KOS SSLC Question Paper 2022 Mathematics

Karnataka Open School
(KOS)

Question Paper
&

Answer Key

2022

Code No. :

PÜ®ÝìoPÜ ±èÅyÜ ÎûÜ| ±ÜÄàûÝ ÊÜáívÜÚ, ÊÜáÇæÉàÍÜÌÃÜí, ¸æíWÜÙÜãÃÜá, 560 003
KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESHWARAM,
BENGALURU, 560 003
PÜ®ÝìoPÜ ÊÜááPܤ ÍÝÇæWÜÙÜ ±ÜÄàûæ, H²ÅÇ…, 2022
Karnataka Open School Examination, April, 2022
MATHEMATICS
Subject / ËÐÜ¿á
WÜ~ñÜ
Date of Exam. / ±ÜÄàûæ¿á ©®ÝíPÜ 25. 04. 2022
Maximum Marks / WÜÄÐÜu AíPÜWÜÙÜá 100
Duration of Exam. / ¯ÜÄàûæ AÊܘ 3 hours / 3 WÜípæWÜÙÜá
Time allotted to read the instructions /
15 minutes / 15 ¯ËáÐÜWÜÙÜá
ÓÜãaܬæWÜÙܬÜá® K¨ÜÆá ­WܘWæãÚÔÃÜáÊÜ AÊܘ

