Combined Maths Manoj Solangaarachchi - B.Sc.

COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBIN
COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBIN
COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBIN

wOHhk fmdÿ iy;sl m;% úNd.h (Wiia fm<) – 2024

General Certificate of Education (Adv. Level) Examination – 2024
COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBIN
COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBIN
COMBINED
ixhqla; .Ks;h I
MATHEMATICS MANOJ SOLANGAARACHCHI COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBIN
COMBINED
COMBINED
COMBINED
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MATHEMATICS
MATHEMATICS
MANOJ
MANOJ
SOLANGAARACHCHI
SOLANGAARACHCHI
Combined Mathematics I
MATHEMATICS
MATHEMATICS
MANOJ
MANOJ
SOLANGAARACHCHI
SOLANGAARACHCHI
COMBINED
COMBINED
COMBINED
COMBINED
MATHEMATICS
MATHEMATICS
MATHEMATICS
MATHEMATICS
MANOJ
MANOJ
MANOJ
MANOJ
SOLANGAARACHCHI
SOLANGAARACHCHI
SOLANGAARACHCHI
SOLANGAARACHCHI
COMBINED
COMBINED
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COMBINED
MATHEMATICS
MATHEMATICS
MATHEMATICS
MATHEMATICS
MANOJ
MANOJ
MANOJ
MANOJ
06
SOLANGAARACHCHI
SOLANGAARACHCHI
SOLANGAARACHCHI
SOLANGAARACHCHI
COMBIN
COMBIN
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COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBINED MATHEMATICS MANOJ SOLANGAARACHCHI COMBIN

A fldgi

(01) n hkq Ok ksÅ,hla kï" 25n + 1 – 24n + 5735 hk m%ldYh (24)2 ka

fnfok nj .Ks; wNHqyk uQ,O¾uh uÕska fmkajkak'
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(02) (2 + 3)4 ys ksÅ, fldgi fidhkak'

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(03) x2 – ax + b = 0 ys uQ, ,  kï"

1 yd 1 uQ, jk j¾.
( – 1) ( – 1)
iólrKh fidhkak' tys uQ, iumd; jkafka a2 – 4b = 0 kï njo Tmamq
lrkak'
.....................................................................................................................................................

(04) 5  2 úi|kak'
5x – 1 2x + 1
.....................................................................................................................................................

(05) lim 3 – 2 sin x

x /3 ( – 3x)
.....................................................................................................................................................

(06) y = sin-1 x kï" (1 – x2) d2y – 3x dy – y = 0 nj fmkajkak'

1 – x2 dx2 dx
3
x = 0 § d y w.hkak'
x = 0 § dx3
.....................................................................................................................................................

/2

(07)
0
 1 – sin  d fidhkak'
.....................................................................................................................................................
(08) sin-1 6x + sin-1 63x = –  iólrKh úi|d x i|yd tla w.hla muKla
2

- 1 - | Combined Maths | Manoj Solangaarachchi - B.Sc. Model Paper – 06

 we;s nj fmkajkak'
.....................................................................................................................................................

(09) (ae, 0) yd (– ae, 0) kï ksh; ,CIH foll isg thg we;s ÿrj, tl;=j
2a jk mßÈ ,CIHhla .uka lrhs' tu ,CIHfha m:fha iólrKh
x2 + y2 = 1 nj fmkajkak'
a + a (1 – e )
2 2 2

.....................................................................................................................................................

(10) iqmqreÿ wxlkfka ABC  i|yd c + b tan A = tan A + B nj

c–b 2 2
fmkajkak'

.....................................................................................................................................................
B fldgi

(11) (a) a ;d;a;aúl kï" x2 + 2 (a – 3) x + 2a – 12 = 0 iólrKfha uQ,

;d;a;aúl nj fmkajkak' fuu iólrKfha uQ,j, wka;rh 6 kï a
g ;sìh yels w.hka fidhkak'

(13) (b) f(x)  x4 + ax3 + bx2 – 3x – 2 nyq mofhys (x – 2) iy (x + 1) idOl

fõ' a iy b fidhd b;sß idOl fidhkak' f(x)  0 jk x w.hka
fidhkak'

