V‚U;hVfmUd;gVfkUdjVys;s Ug - eduLanka Online … · · 2011-09-2818'lg2=x olg3=y...
Transcript of V‚U;hVfmUd;gVfkUdjVys;s Ug - eduLanka Online … · · 2011-09-2818'lg2=x olg3=y...
18' o o úg ljr f,i m%ldY l, yelso@lg 2 = x lg 3 = y lg 12
¸ ¸¸ ¸¸¸ ¸¹ ¹
¸ ¸¸ ¸¸¸ ¸¹ ¹
¸ ¸¸ ¸¸¸ ¸¹ ¹
¸ ¸¸ ¸¸¸ ¸¹ ¹
¸ ¸¸ ¸¸¸ ¸¹ ¹
¸ ¸¸ ¸¸¸ ¸¹ ¹
¸ ¸¸ ¸¸¸ ¸¹ ¹
¸ ¸¸
¸¸¸ ¸¹
¹
' ' ' ' '
19' tla;rd >kldN yev;s fmÜáhl Odß;dj 231 fõ' fuu fmÜáfha È." m<," Wi 1
ne.ska jeä l< fyd;a Odß;dkh jeä ùu fldmuKo@
' 78 ' 153 ' 231 ' 384 ' 400
20' È. 20 jQ lïì lene,a,la folg lmd iup;=ri% folla iod .kakd ,È' fuu iup;=ri%
fofla j¾.M,h 25 kï" lemQ lïì len,s fofla È. fidhkak'
' 18" 10 ' 8"20 ' 12" 16 ' 9" 25 ' 13" 15
21' k.r fol w;r ÿr fõ' k.rfhka iuka mdmeÈhl msg;aj k.rhg
meñfka' k.rfhka iuka msg;ajkjd;a iu.u k.rfhka lu,a h;=re meÈhl ke.S
iuka yuq jQ jydu kej; fj; meñk wdmiq yeÍ kej; iuka yuq ùug hhs' Tyq yuq jQ
jydu kej; wmiq yeÍ fj; meñfka' fuu l%shdj wlkavj lu,a isÿ lf,a kï iuka
fj; meñfkk úg lu,a .uka lr we;s ÿr jkqfha "
mdmeÈfha fõ.h 20 jk w;r h;=re meÈfha fõ.h fõ'
' 40 ' 70 ' 80 ' 100 ' 140
22' tla;rd iúÈ nyq wi%hl wNHka;r fldaKhl w.h 150 fõ' ty mdo .Kk lSho@
' 3 ' 6 ' 9 ' 12 ' 15
23' uu ,Õ we;s uqo,g jvd u,a,S ,Õ we;s uqo, fo.=khlg jvd re' 7 la jeäh' wm
fofokd ,Õ we;s uqof,a fo.=kh 314 la fõ kï uu yd u,a,S ,Õ we;s uqo,a ms<sfj,ska re"
' 50" 107 ' 107" 50 ' 214" 100 ' 100" 214 ' 114" 200
24' iu mdo ;%sfldaKhl mdohl È. fi( ñ( 10 ls' ;s%fldaKfha j¾.:,h j¾. fi( ñ( j,ska
lSAho@'
' 30 ' 25 ' 25 3 ' 60 ' 100
25' my; ±fjk tAjdhska l=,lhla jkqfha"
' Tn mka;sfha ,iaik YsIHdjka ' .fï uy; ñksiaiq
' mka;sfha fi(ó( 120 g jvd Wi <uhs ' mka;sfha oCI isiqka
' fyd| <uhs
2 x y 2y + x 2x + y x + y x y
m m
m
2 2
3
3
m
m
A, B 40 km A B
A B
B
B B
km
km h 70 km h
2
-1 -1
0
Ö
VUVUVUVU.‚;h fmd;g fkdj ys;g.‚;h fmd;g fkdj ys;g.‚;h fmd;g fkdj ys;g
.‚;h wñysßfkdj".‚;h iqkaorh"olskakg tA iqkaor;ajh"tA iqkaor;ajh ;=,skaÔú;h Èkkakgmq¿jk'''"
ksjerÈ uÕ fmkaùu"W;aiyh yd Wkkaÿj;=,ska''''