TEAR HERE TO OPEN THE QUESTION PAPER
Time / ÓÜÊÜá¿á 9-30 A.M. to 12-45 P.M.
A»Ü¦ìWÜÚWæ ÓÝÊÜޮܠÓÜãaÜ®æWÜÙÜá / General Instructions to the Candidates :
1. A»Ü¦ìWÜÙÜá ñܮܰ ®æãàí¨Ü~ ÓÜíTæ¿á®Üá° ±ÜÅÊæàÍÜ ±ÜñÜŨÜÈÉ ÊÜáá©ÅÔÃÜáÊÜíñæÁáà EñܤÃÜ&±ÜâÔ¤Pæ¿áÈÉ
¯àwÃÜáÊÜ ¯WÜ©ñÜ ÓܧÙܨÜÈÉ ÓܳÐÜrÊÝX ŸÃæÀáÄ.
Candidates should write their Register Number on the Answer Booklet as printed in their
hall ticket.
2. A»Ü¦ìWÜÙÜá ÖæaÜácÊÜÄ EñܤÃÜ ÖÝÙæWÜÙÜ®Üá° ±Üvæ¨ÜÈÉ, EñܤÃÜ ÖÝÙæWÜÙÜ ÊÜááS±Üâo¨Ü Êæáà騆 ¯WÜ©ñÜ ÓܧÙܨÜÈÉ
ÊÜááS EñܤÃÜ&±ÜâÔ¤Pæ¿á PÜÅÊÜá ÓÜíTæ¿á®Üá° ŸÃæ¿áñÜPÜR¨Üáª.
Candidates should write their Main Answer Booklet Number on the additional answer
sheets in the space provided.
3. D ±ÜÅÍ氱ܣÅPæ¿á®Üá° ×ÊÜáá¾S hÝPæp… ÊÜáãÆPÜ ÊæãÖÜÃÜá ÔàÇ… ÊÜÞvÜÇÝX¨æ. ±ÜÄàûæ ±ÝÅÃÜí»ÜÊÝWÜáÊÜ ÓÜÊÜá¿áPæR
¯ÊÜá¾ ±ÜÅÍ氱ܣÅPæ¿á ŸÆŸ© ±ÝÍÜÌìÊÜ®Üá° PÜñܤÄÔ, ±ÜÅÍ氱ܣÅPæ¿áÈÉ GÇÝÉ ±ÜâoWÜÙÜá CÊæÁáà Gí¨Üá ±ÜÄàüÔPæãÚÛ.
This Question Paper has been sealed by reverse jacket. You have to cut on the right side
to open the Question Paper at the time of commencement of the examination. Check
whether all the pages of the Question Paper are intact.
4. A»Ü¦ìWÜÙÜá ¯WÜ©±Üwst ÓܧÙÜÊÜ®Üá° ÖæãÃÜñÜá±ÜwÔ C¯°ñÜÃæà ¿ÞÊÜâ¨æà ±ÜâoWÜÙÜÈÉ ®æãàí¨Ü~ ÓÜíTæÂ, WÜáÃÜáñÜá
ÖÝWÜã bÖæ® C­®ñÜÃæ ¿ÞÊÜâ¨æà ÊÜÞ×£WÜÙܬÜá® ŸÃæ¿á¸ÝÃܨÜá. Jí¨Üá ÊæàÙæ, D ŸWæ¿á ¿ÞÊÜâ¨æà ÊÜÞ×£WÜÙܬÜá®
EñܤÃÜ&±ÜâÔ¤Pæ¿áÈÉ ŸÃæ¨Ü ±ÜûܨÜÈÉ AíñÜÖÜ EñܤÃÜ&±ÜâÔ¤Pæ¿á®Üá° ÊÜåèÆÂÊÜޱܮÜPæR ±ÜÄWÜ~ÓÜÇÝWÜáÊÜâ©ÆÉ.
Candidates should not write Register Number, mark, sign or any other information in the
Answer Booklet except in the specified place. In case, it is found any information in the
sheets of the answer scripts such answer scripts will not be considered for evaluation.
5. ¯ÜÄàûÝ ÓÜÊÜá¿á¨ÜÈÉ A»Ü¦ì¿áá ¯ÜÄàûÝ AÊÜÂÊÜÖÝÃܨÜÈÉ ñæãvÜXÔPæãíwÃÜáÊÜâ¨Üá PÜívÜáŸí¨ÜÈÉ ÖÝWÜã
±ÜÄàûÝ ÓÜãaÜ®æWÜÙÜ®Üá° EÆÉí™Ô¨ÜªÈÉ AíñÜÖÜ A»Ü¦ì¿á ËÃÜá¨Üœ ¯ÜÄàûÝ ­¿áÊÜÞ¬ÜáÓÝÃÜ ÎÓÜᤠPÜÅÊÜáPæR
WÜáıÜwÓÜÇÝWÜáÊÜâ¨Üá ÊÜáñÜᤠAíñÜÖÜ A»Ü¦ì¿á EñܤÃÜ&±ÜâÔ¤Pæ¿á®Üá° ÊÜåèÆÂÊÜޱܮÜPæR ±ÜÄWÜ~ÓÜÇÝWÜáÊÜâ©ÆÉ.
Candidate found to be indulging in malpractice during examination and violating
Tear here

examination instructions, action will be taken against such candidate as per the
examination rules and his / her Answer Booklet will not be considered for evaluation.

6. EñܤÃÜ ŸÃæ¿áÆá PܱÜâ³ /¯àÈ ÍÝÀá¿á ¸ÝÇ… ±ÝÀáíp… ±æ®… ÊÜÞñÜÅ E±ÜÁãàXÓÜñÜPÜR¨Üáª.
Use black / blue ball point pen only to write the answers.

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ÓÜãaÜ®æWÜÙÜá i) GÇÝÉ ±ÜÅÍæ°WÜÙÜã PÜvÝx¿á.
ii) ±ÜÅÍæ° ÓÜíTæÂWÜÙÜ®Üá° EñܤÃÜ ±Ü£ÅPæ¿áÈÉ ñܱܳ¨æà ®ÜÊÜáã©Ô.
iii)

