ixhqla; .Ks;h ixhqla; .Ks;h ixhqla; .Ks;h ixhqla; .Ks;h ixhqla; .Ks;h ixhqla; .Ks;h ixhqla; .

Ks;h
Combined Mathematics Combined Mathematics Combined Mathematics Combined Mathematics Combined Mathematics
ixhqla; .Ks;h ixhqla; .Ks;h ixhqla; .Ks;h ixhqla; .Ks;h ixhqla; .Ks;h ixhqla; .Ks;h ixhqla; .Ks;h
Combined Mathematics Combined Mathematics Combined Mathematics Combined Mathematics Combined Mathematics

wOHhk fmdÿ iy;sl m;% (Wiia fm<) úNd.h" 2021

General Certificate of Education (Adv. Level) Examination 2021
General Certificate of Education (Adv. Level) Examination 2021
13
Paper Class
ixhqla; .Ks;h ÿIHka; uynÿf.a 10 S

A fldgi ld,h meh 3 hs

m%Yak ish,a,gu ms<s;=re imhkak'

1. 2x – 1 = –
iólrKh x i|yd úi|kak'

2.  wiudk;djh úi|kak'

3. A=[ ] úg ish¿ Ok ksÅ,uh n i|yd" An = [ ] nj .Ks; wNHqykfhka

fmkajkak'

4. 3232, 3 ka fnÿ úg fYaIh fidhkak.

5. y = sin–1 2x, x úIhfhka wjl,kh lrkak.

𝑑𝑥
6. fidhkak.
𝑥2 + 𝑥2 +2 𝑥2 +

7. uQ, ,laIHfha isg x2 + y2 – 6x – 6y + 9 = 0 jD;a;hg we|s iam¾Yl foflys iólrK

fidhkak.

8. ABC ;%sfldaKfha, A (2, – 3), B (– 2, 1) jk w;r tys flakaølh 2x + 3y = 1 ir,

f¾Ldj u; fõ. C ,laIHfha m:h fidhkak.

9. y2 = 4x mrdj,h u; jQ ,laIHhl § thg w|sk ,o iam¾Ylh (5, – 6) ,laIHh yryd

hhs. iaam¾Y ,laIHh fidhkak.

10. ;%sfldaKhl mdo w;r wkqmd;h 1 : √ : 2 fõ' tu ;%sfldaKfha fldaK w;r wkqmd;h
ms<sfj,ska 1 : 2 : 3 nj fmkajkak.
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 B fldgi

01. (a) a1x2 + 2b1x + c1 = 0 iy a2x2 + 2b2x + c2 = 0 j¾.c iólrKj,g fmdÿ

uQ,hla ;sfí.
[ b12 – a1c1 ] x2 + [ 2b1b2 – a1c2 – a2c1 ] x + [ b22 – a2c2 ] = 0 j¾.c
iólrKhg iudk uQ, mj;sk nj fmkajkak' (a1 yd a2 ksYaY=kH ;d;a;aúl
ixLHd fõ. j¾.c iólrK neúka a1  0" a2  0)

(b) f(x) hkq x ys y;r jk n,fha nyqmohls' f(0) = 12 fõ' x – 2 hkq f(x) ys
fojrla mqkrdj¾:k jk idOlhls' f(x) hkak x2 + 1 ka fn¥ úg fYaIh 6 –
8x fõ' f(x) ks¾Kh lrkak'

(c) (i) ys Nskak Nd. fidhkak'

(c) (ii) tkhska" | | ys Nskak Nd. wfmdaykh lrkak'

02. (a) f(x) = x + | x | – 2x | x | + 3 fõ' f(x)  11 ys úi÷u fidhkak'

(b) [ ]+[ ]+[ ]  ab + bc + ac nj fmkajkak'

fuys a, b, c hkq Ok ;d;a;aúl ixLHd fõ'

(c) = nj idOkh lrkak'

fuys a yd b hkq 1 g wiudk Ok ;d;a;aúl ixLHd fõ'

+ + = 2 nj wfmdaykh lrkak'

fuys x yd y hkq 1 g jeä ;d;a;aúl ixLHd fõ'

(d) Un = 2 cos n fõ' fuys n hkq Ok ksÅ,hls' Un + 1 = U1Un – Un – 1 nj

fmkajkak'

U7 = –7 + 14 – 7U1 nj o fmkajkak'