.‚;fha ixl,am"
.‚;fha udj; -±k .kak" ±l .kakW;aiyjka;Tn tkak'''''
iqkaor jQ .‚;fhawiajekak ,efnkqksh;h''''
.‚;h wñysßfkdj".‚;h iqkaorh"olskakg tA iqkaor;ajh"tA iqkaor;ajh ;=,skaÔú;h Èkkakgmq¿jk'''"
ksjerÈ uÕ fmkaùu"W;aiyh yd Wkkaÿj;=,ska''''
.‚;fha ixl,am"
.‚;fha udj; -±k .kak" ±l .kakW;aiyjka;Tn tkak'''''
iqkaor jQ .‚;fhawiajekak ,efnkqksh;h''''
.‚;h wñysßfkdj".‚;h iqkaorh"olskakg tA iqkaor;ajh"tA iqkaor;ajh ;=,skaÔú;h Èkkakgmq¿jk'''"
ksjerÈ uÕ fmkaùu"W;aiyh yd Wkkaÿj;=,ska''''
.‚;fha ixl,am"
.‚;fha udj; -±k .kak" ±l .kakW;aiyjka;Tn tkak'''''
iqkaor jQ .‚;fhawiajekak ,efnkqksh;h''''
BSc. (Physical - Kelaniya)BSc. (Physical - Kelaniya)(Pure Mathematics / Statistics & Computer Science / Chemistry)(Pure Mathematics / Statistics & Computer Science / Chemistry)
TeL: 071-6341436 / 078-6050650 / E-Mail: [email protected]: 071-6341436 / 078-6050650 / E-Mail: [email protected]
BSc. (Physical - Kelaniya)(Pure Mathematics / Statistics & Computer Science / Chemistry)
TeL: 071-6341436 / 078-6050650 / E-Mail: [email protected]
08'olajd we;s iup;=ri%fha me;a;l È. 7 kï
jD;a;fha w÷re lr we;s fldgfia j¾.M,h lSho@
09' tla;rd Rcq fldaKS ;%sfldaKhl fldaKfha w.h } 5$12 fõ' fuys
ys w.h jkqfha"
10' j¾. iólrKfha uQ, jkqfha"
cm
x + 4x = 0
cm
tan
2
¸' 12 ¸¸' 28 ¸¸¸' 49 ¸¹' 75
¹' 77
¸ 12$5 ¸¸ 12$13 ¸¸¸ 13$12 ¸¹ 13$5 ¹ 5$13
¸ -4 fyda 4 ¸¸ 4 fyda 0 ¸¸¸ -4 fyda 0 ¸¹ 4 fyda 4 ¹ 4 mu‚
¸ 0 ¸¸ 1 ¸¸¸ 2 ¸¹ 3 ¹ 4
¸ 17'5 ¸¸ 35 ¸¸¸ 70
¸¹ 105 ¹ lsj fkdyel
¸ 2 ¸¸ 3 ¸¸¸ 5 ¸¹ 6 ¹ 12
¸ 3 ¸¸ 5 ¸¸¸ 8 ¸¹ 13 ¹ 20
¸ 3$2" 0 ¸¸ 2$3" 0 ¸¸¸ 3 2" 1 ¸¹ 3$2 ¹ 0" 2$3
¸ 9 ¸¸ 10 ¸¸¸ 15 ¸¹ ¹ 40
¸ f.a Wml=,lhls ¸¸ f.a Wml=,lhls
¸¸¸ f.a wjhjhls ¸¹ f.a wjhjhls ¹ lsis;a fkdfõ'
q tan tan
A B = , n(A) = 8, n(B) = 5 n(A B)
A B B C
A C
"a B"
a, B B , a
a, B B, a
q q
Ç f È
Î
' ' ' ' '
' ' ' ' '
11' kï ys w.h fidhkak'
' ' ' ' '
12' ys w.h wxYl lSho@
' ' '
' '
13' fofla ;=k kHdihla 2 ka .=K l< úg ,efnk kHdifha wjhj ixLHdj lSho@
' ' ' ' '
14' kï lSho@
' ' ' ' '
