coordinate geometry

1Formative Assessment Manual for Teachers Real Numbers

CHAPTER-1Real Numbers

Learning Objectives 7RUHYLVLW1XPEHU6\VWHPVIURP1DWXUDOVWR5HDO1XPEHUV 7ROHDUQ(XFOLGV'LYLVLRQ/HPPD 7RXQGHUVWDQGDSSO\(XFOLGV'LYLVLRQDOJRULWKPIRUILQGLQJ+&)RIWZRQXPEHUV 7RXQGHUVWDQG)XQGDPHQWDOWKHRUHPRI$ULWKPHWLF 7RILQG+&)/&0XVLQJSULPHIDFWRUL]DWLRQ 7RSURYH HWFDVLUUDWLRQDOQXPEHUV 7RUHYLVLWGHFLPDOH[SDQVLRQRIUHDOQXPEHUV 7RILQGWKHFRQGLWLRQRQUDWLRQDOQXPEHUVWRKDYHWHUPLQDWLQJGHFLPDOH[SDQVLRQSuggested Formative Assessment tasksTask-1: Crossword Puzzle Worksheet7RSLF 5HDO1XPEHUV&RQWHQW&RYHUDJH :KROH&KDSWHU/HDUQLQJ2EMHFWLYHV 7R WHVW WKHEDVLFFRQFHSWV UHODWHG WR WKHFKDSWHU7DVN &URVVZRUG3X]]OH([HFXWLRQRIWDVN 7KLVWDVNPD\EHSHUIRUPHGLQWKHFODVVURRP6WXGHQWVFDQEHJLYHQWKHSKRWRFRS\RIWKHZRUNVKHHW'XUDWLRQ PLQXWHV&ULWHULDIRUDVVHVVPHQW 7LPHLQYROYHGLQVROYLQJWKHZRUNVKHHW

5DWLQJVFDOHIRUWKHZRUNVKHHW)ROORZXS 3UDFWLFHZRUNVKHHWV

91

Formative Assessment Manual for Teachers Coordinate Geometry

CHAPTER-7Coordinate Geometry

Learning Objectives : /HDUQLQJ2EMHFWLYHV 7RUHLQIRUFHWKHSORWWLQJRISRLQWVLQWZRGLPHQVLRQDO&DUWHVLDQFRRUGLQDWHV\VWHP 7ROHDUQWRILQGWKHGLVWDQFHEHWZHHQWZRSRLQWVRQDSODQH 7RILQGWKHFRRUGLQDWHVRIDSRLQW3ZKLFKGLYLGHVWKHOLQHVHJPHQWMRLQLQJWKHSRLQWV$%LQWHUQDOO\LQWKHUDWLRPQ 7RILQGWKHPLGSRLQWRIOLQHVHJPHQWMRLQLQJSRLQWV34 7RDSSO\WKHNQRZOHGJHRIFRRUGLQDWHJHRPHWU\IRUILQGLQJWKHDUHDRIDWULDQJOHSuggested Formative Assessment tasksTask-1: Play & learn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





92

Coordinate Geometry Formative Assessment Manual for Teachers

Game Directions :

Number of Players : 2

Material required :

&RRUGLQDWH6QDNH/DGGHU*DPH6KHHW 5HG%OXHGLFHQXPEHUVRQRQHGLFHRIHDFKFRORUDVWRQXPEHUVRQDQRWKHUGLFHRI HDFK FRORU DV WR %RDUGSLHFHIRUHDFKSOD\HUWRORFDWHKLVKHUSRVLWLRQGame Direction :