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03. (a) ish¿ Ok ksÅ,uh n i|yd" + + – hkq ksÅ,hla nj .Ks;

wNHqykh u.ska idOkh lrkak'

(b) (i) n hkq Ok ksÅ,hla úg" 3 + 33 + 333 + 3333 + ……… ys uq,a mo n ys

ftlHh (10n – 1) – nj fmkajkak'

(ii) + + + …… n ys wdrïNl mo n ys tl;=j fidhkak'

(c) (i) Z= + yd Re(z) = Im(z) fõ'  fidhkak'

(ii) Z1 = 2 + i, Z2 = – 2 + 4i fõ' = + jk úg Z j, w.h a + ib

wdldrfhka m%ldY lr tys udmdxlh yd úia;drh fidhkak'

(d) (i) = a + ib fõ' a2 + b2 = 4a – 3 nj fmkajkak'

(ii) [ ] hkq ;d;a;aúl ixLHdjla nj fmkajkak'

(e) | Z – 1 | = 2 | Z + 1 | iólrKh ;Dma; lrk Z ksrEmKh lrk ,CIHhkays

m:h jD;a;hla nj fmkajkak' tys wrh yd flakaøh fidhkak'

04. (a) iSudj w.hkak'

[ ]
(i)

(ii) [ ]

[ ]
(iii)

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 (b) y = o" y(r) hk o fõ kï" [1 + x2] y(3) + 6xy(2) + 6y(1) = ex nj
fmkajkak'

.Ks; wNHqykfhka fyda wka l%uhlska fyda r  3 i|yd

(1 + x2) y(r) + 2rxy(r – 1) + r ( r – 1)y(r – 2) = ex nj idOkh lrkak'

(c) y= m%ia;drfha o< igykla w|skak'

𝑑𝑥
05. (a) t = tan wdfoaYh Ndú;fhka = nj fmkajkak'
+ s n𝑥

2 sin x =  (1 + sin x) +  jk mßÈ ,  ksh;hka fidhkak'

c s𝑥 + 2s n𝑥
tkhska" dx w.hkak'
+ s n𝑥

𝑥𝑛
(b) ish¿ Ok ksÅ,uh n i|yd 𝑥 𝑛 𝑑𝑥 = + C [ C – ksh;hla ] nj
𝑛+
.Ks;

wNHqykh u.ska idOkh lrkak' fuys C hkq wNsu; ksh;hls'

(c) = + fõ'

tkhska" = + + + nj fmkajkak'

by; m%;sM,h Ndú;fhka Nskak Nd.j,g fjka lrkak'

tuÕska" w.hkak'

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06. (a) OA, OB ir, f¾Ldj, iólrK ms<sfj<ska x + 2y = 0 yd x – 2y = 0 fjhs'
P (, ) ,CIHh Tiafia OA g iudka;rj w|sk ,o f¾Ldjla M ys§ OB g
yuqfjhs' P isg OB g iudka;rj w|sk ,o ;j;a f¾Ldjla L ys§ OA g
yuqfjhs' L yd M yryd ms<sfj<ska OA g yd OB g ,ïNlj w|ska ,o f¾Ld Q

ys§ fþokh fõ' Q ys LKavdxl [   ] nj Tmamq lrkak'

P j,ska i,l=Kq flfrkafka x wCIhg 45 lska wdk; ir, f¾Ldjls' Q

j,ska o ir, f¾Ldjla i,l=Kq flfrk nj;a fuu f¾Ldj x wCIhg tan-1 4
lska wdk; nj;a fmkajkak'

(b) 2x – 3y + 26 = 0 f¾Ldj x2 + y2 – 4x + 6y – 104 = 0 jD;a;hg iam¾Ylhla nj

fmkajkak' iam¾Yl ,CIHh Tiafia we;s úYalïNfha iólrKh fidhkak'

07. (a) cos m%fïhh m%ldY lrkak'

iqmqreÿ wxlkfhka ABC ;s%fldaKhla i|yd + + = +

fõ' ABC hkq RcqfldaŒ ;s%fldaKla nj idOkh lrkak'

(b) + = 1 fõ' + = 1 nj fmkajkak'

(c) tan-1 [ ] + tan-1 [ ] + tan-1 [ ]= fõ'  2 = a2 + b2 + c2 nj fmkajkak'

ÿIHka; uynÿf.a

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