tdT nra;j nghUnshd;W 20% ,yhgj;Jld; tpw;fg;gl;lhy; tpw;w
tpiyiaf; fhz;f.

……………………………………………………………………………………………………………

07. 42 − 5𝑛 vz;Nfhyj;jpd; 2 vj;jidahtJ cWg;G MFk;?

……………………………………………………………………………………………………………

08. { 2 , 3 , 5 } vd;w njhilapYs;s njhilg;gpupTfspd; vz;zpf;if ahJ?

……………………………………………………………………………………………………………
𝑥
09. jug;gl;l cUtpy; 𝑥 ,d; ngWkhdj;ijf; fhz;f.

…………………………………………………………
700
10. 14𝑐𝑚 MiuAila tl;lj;jpd; gupjpiaf; fhz;f.

……………………………………………………………………………………………………………

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 29 ~
 1 2 4
11. RUf;Ff. ( 4 + 5 ) ,d;
13

……………………………………………………………………………………………………………

12. 𝑣 = 𝑢 + 𝑎𝑡 ,y; 𝑎 I vOtha; khw;wk; nra;f.

……………………………………………………………………………………………………………

13. fhuzpg;gLj;Jf. 3𝑥 2 − 27

……………………………………………………………………………………………………………

14. jug;gl;l cUtpy; (𝑃 ∩ 𝑄′ ) I epow;Wf.

P Q
………………………………………………………

4𝑥
15. jPu;f;f. −3= 1
3

……………………………………………………………………………………………………………

16. xU xOq;fhd gy;Nfhzp xd;wpd; mff;Nfhzk; 1350 vdpd;>

(i) Gwf;Nfhzk; xd;wpd; gUkd; ahJ? …………………………………..

(ii) gf;fq;fspd; vz;zpf;ifia fhz;f. …………………………………..

17. 3𝑦 − 4𝑥 = 6 vDk; Neu;Nfhl;bd; gbj;jpwd; (m) ntl;Lj;Jz;L (c) vd;gtw;iwf; fhz;f.

……………………………………………………………………………………………………………

1 1
18. 𝑎 = −2 > 𝑏 = vdpd; 𝑎 + 8𝑏 ,d; ngWkhdj;ijf; fhz;f.
4 2

……………………………………………………………………………………………………………

(𝑎−𝑏) (2𝑎+𝑏)
19. − RUf;Ff.
(𝑎+𝑏) (𝑎+𝑏)

……………………………………………………………………………………………………………

20. jug;gl;l cUtpy; 𝑥 ,d; ngWkhdj;ijf; fhz;f.

5𝑐𝑚 13𝑐𝑚
………………………………………………………

21. 𝑥
(2 , −3) >(1 , −6) Mfpa Gs;spfis ,izf;Fk; Nfhl;bd; rkd;ghL ahJ?

……………………………………………………………………………………………………………

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 30 ~
22. 1 – 6 tiu ,yf;fkplg;gl;l Nfhlhj rJuKfp jhaf;fl;il xd;iw cUl;Lk;NghJ Kjd;ik
vz; fpilg;gjw;fhd epfo;jfitf; fhz;f.

……………………………………………………………………………………………………………

23. fhuzpg;gLj;Jf. 𝑎2 − 3𝑎 − 18

……………………………………………………………………………………………………………

24. jug;gl;l Kf;Nfhzp PQR ,d; P

(i) ∆PQR ,d; gug;gsitf; fhz;f.

T
20𝑐𝑚
(ii) PR ,d; ePsk; ahJ?
Q 12𝑐𝑚 S R

25. PQ , PR Mfpa Neu;NfhLfspd; rk J}uj;jpYk;> P , R ,ypUe;J rkJ}uj;jpy; cs;s Gs;sp A

,d; xOf;fpid gUk;gbg;glk; %yk; fhl;Lf.

P R

gFjp – II
vitNaDk; 6 tpdhf;fSf;F tpil vOJf.
01. (a) vz;njhlup xd;wpd; nghJ cWg;G 50 – 3n vdpd;>

(i) ,t;ntz; njhlupapd; Kjy; 4 cWg;Gf;fisAk; vOJf.

……………………………………………………………………………………………………

(ii) 20 Mk; cWg;igf; fhz;f.

……………………………………………………………………………………………………

(iii) (-55) ,j;njhlupd; vj;jidahk; cWg;ghFk;?

……………………………………………………………………………………………………

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 31 ~
 (b) jug;gl;l cUtpy; a , b , c vd;gtw;iwf; fhz;f.

𝑎 =……………….
400
𝑏 =………………
𝑐
600 𝑏 …
𝑎 𝑐 =………………
…..

(c) ngl;b xd;wpy; rkmsTila 5 nts;is epw G+f;fSk;> 3 rptg;G epw G+f;fSk;> 4 kQ;rs;
epw G+f;fSk; cs;sd. mg;uj; vOkhwhf xU G+it vLf;fpd;whd;.
(i) fpilf;Fk; NgWfspd; khjpupntspia vOJf.

……………………………………………………………………………………………………

(ii) vOkhwhf xU G+it vLj;jNghJ kQ;rs; epw G+ fpilg;gjw;fhd epfo;jfitf; fhz;f.