7RVWDUWZLWKILUVWSOD\HUKDVWRFKRRVHDUHGGLFHUDQGRPO\RXWRIWZRUHGGLFHDEOXHGLFHUDQGRPO\RXWRIWZRUHGGLFH5HGLVIRU[D[LV%OXHLVIRU\D[LV7KHQWKHSOD\HUKDVWRWKURZWKHWZRGLFHVLPXOWDQHRXVO\ORFDWHWKHFRRUGLQDWHVRQWKHJDPHVKHHW6XSSRVHKHJHWVRQUHGRQEOXHGLFHWKHQWKLVZLOOFRUUHVSRQGWRRQJDPHVKHHWSXWKLVKHUERDUGSLHFHDWWKDWSRVLWLRQ 7KHVHFRQGSOD\HUZLOOPRYHLQWKHVDPHZD\ 6QDNHVODGGHUZLOODFWDVLQQRUPDOVQDNHODGGHUJDPHVQDNHZLOOEULQJWKHSRVLWLRQGRZQODGGHUZLOOJLYHDOLIW 7KHJDPHHQGVZKHQRQHRI WKHSOD\HUUHDFKHVILUVW





93


Follow up Task :Plotting Pictures+DYHVWXGHQWVSORWDQGFRQQHFWVHWVRIFRRUGLQDWHVWKDWUHVXOWLQYDULRXVVKDSHVVXFKDVDVDLOERDWDFKLPQH\RUDSDOPWUHH)RUH[DPSOHLIVWXGHQWVSORWDQGFRQQHFWWKHSRLQWV DQGLWIRUPVDKH[DJRQ+DYHVWXGHQWVGUDZVKDSHVRQJUDSKSDSHUDQGWKHQOLVWWKHFRRUGLQDWHVJLYHRWKHUVWXGHQWVWKHFRRUGLQDWHVIRUWKHVHGHVLJQVWRJUDSK

What are the coordinates that defgine this sailboat ?

Answer : Task-2: Practice Sheet7RSLF &RRUGLQDWH*HRPHWU\1DWXUHRI7DVN 3RVWFRQWHQW&RQWHQW&RYHUDJH 'LVWDQFHEHWZHHQWZRSRLQWVRQDFRRUGLQDWHSODQH/HDUQLQJREMHFWLYHV 6SHFLI\DQG'HVFULEHORFDWLRQRIWKHFLWLHVXVLQJFRPPRQODQJXDJHDQGJHRPHWULFYRFDEXODU\

)LQGWKHGLVWDQFHEHWZHHQSRLQWVDORQJKRUL]RQWDODQGYHUWLFDOOLQHVRIDFRRUGLQDWHV\VWHP7DVN &ODVV:RUNVKHHW([HFXWLRQRIWDVN 7KHWDVNFDQEHSHUIRUPHGLQWKHODVWPLQXWHVRIWKHWHDFKLQJVHVVLRQ$ZRUNVKHHWPD\EHJLYHQWRVWXGHQWVLQJURXS'XUDWLRQ SHULRG&ULWHULDIRUDVVHVVPHQW 7HDFKHU PD\ SUHSDUH D UDWLQJ VFDOH DFFRUGLQJ WR WKHPDUNVDVVLJQHGWRWKLVWDVN)ROORZXS :RUNVKHHWIRUSUDFWLFHPD\EHJLYHQ





94


Figure 1

Class Worksheet)LQGWKHFRRUGLQDWH[\RIWKHYDULRXVFLWLHVRI,QGLDPHQWLRQHGLQWKHZRUNVKHHWEHORZXVLQJWKHILJXUH





95


Cities Coordinates Cities Coordinates

1HZ'HOKL -DLSXU0XPEDL &KDQGLJDUK.RONDWD *XZDKDWL&KHQQDL 3DWQD%DQJDORUH (UQDNXODP/XFNQRZ %KXEDQHVKZDU+\GHUDEDG

)LQGWKHGLVWDQFHEHWZHHQWKHYDULRXVFLWLHVRI,QGLDXVLQJGLVWDQFHIRUPXODPHQWLRQHGLQWKHZRUNVKHHWEHORZXVLQJWKHILJXUH-DLSXU %KRSDO &KDQGLJDUK *XZDKDWL 3DWQD