1. 2x 3 – 9x + 3 ¹àhæãàQ¤¿á ÍæÅà~¿á¬Üá® ŸÃæÀáÄ. 1

2
2. ÓÜíûæà²Ô 2 1
 
3

3. x = 0 B¨ÝWÜ, x 2 + 3x – 5 ¹àhæãàQ¤¿á ¸æÇæ¿á®Üá° PÜívÜá×wÀáÄ. 1

4. 6, 10, 14, 18 …… ÓÜÊÜÞíñÜÃÜ ÍæÅà{¿á ÓÝÊÜެܠÊÜÂñÝÂÓÜÊܬÜá® ŸÃæÀáÄ. 1

5. 10 : 15 ÃÜ ÓÜíü±Ü¤ ÃÜã±Ü ŸÃæÀáÄ. 1

6. A«ÜìÊÜêñܤSívܨÜÈÉ EípÝWÜáÊÜ Pæãà¬Ü¨Ü AÙÜñæ¿á¬Üá® ŸÃæÀáÄ. 1

7. 3 Óæí.Ëáà. £ÅgÂËÃÜáÊÜ ÊÜêñܤ¨Ü ÊÝÂÓÜ¨Ü AÙÜñæ GÐÜár 1

8. ÊÜêñܤ¨Ü ÊæáàÈ¬Ü ¿ÞÊÜâ¨æà Jí¨Üá ¹í¨ÜáˬÜÈÉ GÐÜár ÓܱÍÜìPÜWÜÙܬÜá® GÙæ¿áŸÖÜá¨Üá 1

9. Z¬Ü¨Ü ¯Üä|ì ÊæáàÇ澄 ËÔ¤à|ìÊܬÜá® PÜívÜá×w¿ááÊÜ ÓÜãñÜÅÊܬÜá® ŸÃæÀáÄ. 1

10. sin 30° ¿á ¸æÇæ GÐÜár 1

1
11. cos A =
2
B¨ÜÃæ, sec A ¨Ü ¸æÇæ GÐÜár 1

12. 0·12 ÊÜáñÜᤠ0·13 ÃÜ ¬ÜvÜáÊæ GÐÜár »ÝWÜÆŸœ ÓÜíTæÂWÜÙܬÜá® ŸÃæ¿áŸÖÜá¨Üá ¿ÞÊÜâ¨Ý¨ÜÃÜã
GÃÜvÜ®Üá° ÖæÓÜÄÔ. 2

13. ÓÜíûæà²Ô 50+30+82–32 2

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14. HÄPæ PÜÅÊÜá¨ÜÈÉ ŸÃæÀáÄ 2

3
2 , 3 , 6 5

15. ÓÜÖÜg ®æàÃÜ WÜáOÝPÝÃÜÊÜÆÉ¨Ü Ë«Ý®Ü©í¨Ü 48 × 52 ÃÜ ¸æÇæ¿á®Üá° PÜívÜá×wÀáÄ. 2

16. 6, 11, 16, 21, …… ÓÜÊÜÞíñÜÃÜ ÍæÅà{¿á 10 ®æà ±Ü¨ÜÊÜ®Üá° PÜívÜá×wÀáÄ. 2

17. 1, 6, 11, 16, …… ÓÜÊÜÞíñÜÃÜ ÍæÅà{¿á Êæã¨ÜÆ 12 ±Ü¨ÜWÜÙÜ ÊæãñܤÊÜ®Üá° PÜívÜá×wÀáÄ. 2

18. 5 ÈàoÃ… ¯æpæãÅàÇ… ¸æÇæ 440 ÃÜã. B¨ÜÃæ, 8 ÈàoÃ… ¯æpæãÅàÇ… ¸æÇæ GÐÜár 2

19. Qà£ì¿áá 300 ±Üâo¨Ü ±ÜâÓܤPܨÜÈÉ 84 ±ÜâoWÜÙÜ®Üá° K©¨ÝªÙæ. ÖÝWݨÜÃæ BPæ¿áá ÍæàPÜvÝ GÐÜár
±ÜâoWÜÙÜ®Üá° K©¨ÝªÙæ 2

20. Jí¨Üá PÜáoáíŸ¨Ü ÊÝÑìPÜ B¨Ý¿á ÃÜã. 7,500 ÃÜÈÉ ÍæàPÜvÝ 35 »ÝWÜ BÖÝÃÜPÝRX SaÜáì
ÊÜÞw¨ÜÃæ, B PÜáoáíŸÊÜâ BÖÝÃÜPÝRX SaÜáì ÊÜÞw¨Ü ÖÜ|ÊæÐÜár 2

