46(b) R 15 S P Q 47(a)ml;ltiiz : X -3 -2 -1 0 1 2 3 x2 9 4 1 0 1 4 9 Y=2x2 18 8 2 0 2 8 18 ii) thpir...

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Transcript of 46(b) R 15 S P Q 47(a)ml;ltiiz : X -3 -2 -1 0 1 2 3 x2 9 4 1 0 1 4 9 Y=2x2 18 8 2 0 2 8 18 ii) thpir...

Page 1: 46(b) R 15 S P Q 47(a)ml;ltiiz : X -3 -2 -1 0 1 2 3 x2 9 4 1 0 1 4 9 Y=2x2 18 8 2 0 2 8 18 ii) thpir N[hbfs; : (-3,18) (-2, 8)(-1,2) (0,0) (1, 2) (2, 8) (3, 18)

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Page 2: 46(b) R 15 S P Q 47(a)ml;ltiiz : X -3 -2 -1 0 1 2 3 x2 9 4 1 0 1 4 9 Y=2x2 18 8 2 0 2 8 18 ii) thpir N[hbfs; : (-3,18) (-2, 8)(-1,2) (0,0) (1, 2) (2, 8) (3, 18)

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Page 3: 46(b) R 15 S P Q 47(a)ml;ltiiz : X -3 -2 -1 0 1 2 3 x2 9 4 1 0 1 4 9 Y=2x2 18 8 2 0 2 8 18 ii) thpir N[hbfs; : (-3,18) (-2, 8)(-1,2) (0,0) (1, 2) (2, 8) (3, 18)

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Page 4: 46(b) R 15 S P Q 47(a)ml;ltiiz : X -3 -2 -1 0 1 2 3 x2 9 4 1 0 1 4 9 Y=2x2 18 8 2 0 2 8 18 ii) thpir N[hbfs; : (-3,18) (-2, 8)(-1,2) (0,0) (1, 2) (2, 8) (3, 18)

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Page 5: 46(b) R 15 S P Q 47(a)ml;ltiiz : X -3 -2 -1 0 1 2 3 x2 9 4 1 0 1 4 9 Y=2x2 18 8 2 0 2 8 18 ii) thpir N[hbfs; : (-3,18) (-2, 8)(-1,2) (0,0) (1, 2) (2, 8) (3, 18)

HALF YEARLY EXAMINATION

,DEC/JAN-2012-13

TENTH STD MATHEMATICS gFjp- I xU kjpg;ngz; tpdhf;fs; :

1. m) (2>4) 2. <) AP kw;Wk; GP MFk;

3. M) a/b

4. m) a2+ab+b2 5. <) 31 6. M) -7

7. ,) y=-7 8. <) (2>2) 9. M) 5.74 nrkP 10. ,) 15 nrkP

11. ,)sin𝜽

12. M)25√3kP 13. m) 10nrkP 14. <) 0

15. ,)5/6

gFjp- II ,uz;L kjpg;ngz; tpdhf;fs;:

16. (AUB) = { 4,8,16,20,24 ,28} , (AUB)’ = {12} (A∩B) = {16} , (A∩B)’ = {4,8,12,20,24,28 }

17. R ={(1,1)(2,1)(3,3)(4,3)(5,5)} fzk; x cs;s xt;nthU cWg;gpw;Fk; xNu

XU epoy; R vd;Dk; cwT rhh;ghFk;

18. F1-F2=1 , Fn =Fn-1+Fn-2 , F3=F3-1+F3-2 =F2+F1 = 1+1 =2

F4=F4-1+F4-2= F3+F2= 2+1 = 3

Kjy; ehd;F cWg;Gf;fs; : 1,1,2,3

19. (𝟏−𝒙𝟐)

(𝒙𝟑+𝟏) x

(𝟏−𝒙𝟑)

(𝟏−𝒙𝟐) =

(𝟏−𝒙𝟑)

(𝒙𝟑+𝟏)

20. a 2 + b -1 = 10 3 1 5 2a + -b = 10

3a b 5

2a –b = 10 --------(1)

3a + b = 5 ---------(2) ,

(1)+(2) = 5a =15, a = 3 ,

a –it (1) –y; gpujpapl > b=-4

21. mzp A –d; thpir 2x3 kw;Wk; mzp B –apd; thpir 2x2 . mzpfspd; thpir ntt;Ntwhf ,Ug;gjhy; $l;l ,ayhJ