1HZ'HOKL0XPEDL.RONDWD&KHQQDL%DQJDORUH/XFNQRZ+\GHUDEDG(UQDNXODP%KXEDQHVKZDU

Note:2QHXQLWPHDVXUHVNP





96


Task-3: Class Quiz/Oral Assessment7RSLF &RRUGLQDWH*HRPHWU\1DWXUHRI WDVN 3RVW&RQWHQW&RQWHQW&RYHUDJH 3ORWWLQJRISRLQWV'LVWDQFHIRUPXOD6HFWLRQIRUPXOD$UHDRIWULDQJOH/HDUQLQJ2EMHFWLYHV 7RSORWWKHSRLQWVLQFRRUGLQDWHSODQH

7R DSSO\ GLVWDQFH IRUPXOD WR ILQG WKH GLVWDQFHEHWZHHQWZRSRLQWV 7RXVH6HFWLRQ IRUPXOD WR ILQGDSRLQWEHWZHHQWZRJLYHQSRLQWVZLWKDJLYHQUDWLR 7RILQGWKHDUHDRIDWULDQJOH

7DVN &ODVV4XL]2UDODVVHVVPHQW([HFXWLRQRIWDVN 7KLVWDVNPD\EHSHUIRUPHGE\VSDULQJSHULRGVDIWHUWKHFRPSOHWLRQRIWKHFKDSWHU7KHFODVVPD\EHGLYLGHGLQWHDPV5DPDQXMDQ$U\DEKDW6KDNXQWDOD'HYL5HQH'LVFDUWHV7KHWHDFKHUFDQNHHSZULWLQJWKHVFRUHVRQERDUGDIWHUHDFKURXQG'XUDWLRQ SHULRGV&ULWHULDIRUDVVHVVPHQW 7HDFKHUPD\SUHSDUHDUDWLQJVFDOHDFFRUGLQJWRPDUNVDVVLJQHGWRWKLVWDVN)ROORZXS :RUNVKHHWIRUSUDFWLFLQJPD\EHJLYHQ

Suggested Rounds & questions for the quiz:Rapid Fire Round:,QWKLVURXQGPHQWDOPDWKVKRXOGEHHQFRXUDJHGXVHRISDSHUSHQVKRXOGQRWEHDOORZHG1. 7KHGLVWDQFHRIWKHSRLQW3IURPWKH[D[LVLV

$ % & ' 2. 7KHGLVWDQFHEHWZHHQWKHSRLQWV$DQG% LV

$ % & ' 3. 7KHGLVWDQFHRIWKHSRLQW3IURPWKHRULJLQLV

$ % & ' 4. 7KHGLVWDQFHEHWZHHQWKHSRLQWV DQG LV

$ % & '





97


5. $2%&LVDUHFWDQJOHZKRVHWKUHHYHUWLFHVDUHYHUWLFHV$2DQG%7KHOHQJWKRILWVGLDJRQDOLV$ % & '

6. 7KHSHULPHWHURIDWULDQJOHZLWKYHUWLFHVDQGLV$ % & '

7. 7KHDUHDRID WULDQJOHZLWKYHUWLFHV$% DQG& LV$ % & '

8. 7KHSRLQWV DUH WKHYHUWLFHVRI D$ 5LJKWWULDQJOH % ,VRVFHOHVWULDQJOH& (TXLODWHUDOWULDQJOH ' 6FDOHQHWULDQJOH

9. 3RLQWRQ[D[LVKDVFRRUGLQDWHV$ D % D & D D ' D D

10. 3RLQWRQ\D[LVKDVFRRUGLQDWHV$ D E % D & E ' D E

Buzzer Round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raming Question Round:,QWKLVURXQGHDFKWHDPQHHGVWRIUDPHTXHVWLRQVIURPWKHFKDSWHU7KLVVKRXOGEHDWLPHERXQGURXQG