……………………………………………………………………………………………………

(iii) vOkhwhf xU G+it vLj;jNghJ rptg;G my;yJ nts;is epwkhf

,Ug;gjw;fhd epfo;jfitf; fhz;f.

……………………………………………………………………………………………………

5𝑥−3 3𝑥−4
03. (a) RUf;Ff. − (b) jPu;f;f. 5𝑎 − 2𝑏 = 19
𝑎−𝑏 𝑎−𝑏
3𝑎 + 2𝑏 = 21

(c) jPu;f;f. 𝑥 2 − 12𝑥 − 28

15𝑎2 𝑏2
(d) RUf;fp tpilia Neu;r;Rl;bahf jUf.
3𝑎−5 𝑏0

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 32 ~
04. (a) tpahghup xUtd; ifalf;f njhiyNgrp xd;iw 20% ,yhgk; itj;J tpiy Fwpf;fpd;whd;.
cld; fhR tpw;gidapd; NghJ Fwpj;j tpiyapy; 10% fopT nfhLj;J &gh 12 960 ,w;F
tpw;gid nra;fpd;whd;.
(i) ifalf;f njhiyNgrpf;F Fwpj;j tpiyiaf; fhz;f.

……………………………………………………………………………………………………

(ii) ifalf;f njhiyNgrpia tpahghup thq;fpa tpiyiaf; fhz;f.

……………………………………………………………………………………………………

(iii) tpahghup mile;j ,yhgr; rjtPjj;ijf; fhz;f.

……………………………………………………………………………………………………

04. 𝑦 = 1 − 2𝑥 vDk; tiuig tiutjw;F fPNo cs;s ml;l;tizia G+uzg;gLj;Jf.

𝑥 −2 −1 0 1
𝑦 5 1 −1
(i) Neu;Nfhl;il tiuf.

(ii) ,e;Neu;Nfhl;Lf;F rkhe;jukhfTk; (0,2) vDk; Gs;spapD}lhfTk; nry;Yk;

Neu;Nfhl;bd; rkd;ghl;ilf; fhz;f.

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 33 ~
05. (i) ̂ C = 900 cila Kf;Nfhzp ABC I mikf;f.
𝐴𝐵 = 6𝑐𝑚 , 𝐴𝐶 = 5𝑐𝑚 , BA
(ii) Gs;sp C ,ypUe;J gf;fk; AB ,w;F nrq;Fj;J CD I tiuf.

(iii) AC vDk; Gs;spf;F rkJ}uj;jpYk; gf;fk; AC ,d; kPJk; mikAk; Gs;spia D vdg;
ngaupLf.
(iv) D I ikakhfTk; DC I MiuahfTk; nfhz;l tl;lj;ij tiuf.
(v) DC I mse;J vOJf.

06. (a) ∈ = { 1 – 12 tiuahd epiw vz;fs; }

𝑃 = { 12 ,Yk; Fiwe;j tiuahd xw;iw vz;fs; }

𝑄 = { 12 ,d; fhuzpfs; }

(i) NkNy jug;gl;l njhilfSf;fhd %yfq;fis vOJf.

∈ =…………………………………………………………………..

𝑃 =…………………………………………………………………..

𝑄 = …………………………………………………………………..

(ii) NkNy jug;gl;l njhilfSf;fhd nghUj;jkhd ntd;cUtpy; fhl;Lf.

(iii) 𝑃 ∩ 𝑄′ ,d; %yfq;fis fhz;f.

……………………………………………………………………………………………………

(iv) ∩ (𝑃 ∪ 𝑄) ,d; %yfq;fis fhz;f.

……………………………………………………………………………………………………

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 34 ~
 (v) njhil Q ,w;F vj;jid njhilg;gpupTfs; cz;L?

…………………………………………………………………………………………………

(b) fdTU tbt ghj;jpuk; xd;wpd; ePsk; 2.5m mfyk; 2m cauk; 1m MFk;.

(i) fdTUtpd; fdtsit 𝑚3 ,y; fhz;f.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

(ii) fdTUtpd; nfhs;ssit 𝑙 ,y; fhz;f.

……………………………………………………………………………………………………

07. juk; 9 khztu;fs; fzpjg;ghlj;jpy; ngw;w Gs;spfs; gw;wpa jftypd; tpguk; fhl;lg;gl;Ls;sJ.
tFg;ghapil khztu; eLg;ngWkhdk; 𝒇𝒙
vz;zpf;if (𝒙)
10 – 20 3

20 – 30 5

30 – 40 7

40 – 50 4

50 – 60 6

60 – 70 5

(i) Mfhu tFg;G ahJ?

……………………………………………………………………………………………………

(ii) eLg;ngWkhd epuiy G+uzg;gLj;Jf.

(iii) 𝑓𝑥 epuiy G+uzg;gLj;Jf.

(iv) xU khztd; ngw;w Gs;spapd; ,iliaf; fhz;f.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK

fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 35 ~
Grade-09 Unit Collection Mr. A.K. Abdul Haleem Maths Sonic AK
fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 36 ~