↔ ↔ ↔
21. bñÜŨÜÈÉ AB, CD, EF ÓÜÊÜÞíñÜÃÜ ÃæàTæWÜÙÜ®Üá° PQ dæà¨ÜPÜ ÃæàTæ¿áá X, Y ÊÜáñÜᤠZ ¹í¨ÜáWÜÙÜÈÉ
dæà©Ô¨ÜÃæ < 1 ÊÜáñÜᤠ< 2 ÃÜ ¸æÇæ¿á®Üá° PÜívÜá×wÀáÄ. 2

22. Jí¨Üá £Å»Üág¨Ü GÃÜvÜá Pæãà®ÜWÜÙÜ ÊæãñܤÊÜâ A¨ÜÃÜ ÊÜáãÃÜ®æà Pæãà®ÜPæR ÓÜÊÜáÊÝX¨ÜªÃæ, ÊÜáãÃÜ®æà

Pæãà¬ÜÊÜâ ÆíŸPæãà¬ÜÊÝXÃÜáñܤ¨æ Gí¨Üá ÓݘÔ. 2

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23. ( 3, 4 ) ÊÜáñÜᤠ( 7, 4 ) ¹í¨ÜáWÜÙÜ®Üá° ÓæàÄÔ EípÝ¨Ü ÃæàTÝSívÜ¨Ü ÊÜá«Ü¹í¨ÜáÊÜ®Üá°
PÜívÜá×wÀáÄ. 2

24. PæÙÜWæ ¯àw¨Ü BÊÜ꣤ ËñÜÃÜOÝ ±Üqr¿áÈÉ TÝÈ ¹or ÓܧÙÜWÜÙÜ®Üá° ñÜáí¹Ä 2

ÊÜWÜìWÜÙÜá ñÝÙæ WÜáÃÜáñÜá BÊÜ꣤

5 — 10 |||

10 — 15 4

15 — 20 ||||

20 — 25 5

n=

25. bñÜŨÜÈÉ PæãqrÃÜáÊÜ ®Üûæ¿á®Üá° ®æãàw PæÙÜX®Ü ±ÜÅÍæ°WÜÙÜ®Üá° EñܤÄÔ 2

a) Êæáà騆 ®Üûæ¿á Ë«ÜÊÜ®Üá° ÖæÓÜÄÔ.

b) 55 — 60 Pæ.i. ñÜãPÜÊÜ®Üá° Öæãí©ÃÜáÊÜ Ë¨Ý¦ìWÜÙÜ ÓÜíTæ GÐÜár

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26. PæÙÜX®Ü ¨ÜñݤíÍÜWÜÙÜ ÊÜá«ÜÂPÜÊÜ®Üá° PÜívÜá×wÀáÄ 2

15, 16, 9, 13, 18, 16, 10, 20.

27. a) Jí¨Üá Zo®æ¿á ÓÝ«ÜÂñæ¿á ÓÜí»ÜÊܯà¿áñæ¿á®Üá° PÜívÜá×w¿ááÊÜ ÓÜãñÜÅ ŸÃæÀáÄ.

b) SbñÜ Zo¬æ¿á ÓÜí»ÜÊÜ­à¿áñæ¿á ¸æÇæ¿á¬Üá® ŸÃæÀáÄ. 2

28. 20,000 ÃÜã.WÜÚWæ 2 ÊÜÐÜìWÜÙÜÈÉ ÓÝÈ¿Þ®Ý ÍæàPÜvÝ 6 ÃÜíñæ Ÿwx ¨ÜÃܨÜíñæ ¨æãÃÜPÜáÊÜ
aÜPÜÅŸwx¿á¬Üá® PÜívÜá×wÀáÄ. 3