98


Task-4: MCQ7RSLF &RRUGLQDWH*HRPHWU\1DWXUHRI WDVN 3RVW&RQWHQW&RQWHQW&RYHUDJH &RPSOHWH&KDSWHU7DVN 0&4([HFXWLRQRIWDVN 3ULQWHGDVVLJQPHQWPD\EHJLYHQDIWHUFRPSOHWLQJWKHFKDSWHU$IWHUFRPSOHWLRQRIZRUNVKHHWWHDFKHUFDQDVNFKLOGUHQWRLQWHUFKDQJHWKHLUVKHHWVDTXLFNHYDOXDWLRQFDQEHGRQHE\FODVVGLVFXVVLRQ'XUDWLRQ PLQXWHV&ULWHULDIRUDVVHVVPHQW 7HDFKHU PD\ SUHSDUH D UDWLQJ VFDOH DFFRUGLQJ WR WKHPDUNVDVVLJQHGWRWKLVWDVN

Multiple Choice Questions1. 3RLQW$ LVDWDGLVWDQFHRI

$ XQLWVIURPRULJLQ % XQLWVIURPRULJLQ& XQLWVIURPRULJLQ ' XQLWVIURPRULJLQ2. ,I WKHSRLQWV [ DUHFROOLQHDU WKHQYDOXHRI[ LV$ % & ' 3. 7KHHQGSRLQWVRIGLDPHWHURIFLUFOHDUH7KHUDGLXVRIWKHFLUFOHLV

$ % & ' 4. 7KHUDWLRLQZKLFK[D[LVGLYLGHVWKHOLQHVHJPHQWMRLQLQJWKHSRLQWVLV$ % & ' 5. 7KHSRLQWZKLFKGLYLGHVWKHOLQHVHJPHQWMRLQLQJWKHSRLQWVDQGLQUDWLRLQWHUQDOO\OLHVLQWKH$ ,TXDGUDQW % ,,TXDGUDQW & ,,,TXDGUDQW ' ,9TXDGUDQW6. 7KHSRLQWZKLFK OLHV RQ WKH SHUSHQGLFXODU ELVHFWRU RI WKH OLQH VHJPHQW MRLQLQJ WKH SRLQWV$ DQG% LV$ % & ' 7. 7KHIRXUWKYHUWH['RIDSDUDOOHORJUDP$%&'ZKRVHWKUHHYHUWLFHVDUH$%DQG& LV$ % & ' 8. ,IWKHSRLQW3OLHVRQWKHOLQHVHJPHQWMRLQLQJSRLQWV$DQG%WKHQ$ $3 $% % $3 3% & 3% $% ' $3 $%





100


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ask-6: Remedial Worksheet7RSLF &RRUGLQDWH*HRPHWU\1DWXUHRI WDVN 'HOLYHU\RIFRQWHQW3RVW&RQWHQW&RQWHQW&RYHUDJH 3ORWWLQJRISRLQWV'LVWDQFHIRUPXOD6HFWLRQIRUPXOD$UHDRIWULDQJOH/HDUQLQJ2EMHFWLYHV 7RSURYLGHUHPHGLDOPHDVXUHVRQVSHFLILFWRSLFVEDVHGRQLQGLYLGXDOQHHGV7DVN 1HHG EDVHGZRUNVKHHWV([HFXWLRQRIWDVN $IWHUGLDJQRVWLFWHVWEHIRUHWDNLQJUHPHGLDOWHVWWHDFKHUVKRXOGWDNHDOOSRVVLEOHFXUHVDQGUHPHGLHVLQWKHWHDFKLQJSURFHVVZKLFKFRXOGEH

D &DWHJRU\ZLVHUHPHGLDOFODVVHVQRWPRUHWKDQWRVWXGHQWVLQHDFKFODVV:LWK WKH ODUJH FODVV VL]H WKLV FRXOG EHWWHU EHDFKLHYHGZLWKJURXSZRUN7HDFKHUFDQGLYLGHWKHFODVVLQVPDOOJURXSVRIVWXGHQWVLQHDFKJURXSWKHUHVKRXOGEHRQHJRRGSHUIRUPHUZKRFDQKHOSRXW RWKHU PHPEHUV RI KLVKHU JURXS ZKR DUHFRPSDUDWLYHO\XQGHUDFKLHYHUVEDVHGRQWKHUHVXOWRIGLDJQRVWLFWHVWFODVVREVHUYDWLRQ