(c) x2 + 2px + q2 = 0 iólrKfhys uQ, 1, 1 o x2 + 2mx + n2 = 0

iólrKfha uQ, 2, 2 o fõ'
(i) 1 + 2 = 1 + 2 kï p2 + n2 = q2 + m2 nj;a"
(ii) 12 + 12 = 0 kï q2n2 = p2n2 + q2m2 nj;a" Tmamq lrkak'
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(12) (a) 3 + 4 + 5 + ……
1 2 3
2 .2.1 2 .3.2 2 .4.3
fYa%Ksfha r jk moh fidhkak'

th Ur kï" Ur = f(r) – f(r + 1) jk mßÈ Ys%;hla fiùfuka"

n
 Ur = 1 – 1 nj fmkajkak'.
r=1 n
2 (n + 1)


S =  Ur kï" fYa%Ksh wNsidÍ nj fmkajd"
r=0

S w.h fidhkak'

- 2 - | Combined Maths | Manoj Solangaarachchi - B.Sc. Model Paper – 06

 (b) y = | x2 – 8 | ys o, igykla w¢kak'
tkhska" | x2 – 8 |  2x wiudk;dj ;Dma; lrk x ys w.h fidhkak'
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(13) (a) lim 1 + 2 + x – 3 fidhkak'

x 2 x–2

(15) (b) y = (x + 1 + x2)n kï 1 + x2 dy = ny nj fmkajkak'

dx

(15) (b) ;jo" (1 + x2) d2y + x dy = n2y nj fmkajd x = 0 § d3y fidhkak'

(15) (b) ;jo" (1 + x2) dx2 dx dx3

(15) (c) wrh r jQ jD;a;hl wka;¾.; l< yels RcqfldaKdY%fha j¾.M,h

Wmßu jkafka th iup;=ri%hla jQ úg nj fmkajkak' tu j¾.M,fha
jákdlu r j,ska fidhkak'

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(14) (a) iqÿiq wdfoaYhla Wmfhda.S lr .ksñka

1
 (x 4/3
1
2/3
+x )
dx w.hkak'

 
(15) (b) I =
0
 e –2x cos x dx yd J =
0
 e –2x sin x dx hehs .ksuq'

(15) (b) fldgia jYfhka wkql,k l%uh Wmfhda.S lr .ksñka I = 2J yd

J = 1 + e –2 – 2I nj fmkajkak' tkhska I yd J ys w.hka ,nd .kak'

(15) (c)
1
 x2 – 5x
(x – 1)(x + 1) 2
dx fidhkak'

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(15) ax + by + c = 0, ax + by + c = 0 f¾Ld fþokh jk ,CIH ;=<ska hk ir,

f¾Ldjl idOdrK iólrKh fidhkak'

- 3 - | Combined Maths | Manoj Solangaarachchi - B.Sc. Model Paper – 06

 ABC  hl BC, CA, AB mdoj, iólrK mss<sfj,ska 3x – y + 5 = 0,
2x + 3y – 1 = 0, x + 2y – 3 = 0 o fõ' A ;=<ska BC g ,ïnj we;s f¾Ldj B
;=<ska CA g iudka;rj we¢ f¾Ldj D ys§ lmhs' D yd uQ, ,CIHh hd
lrk f¾Ldfõ iólrKh fidhkak'

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(16) (a) sin ( cos ) = cos ( sin ) kï" cos    = 1 nj idOkh

4 22
lrkak'

(16) (b) , , ,  hkq lsisÿ follg iudk gexck fkdue;a;djQ o

tan  +  = 3 tan 3 iólrKfha uQ, jQ o fldaK kï"
4
túg" tan  + tan  + tan  + tan  = 0 nj fmkajkak'

  
(15) (c) ABC ;s%fldaKfha OA, OB, OC f¾Ld we| ;sfnkafka OAB, OBC, OCA
fldaK tl tlla  g iudk jk mßÈh'
cot  = cot A + cot B + cot C,
cosec2  = cosec2 A + cosec2 B + cosec2 C nj idOkh lrkak'



Manoj Solangaarachchi
(B. Sc.)

- 4 - | Combined Maths | Manoj Solangaarachchi - B.Sc. Model Paper – 06