29. Jí¨Üá ÊÜhÝÅPÜꣿá GÃÜvÜá ±ÝÍÜÌìPæãà®ÜWÜÙÜ A®Üá±ÝñÜÊÜâ 4 : 5. C¨ÜÃÜ GÇÝÉ Pæãà®ÜWÜÙÜ AÙÜñæ¿á®Üá°
PÜívÜá×wÀáÄ. 3

30. aÜQÅà¿á aÜñÜá»Üáìg¨Ü Jí¨Üá hæãñæ A¼ÊÜááS ¸ÝÖÜáWÜÙÜá ÓÜÊÜá®ÝX¨ÜªÃæ, PÜ|ìWÜÙÜá ÓÜÊÜá®ÝXÃÜáñܤÊæ
Gí¨Üá ÓݘÔ. 3

31. Jí¨Üá £Å»ÜáhÝPÝÃÜ¨Ü gËáà¯®Ü ¸ÝÖÜáWÜÙÜá 22 Ëáà., 25 Ëáà. ÊÜáñÜᤠ23 Ëáà. BXÊæ. ÖæàÃݬ…
ÓÜãñÜÅ ŸÙÜÔ gËáà¯®Ü ËÔ¤à|ìÊÜ®Üá° PÜívÜá×wÀáÄ. 3

32. Jí¨Üá H~¿á®Üá° ®æÆ©í¨Ü 8 Ëáà. GñܤÃܨÜÈÉÃÜáÊÜíñæ Wæãàvæ¿á ÊæáàÇæ JÃÜXÔ¨æ. Wæãàvæ¿áá
ÊÜáñÜᤠH~¿á ±Ý¨ÜWÜÙÜ ®ÜvÜá訆 ¨ÜãÃÜ 6 Ëáà. B¨ÜÃæ, H~¿á E¨ÜªÊÜ®Üá° PÜívÜá×wÀáÄ. 3

33. ±ÜÅ£ ¸ÝÖÜá 8 Óæí.Ëáà. CÃÜáÊÜ ÊÜáãÃÜá Z®ÜWÜÙÜ®Üá° Jí¨ÜÃÜ ±ÜPÜRPæR Jí¨ÜÃÜíñæ hæãàwÔ¨æ, ¶ÜÈñÜ
B¿áñÜZ¬Ü¨Ü ÊæáàÇ澄 ËÔ¤à|ìÊܬÜá® PÜívÜá×wÀáÄ. 3

1 – sin A

cos A
34. = Gí¨Üá ÓݘÔ. 3
1 + sin A 1 + sin A

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35. ÓÜ£àÍܬÜá Jí¨Üá EÚñÝ¿á TÝñæ¿á ¯ÝÓ…ŸáP… Öæãí©¨Ýª¬æ. AÊÜ¬Ü ¯ÝÓ…ŸáP… ¨ÝSÇæWÜÙÜá D
PæÙÜX®Üí£Êæ 3

¶æŸÅÊÜÄ 1 B/F — — 15,000.00

¶æŸÅÊÜÄ 14 5,000.00 — 10,000.00

ÊÜÞa…ì 5 — 7,000.00 17,000.00

ÊÜÞa…ì 6 2,000.00 — 15,000.00

ÊÜÞa…ì 19 — 10,000.00 25,000.00

ÊÜÞa…ì 22 — 5,000.00 30,000.00

H°ÅÇ… 8 — 5,000.00 35,000.00

Ÿwx¿á ¨ÜÃÜÊÜâ ÓÝÈ¿Þ¬Ü ÍæàPÜvÝ 2 ÃÜã. B¨ÜÃæ, H°ÅÇ… AíñÜÂPæR ÓÜ£àÍÜ­Wæ ¨æãÃæ¿ááÊÜ Ÿwr¿á¬Üá®
ÇæPÜRÊÜÞw PÜívÜá×wÀáÄ.