E 3HUVRQDODQGLQGLYLGXDODWWHQWLRQE\WHDFKHUF 1RKXPLOLDWLRQG 6SHFLDOFDUHIXOO\GHYLVHG8$$XQGHUDFKLHYHUVDVVLJQPHQW6LPSOHU6LPSOH&RPSOH[





101


H 5HDG5HUHDG:ULWH5H:ULWH5HSURGXFH'ULOOI *URXSVWXGLHVJURXSOHDUQLQJJ 0LFURQRWHVK 7HDFKLQJVHOHFWHGSRUWLRQRIV\OODEXVRQO\

)RUWDNLQJUHPHGLDOWHVWVWHDFKHUVKRXOGJURXSXSFKLOGUHQIDFLQJVDPHSUREOHPVVKRXOGSUHSDUHHDFKJURXSVQHHGEDVHGZRUNVKHHWV'XUDWLRQ SHULRG&ULWHULDIRUDVVHVVPHQW 2EVHUYDWLRQRIJURXSEDVHGUHPHGLDOWHDFKLQJ

5XEULFIRUUHPHGLDOZRUNVKHHWV)ROORZXS 5HPHGLDOSUDFWLFHVKHHWVRIVXEWRSLFVIUHTXHQWUHWHVWV

Need Based Remedial Worksheets:

Memory Based Remedial Sheet

:ULWH IRUPXODH 'LVWDQFHIRUPXOD 6HFWLRQIRUPXOD 0LGSRLQWIRUPXOD &HQWURLGIRUPXODJLYHQWKHFRRUGLQDWHVRIWKHYHUWLFHVRIWULDQJOH $UHDRIWULDQJOHJLYHQWKHFRRUGLQDWHVRILWVYHUWLFHV

Conceptual Understanding Based Remedial sheet

)LOO LQ WKH EODQNV 7KHFRRUGLQDWHVRIDQ\JHQHUDOSRLQWRQ[D[LVLVBBBB 7KHFRRUGLQDWHVRIDQ\JHQHUDOSRLQW\D[LVBBBB ,Q RUGHU WR SURYH WKH WKUHH JLYHQ SRLQWV $[ \ %[ \ DQG &[ \ DUH WKHYHUWLFHVRIDQHTXLODWHUDOWULDQJOHZHQHHGWRVKRZWKDW$%%&&$DUHBBBBB ,Q RUGHU WR SURYH WKH WKUHH JLYHQ SRLQWV $[ \ %[ \ DQG &[ \ DUH WKHYHUWLFHVRIDQLVRVFHOHVWULDQJOHZHQHHGWRVKRZWKDWBBBBBBBBBBBBBBBBBBBBB ,Q RUGHU WR SURYH WKH WKUHH JLYHQ SRLQWV $[ \ %[ \ DQG &[ \ DUH WKHYHUWLFHVRIDULJKWWULDQJOHZHQHHGWRYHULI\BBBBBBBBWKHRUHP





102


Application Based Remedial Sheet. 7KHEDVH$%RIWZRHTXLODWHUDOWULDQJOHV$%&DQG$%&ZLWKVLGHDOLHVDORQJWKH[D[LVVXFKWKDWWKHPLGSRLQWRI$%LVDWWKHRULJLQ)LQGFRRUGLQDWHVRIYHUWLFHV&DQG&RIWKHWULDQJOHV ,I3DQG4DUH WZR3RLQWVZKRVHFRRUGLQDWHVDUH DWDW UHVSHFWLYHO\DQG6 LV WKHSRLQW DE6KRZWKDW

