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m% : u jdr mÍCIKh - 2016 First Term Test - 2016 ixhqla; .Ks;h I Combine Maths I
meh 2 hs úkdä 30
12 fY%aKsh Grade 12
Two & half hours
m%Yak 4lg ms
01' (a) O, A, B hkq f¾Åh fkdjk ,CIHh ;=kls' OA a o OB b o fõ' ~
I.
~
a b O kï 0 nj;a 0 nj;a fmkajkak ~
~
~
II. (i) P hkq AB u; AP= n AB jk f,i jq ,CIHhla kï o OP r kï o o n 1 úg ~
r (1 n) a n b nj fmkajkak ~
~
~
(ii) fï khska iudka;ri%hl úlrK tlla wfkl iuÉfPaaokh lrk nj fmkajkak
(b)
O, A, B, C hkq O, A, B ,CIHh tal f¾Åh fkdjk mßos jq m%Nskak ,CIH 4 ls' OA a yd ~
OB b jk úg 50C 2 a 3 b fõ ~
I.
~
~
OD a jk fia D ,CIHh f;dard f.k we;akï DC b jk whqßka yd j, w.h ~
~
fidhkak II.
A,B,C tal f¾Åh nj fmkajkak
III.
C ,CIHh A yd B w;r msysgd we;akï AC= CB = 3: 2 nj fmkajkak
(c)I. II.
a yd b ffoYsl jk úg ( a b). (a b) a 2 b 2 nj fmkajkak ~
~
~
~
~
~
a yd b ffoYsl u.ska iudka;ri%hl úl¾K ksrEmkh fõ' fuu iudka;rdi%fha fldaKhla ~
cos1
~
| a 2 b2 | nj fmkajkak | a b || a b |
02' I. Ügkh isÿk ia:dkhg ÿr;a" m
p,s; iólrK Ndú;fhka
fidhkak
1
ms
II.
.uka lrk E1 iy E2 ÿïßh tkacska follg P kï ix{d mqjrejla tlu ld,hl os miq lrk wjia:dfõ os ms
i.
lr we;s ÿr ii.
E1 iy E2 tkacska Q miq lrk fj,dj iy túg tajdfha m%fõ.
iii.
Q iy S w;r ÿr
iv.
f weiqßka F ys w.h
v.
E1 iy E2 tkacska S ÿïßh fmd
03' I. fYaI m%fïhh m%ldY lr idOkh lrkak II.
P(x) hkq x ys fojk fyda jeä n,hl nyqmo Y%s;hls' th (x-a) (x-b) u.ska fnÿ úg fYaIh A(x-a) + B(x-b) fõ' A yd B ksh; fõ' A yd B ksh; P, a yd b weiqßka fidhkak f(x) = x4-2x2+6 f,i os we;' fYaI m%fïhh Wmfhda.s lr .ksñka f(x) g ( x- ) wdldrfha idOl
III.
fkdue;s nj fmkajkak' fuys hkq ;d;aúl ixLHdjls
f ( x) 2 x4 (3k 4) x3 (2k 2 5k 5) x2 (2k 3 2k 2 3k 6) x 6 ys ( x 2 k ) idOlhla kï
IV.
k fidhkak k ys tla tla w.hg f (x) ys b;sß idOlh o fidhkak
18 x x 2 A f ( x) jk mßos A yd f (x) fidhkak 2 ( x 2)( x 2) ( x 2) ( x 2) 2
V.
f (x) , ( x 2) ys nyqmohla f,i m%ldY lrkak ta khska"
18 x x 2 ( x 2)( x 2) 2
04' I. sec cos sin
II. III.
iïmq¾Kfhkau Nskak Nd.j,g fjka lrkak
kï túg
i.
tan2 sin 2 iy
ii.
cos 2 tan 2
2
nj idOkh lrkak
36o kï" túg sin 3 sin 2 nj fmkajd cos 36o
( 5 1) nj wfmdaykh lrkak 4
.Ks; j.= Ndú; fkdlr sin 2 8 cos4 3 8 ys w.h fidhkak 2
IV.
O C 2 kï
1 sin 2C cos 2C tan C nj fmkajkak 1 sin 2C cos 2C
ta khska tan
ys w.h ,nd .kak
(1 sec x tan x)(1 cos ecx cot x) 2(1 tan x cot x sec x cos ecx) nj Tmamq lrkak
V.
x
05'
8
4
úg fuu m%;sM,h i;Hdmkh lrkak
a,b yd c Ok ixLHd jk úg"
I.
II. a.
log a b
1 nj yd log b a
log a b
log c b nj idOkh lrkak log c a
log16 ( xy)
1 1 log 4 x log 4 y nj fmkajkak 2 2
b. ta khska fyda wka l%uhlska fyda log16 xy
7 2
log 4 x 8 iólrK moaO;sh úi|kak log 4 y
III.
( x1 , y1 ) yd ( x2 , y2 ) ,CIHh fol hd lrk f¾Ldj m:n wkqmd;hg wNHka;rj fnok mx nx1 my2 ny1 ,CIHfha LKavdxlh 2 , nj fmkajkak' mn mn
IV.
ABC ;%sfldaKfha A, B iy C Ys¾Ij, LKavdxlms
3