22. A(-2,-2)B(2,0)C(p,q)D(-2,0) vd;f ,izfuj;jpd; %iytpl;lq;fspd; eLg;Gs;spfs; rkk; .

%tpAC-d; eLg;Gs;sp =%tp BD–d; eLg;Gs;sp

(-2+p)/2 , (-2+q)/2 = ( 2-2)/2 , (0+0)/2

(-2+P)/2 = 0 ; (-2+Q)/2 = 0 -2+p = 0 ; p = 2 -2+q = 0 ; q = 2 vdNt (p,q) = (2,2) 23. PA X PB = PC X PD 8x2 = 4x PD ; PD = 16/4 = 4

24. x = asec𝜽 +btan𝜽 ; y = atan𝜽 +bsec𝜽 X2-y2= (asec𝜽 +btan𝜽)2 + (atan𝜽 +bsec𝜽)2 a2sec2𝜽+b2tan2𝜽+2absec𝜽tan𝜽

- a2tan2𝜽 +b2 sec2𝜽 -2abtan𝜽 sec𝜽

a2 (sec2𝜽 - tan2𝜽 ) – b2(tan2𝜽 − 𝐬𝐞𝐜𝟐𝜽 ) a2 (1) – b2(1 ) = a2– b2

25. A BC =10√3 , AB =30cm

tan 𝜽 = AB/BC =30/10√3 =3/√3 tan 𝜽 =√3 , 𝜽 =300

B C Vw;wf;Nfhzk; = 300

26. miu Nfhsj;jpd; tisgug;G = 2 πr2 =2772

πr2 = 2772/2 = 1386 miu Nfhsj;jpd; Gwg;gug;G = 3 πr2

=3x1386 =4158cm2

27. $k;gpd; fd msT =1/3 πr2h =4928 , h=24 1/3 πr2x24 =4928 ; r2 = 4928x3x7 =196

22x24

r2 =142 ; r =14

28. n = 10 , x = 12 , ∑x2 = 1530 ,

σ2 = ∑x2/n - (∑x/n)2 = [1530/10] – [120/10]2

= 153-144 = 9 , σ =3 , CV =[ σ/x ]x100%

= [ 3/12 ]x100 = 100/4 = 25

29. rhjhuz tUlj;jpd; nkhj;j ehl;fs; = 365 mjhtJ 52 thuq;fs; kw;Wk; xU ehs;

52 thuq;fspy; 52 nts;spf;fpoikfs; ,Uf;Fk; kPjKs;s xU ehs; VO ehl;fspy; xd;whFk; QhapW > jpq;fs; >nrt;tha; > Gjd; >tpahod; >nts;sp > rdp > n(s)= 7 nts;spf;fpoik tUk; epfo;r;rp C vd;f P(C)= n(C)/n(s) = 1/7

30.(a) 6x2 – 5x +1 = (2x-1)(3x-1) 9x2+12x-5 (3x+5)(3x-1)

(2x-1)/ (3x+5) (or ) 30(b) lx2+mx1 ly2 +my1

l+m l+m 1(4) +6(-3) 1(-9) + 6(5) 7 7 (4 –18 )/7 , (-9+30)/7 = -14/7 , 21/7 = (-2,3)

Page 6: 46(b) R 15 S P Q 47(a)ml;ltiiz : X -3 -2 -1 0 1 2 3 x2 9 4 1 0 1 4 9 Y=2x2 18 8 2 0 2 8 18 ii) thpir N[hbfs; : (-3,18) (-2, 8)(-1,2) (0,0) (1, 2) (2, 8) (3, 18)

gFjp- III Ie;J kjpg;ngz; tpdhf;fs;:

31. please refer Page no .13 of the text book vLj;Jf;fhl;L : 1.7 (VENN DIAGRAM ) 32. A = {6,9,15,18,21} B = {1,2,4,5,6 } f : A →B f(x) = (x-3)/3 f( 6) = (6-3) / 3 = 3/3 = 1 f(9) = (9-3) /3 = 6/3 = 2 f(15) = (15-3)/3 = 12/3 = 4 f(18) = (18-3)/3 = 15/3 = 5 f(21) = (21-3) /3 = 18/3 = 6

i) thpir N[hbfspd; fzkhf :

f ={(6,1), (9,2), (15,4),

(18,5)(21,6)}

ii) ii) ml;ltizahf :

X 6 9 15 18 21

f(x) 1 2 4 5 6

iii) mk;Gf;Fwp glkhf :