36. D ÓÜËáàPÜÃÜ|WÜÙÜ®Üá° ®Üûæ¿á ÓÜÖÝ¿á©í¨Ü ¹wÔ 3

x+y=7

x–y=1

37. PæÙÜX¬Ü ԨݜíñÜWÜÙܬÜá® ­ÃÜã°Ô 3

a) ¸Ý.Pæãà.¸Ý.

b) Pæãà.¸Ý.Pæãà.

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38. 4 Óæí.Ëáà. ÊÜáñÜᤠ6 Óæí.Ëáà. ±ÝÍÜÌì¸ÝÖÜáWÜÙÜáÙÜÛ ÊÜáñÜᤠAÊÜâWÜÚí¨Ü EípÝ¨Ü Pæãà®Ü 60º
CÃÜáÊÜíñæ ÓÜÊÜÞíñÜÃÜ aÜñÜá»ÜáìgÊÜ®Üá° ÃÜbÔ. 3

39. GÃÜvÜá ¹àhæãàQ¤WÜÙÜ ÊÜá.ÓÝ.A. ( x – 2 ) ÊÜáñÜᤠÆ.ÓÝ.A. x 4 + 2x 3 – 8x – 16 BXÊæ. Jí¨Üá
¹àhæãàQ¤¿áá ( x 3 – 8 ) B¨ÜÃæ, ÊÜáñæã¤í¨Üá ¹àhæãàQ¤¿á®Üá° PÜívÜá×wÀáÄ. 4

40. x 2 – 8x + 15 = 0 ÓÜËáàPÜÃÜ|¨Ü ÊÜáãÆWÜÙÜ ÓÜÌ»ÝÊÜÊÜ®Üá° ËÊæàbÔ. ÊÜáãÆWÜÙÜá ÊÝÓܤÊÜÊÝX¨ÜªÃæ,
AÊÜâWÜÙÜ®Üá° PÜívÜá×wÀáÄ. 4

41. 5 Óæí.Ëáà. ¸ÝÖÜáÊÜâÙÜÛ ÓÜÊÜá¸ÝÖÜá £Å»Üág ABC ¿á®Üá° ÃÜbÔ, C¨ÜPæR ±ÜÄÊÜêñܤÊÜ®Üá° GÙæÀáÄ. 4

42. ÓÜÊÜáÃÜã±Ü £Å»ÜágWÜÙÜ ËÔ¤à|ìWÜÙÜá AÊÜâWÜÙÜ A®ÜáÃÜã±Ü ¸ÝÖÜáWÜÙÜ ÊÜWÜìWÜÙÜ A®Üá±ÝñܨÜÈÉÃÜáñܤÊæ
Gí¨Üá ÓݘÔ. 4

43. PæÙÜX®Ü ¨ÜñݤíÍÜWÜÚWæ Óܤí»Ü ®Üûæ¿á®Üá° ÃÜbÔ 4

ñÜãPÜ (Q.WÝÅí.WÜÙÜá) ÖÜ~¡®Ü ŸáqrWÜÙÜ ÓÜíTæÂ

70 4

80 5

90 7

100 8

110 5

120 4

120 3

44. ÃÜË¿áá 100 Ëáà. GñܤÃÜËÃÜáÊÜ PÜorvÜ¨Ü ñÜá©¿áÈÉ ¯íñÜá PÜorvÜ¨Ü GÃÜvÜã PÜvæWÜÙÜÈÉ GÃÜvÜá
PÝÃÜáWÜÙÜ®Üá° ËàüÓÜáñݤ®æ. CÊÜâWÜÙÜ BÙÜ¨Ü Pæãà®ÜWÜÙÜá 45º ÊÜáñÜᤠ60º B¨ÜÃæ, PÝÃÜáWÜÙÜ ®ÜvÜáË®Ü
¨ÜãÃÜÊÜ®Üá° PÜívÜá×wÀáÄ. 4

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