15' ir< f¾Ldfõ wkql%ukh yd wka;#Lkavh ms,sfj<ska olajd we;af;a@
' ' ' $ ' 0" '
16' k.rfha isg k.rhg hdug ud¾. 5 la fõ' k.rfha isg k.rhg hdug ud¾. 4
ls' kr.fha isg k.rhg mqoa.,fhl=g wdldr lShlg .uka l< yelso@
' ' ' ' 20 '
17' fuys f;areu l=,l weiqfrka m%ldY l, úg'
' '
' ' '
2
log x = 0 x
x
2y = 3x
3
350
8 miq.sh Èkl ksu,af.a jegqm wu;r §ukd iuÕ re' 425 ls' ksu,af.a Èkl jegqm wu;r
§ukd j,g jvd re' 75 lska jeäh'
01' ksu,af.a uQ,sl jegqm lSho@
' re' 75 ' re' 150 ' re' 175 ' re 250 ' re 275
02' ksu,a ,enQ wu;r §ukdj lSho@
¸ ¸¸ ¸¸¸ ¸¹ ¹
¸' re' 75 ¸¸' re' 150 ¸¸¸' re' 175 ¸¹' re 250 ¹' re 275
¸' re' 500 ¸¸' re' 1000 ¸¸¸' re' 2000 ¸¹' re 3000 ¹' re 4000
¸' 5"5 ¸¸' 6"5 ¸¸¸' 12"10 ¸¹' 10"12 ¹' 8"4
¸' 1$3 ¸¸' 3 ¸¸¸' 2$3 ¸¹' 3$2 ¹' 2
¸' 20 ¸¸' 40 ¸¸¸' 60 ¸¹' 80 ¹' 100
¸' 4 ¸¸' 8 ¸¸¸' 10
¸¹' 12 ¹' 20
03' msfhla ;u mq;=ka fofokd w;r re' 6000 la fnod ÿkafka f;jeks mq;dg re' 100 ,efnk
úg fojeks mq;dg re' 200la o" m<uq jekakdg re' 300 la o jk mßÈ fõ' fojekakdg
,enqKq uqo, fldmuko@
04' lvhl lsß melÜ 400g yd 500g melÜ f,i we;' lvfha lsß melÜ 11 l lsß 5 úks
kï 400g yd 500g melÜ .Kk ms<sfj,ska olajd we;af;a"
05' tAldldrj .,k .Õl by,g fndaÜgqjlg ls(ó( 2l ÿrla hdug meh 03la o tu ÿr kej;
my, tAug meh 1 la o jeh fõ' .Õ .,k fõ.h j,ska fidhkak'
06' tlu ÈYdjg .uka lrk ldrhla g%la r:hla Wfoa 8'00 g biair lrhs' ldrfha fõ.h
60 o g%la r:fha fõ.h 40 o kï Wfoa 10'00 jk úg jdyk fol fldmuk
ÿr mr;rhlska msysghso@
07' olajd we;s f;dr;=re wkqj iudka;rdi%fha ±lafjk
ys È. jkqfha "
kg
km h
km h km h
cm
-1
-1 -1
xx 8cm
10cm
10cm
9" 10" 11".‚;his;kak .Ks;h - 01 ld,h úkdä 50
ieliqu( wfia, ksYaYxlBSc. (Maths-Kelaniya)
.e,fmk ms<s;=r f;darkak'
wñysß jQ .‚;fha iqkaor;ajh" Wkkaÿfjka olskak''''' tkak - .‚;h iqkaorhs 1 .‚;h lKavdhï yd ;ks mka;s i|yd úuiSï 071-63 414 36 $ 078-60 50 650
fkdñf,
a id(fm, m%ia;dr fm
d;lr.ekSug (
fj; msúfi
kak'
dow
nlo
rd/o
-lev
el/m
athem
atic
s/m
aths-
gra
ph-b
ook
htt
p:/
/ww
w.e
dula
nka.
lkht t
p: /
/ ww
w. e
dul a
nka .
l k