33. xU Mz; xU Ntiyia jdpahf nra;a MFk; ehl;fs; = x vd;f xU ehspy; nra;Ak; Ntiy = 1/x xU rpWtd; jdpahf nra;a MFk; ehl;fs; = y vd;f xU ehspy; nra;Ak; Ntiy = 1/y 8 Mz;fs; kw;Wk; 12 rpWth;fs; Nrh;e;J xU ehspy; nra;Ak; Ntiy = 1/10 8/x +12/y = 1/10 -----(1) 6 Mz;fs; kw;Wk; 8 rpWth;fs; Nrh;e;J xU ehspy; nra;Ak; Ntiy = 1/14 6/x +8/y = 1/14 -----(2 ) 8a +2b = 1/10 ( 1/x = a , 1/y = b ) 6a +8b = 1/14 rkd;ghLfs; (1) kw;Wk; (2) –I jPh;f;f fpilg;gJ a=1/140 , b = 1/280 mjhtJ x = 140 , y = 280 xU Mz; xU Ntiyia jdpahf nra;a

MFk; ehl;fs; = 140 xU rpWtd; jdpahf nra;a MFk; ehl;fs; = 280 35. fhuzpgLj;Jf : x 3 - 3x2 - 10x + 24

jPh;T : p(x) = x 3 - 3x2 - 10x + 24 vd;f . ,f;Nfhitf;F p(1) ≠ 0 kw;Wk; p(-1) ≠ 0 vdNt (x-1) kw;Wk; (x+1) Mfpad fhuzpfs; my;y . MfNt NtW kjpg;Gfis gpujpapl;L : p(x) f;F fhuzpfis fhzyhk; .

2 1 -3 -10 +24 0 2 -2 -24 1 -1 -12 0

vdNt p(x) - f;F (x - 2) xU fhuzpahFk; kw;nwhU fhuzp : x2 –x – 12 mjid fhuzpgLj;j : (x-4) (x+3) MfNt fhuzpfs; : (x - 2) (x-4) (x+3)

36. ax4 -bx3+40x2+24x+36 - xU KO th;f;f

Nfhit vdpy; a,b -d; kjpg;G fhz; .

6 +2x +3x2 6 36 + 24x + 40x2 – bx3 + ax4

12+2x + 24x + 40x2

+ 24x + 4 x2 12+4x+3x2 +36x2 – bx3 + ax4

+36x2 +12x3 + 9x4 0 a= 9 , b = -12

37. please refer Page no .141 of the text book vLj;Jf;fhl;L : 4.16 38. (h,0) (a,b)(0,k) Mfpad xNu Nfhl;by; mikAk; Gs;spfs; vdpy; Δ=0 ½[x1(y2-y3)+x2(y3-y1)+x3(y1-y2) = 0 ½[h(b-k)+ a(k-0)+0(0-b) = 0 ½[hb-hk+ak] =0 ; hb-hk+ak =0 hb +ak =hk ÷ hk b/k +a/h = 1 39. A(-2,6) B( 3,-4) vd;w Gs;spfis 2;:3 vd;w tpfpjj;jpy; cl;Gwkhf gphpf;Fk; Gs;sp lx2+mx1 ly2 +my1

l+m l+m 2(3) +3(-2) 2(-4)+3(6) 5 5 (6-6)/5 , (-8+18)/5 = 0/5 , 10/5 = (0,2) (0,2) vd;w Gs;sp topahfTk; rha;T 3/2 MfTk; nfhz;l rkd;ghL = y-y1 = m(x-x1) = y-2 = 3/2 (x-0) = 2(y-2) = 3x ; 2y-4 =3x = 3x-2y +4 = 0

6

9

15

18

21

1

2

4

5

6

7

77

7

Page 7: 46(b) R 15 S P Q 47(a)ml;ltiiz : X -3 -2 -1 0 1 2 3 x2 9 4 1 0 1 4 9 Y=2x2 18 8 2 0 2 8 18 ii) thpir N[hbfs; : (-3,18) (-2, 8)(-1,2) (0,0) (1, 2) (2, 8) (3, 18)

40. A

D E

B C

glj;jpy; DE//BC kw;Wk; AB=3AD vd nfhLf;fg;gl;Ls;sJ. AD/AB = 1/3 Δ ADE kw;Wk; ΔABC Mfpatw;wpy; ∠ ADE = ∠ABC ( xj;j Nfhzq;fs; ) ∠A = ∠A ( nghJf;Nfhzq;fs; ) AA –tpjpg;gb Δ ADE ~ Δ ABC ΔADE –d; gug;G = AD2 = ΔADE –d; gug;G = 1/9 ΔABC–d; gug;G = AB2 72 MfNt > ΔADE –d; gug;G = 8 r.nrkP ehw;fuk; DBCE- d; gug;G = ΔABC–d; gug;G - ΔADE –d; gug;G = 72- 8 = 64 nrkP2

41. D AE vd;gJ fl;llk; =hkP

BD vd;gJ NfhGuk; =60kP

C E ∠DEC =300 , ∠DAB=600

ΔDAB-apy; tan600 =BD/AB

B A AB = BD/tan600 = 60/√3 ΔDEC -apy; tan300 = CD/Ec = EC = CD/tan300

AB = (60-h) √3 (EC = AB) (60-h) √3 = 60/√3 (60-h) = 60/3 ; 60-h = 20 ; h = 60-20 = 40

fl;blj;jpd; cauk; =40 kP

43. please refer Page no .301 of the text book vLj;Jf;fhl;L : 11.14

44. jPh;T : $Wntsp s = {(1,1) (1,2) ……(6,6)} n(s) = 36 A vd;gJ Kf vz;fspd; $Ljy; 3-My; tFgLk; fzq;fs; vd;f.

A= { (1,2)(2,1) (1,5)(5,1)(2,4)(4,2)(3,3)(3,6)(6,3)(4,5)(5,4)(6,6)

n(A) = 12

B vd;gJ Kf vz;fspd; $Ljy; 4-My; tFgLk; fzq;fs; vd;f

B= { (1,3)(3,1)(2,2)(2,6) (6,2)(3,5)(5,3)(4,4)(6,6)} n(B) = 9

AnB = { (6,6) } n (AnB) = 1

Kf vz;fspd; $Ljy; 3 my;yJ4 My; tFgl epfo;jfT

P(AUB) = P(A) +P(B) –P(AnB) =12/36+9/36-1/36 = 20/36

Kf vz;fspd; $Ljy; 3 my;yJ4 My; tFglhky; ,Uf;f

epfo;jfT P(AUB)’ = 1 –P(AUB) = 1- (20/36) = 16/36 = 4/9

45(a). please refer Page no .59 of the text book

vLj;Jf;fhl;L : 2.27

45(b) cUis : r = 18 , h = 32 $k;G : h = 24 $k;gpd; fdmsT = cUisapd; fd msT 1/3 πr2h = πr2h 1/3 r2x24 = r2x18x18x24 r2 = 18x18xx4 r2= 182x22 r = 36 rhAuk; l = √362+242 =12√32+22

l = 12√13 nr.kP

gFjp- IV gj;J kjpg;ngz; tpdhf;fs;:

46(a)

fzf;fPL (Calculation) : njhLNfhl;Lj;Jz;bd; ePsk; :PA2 = (op)2 – (OA)2 PA2 = (13)2 – (5)2

PA2 = (169) – (25) PA2 = 144 PA = 12 cm

Page 8: 46(b) R 15 S P Q 47(a)ml;ltiiz : X -3 -2 -1 0 1 2 3 x2 9 4 1 0 1 4 9 Y=2x2 18 8 2 0 2 8 18 ii) thpir N[hbfs; : (-3,18) (-2, 8)(-1,2) (0,0) (1, 2) (2, 8) (3, 18)

46(b)

R

S

P Q

47(a)ml;ltiiz : X -3 -2 -1 0 1 2 3 x2 9 4 1 0 1 4 9

Y=2x2 18 8 2 0 2 8 18 ii) thpir N[hbfs; : (-3,18) (-2, 8)(-1,2) (0,0) (1, 2) (2, 8) (3, 18) iii) msT jpl;lk; : x-mr;R 1nrkP = 1 myF y-mr;R 1nrkP = 2 myFfs; y =2x2 0=2x2+x-6 Y= -x +6

x -2 0 2 Y=-x+6 8 6 4 iv) jPh;T fzk; : { -2 , 1.5 }

47(b) ml;ltiiz : ypl;lh;fspd;

vz;zpf;if(x) 1 2 3 4 5

tpiy &.(Y)

15 30 45 60 75

ml;ltizapypUe;J x-d; kjpg;G mjpfhpf;f y-d; kjpg;Gk; mjpfhpg;gij fhzyhk; .vdNt Neh; khWghl;il Fwpf;fpwJ. vdNt y/x = k , K =15/1=10/2=45/3=60/4 =75/5=15, k=15 , y = 15x jPh;T : tiuglj;jpypUe;J i) tpfpjrk khwpyp k=15 ii) 3 ypl;lh; ghypd; tpiy =45,

Prepared by,

Mr. C. Sugumar,

Headmaster,

Govt High School,

Vilai,

Tiruvannamalai District.

Published By www.Padasalai.Net.