63 64 LV LQGHSHQGHQWRI W )LQG WKH FRRUGLQDWHV RI WKH FHQWUH RI WKH FLUFOH SDVVLQJ WKURXJK WKH SRLQWV DQG$OVRILQG WKHUDGLXV 'HWHUPLQHWKHUDWLRLQZKLFKWKHOLQHVHJPHQW[\ GLYLGHVWKHVHJPHQWMRLQLQJWKHSRLQWV DQG

Task-7: Project Work7RSLF &RRUGLQDWH*HRPHWU\1DWXUHRI WDVN 3RVW&RQWHQW&RQWHQW&RYHUDJH :KROHFKDSWHU/HDUQLQJ2EMHFWLYHV 7RDSSO\WKHNQRZOHGJHRI&RRUGLQDWH*HRPHWU\LQUHDOOLIH7DVN 3URMHFWZRUN([HFXWLRQRIWDVN 7KHFODVVPD\EHGLYLGHGLQWRJURXSVRIWRVWXGHQWV6WXGHQWVOLYLQJLQWKHVDPHQHLJKERUKRRGPD\EHDVVLJQHGLQ RQH JURXS (DFK JURXS LV VXSSRVHG WRZRUN DV DWHDPIRUWKHFRPSOHWLRQRISURMHFW)HZPHPEHUVFDQWDNHUHVSRQVLELOLW\RIJDWKHULQJUHTXLUHGLQIRUPDWLRQIRUWKHSURMHFWRWKHUVFDQZRUNIRUPDNLQJDURXJKGUDIWIURPWKHJDWKHUHGLQIRUPDWLRQ$OOPHPEHUVVKRXOGGLVFXVVWKHGUDIWJLYHWKHLULQSXWV$IWHUILQDOL]LQJIHZPHPEHUVFDQZULWHVWKHUHSRUW

7KHSURMHFWZRUNFRPSOHWHVZLWKWKHVXEPLVVLRQRIUHSRUW$ VPDOO VHPLQDU FRXOG EH FRQGXFWHGZKHUH WKH WHDPOHDGHUVKRXOGSUHVHQWWKHLUZRUNWRWKHFRPSOHWHFODVV'XUDWLRQ WR GD\V&ULWHULDIRUDVVHVVPHQW 7KHSURMHFWZRUNFRXOGEHDVVHVVHG DFFRUGLQJWR WKHIROORZLQJSDUDPHWHUV

7HDP6SLULW ,GHQWLILFDWLRQRISURMHFW 3URFHGXUHDGRSWHG 3UHSDUDWLRQRI5HSRUW &ODVVSUHVHQWDWLRQRIWKHZRUN)ROORZXS





103


Suggested Projects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





104


3URMHFW7LWOH 3ORWDJULGRIFRRUGLQDWHVRQ\RXUFLW\PDSDQGILQGWKHGLVWDQFHVEHWZHHQLPSRUWDQWODQGPDUNV7HDPVL]H VWXGHQWV'XUDWLRQ ZHHN/HDUQLQJ2EMHFWLYH 7R XQGHUVWDQG DQG DSSUHFLDWH WKH XVH RI FRRUGLQDWHJHRPHWU\LQUHDOZRUOG+LQWVDQG6XJJHVWLRQV ,PSRUWDQWODQGPDUNVFRXOGEHKRPHVFKRROVKRSSLQJFRPSOH[HWF

*HW D PDS RI WKHLU FLW\ DQG VXSHULPSRVH WKHFRRUGLQDWHVRQLW ,GHQWLI\WKHFRRUGLQDWHVRIWKHLPSRUWDQWODQGPDUNV &DOFXODWH WKH JUDSKLFDO GLVWDQFH EHWZHHQ WKHODQGPDUNV 8VLQJ WKH VFDOH FDOFXODWH WKH DFWXDO GLVWDQFH LQNPPL





105


3URMHFW7LWOH )LQGRXWKRZDLUSODQHQDYLJDWLRQDQGQDYDOQDYLJDWLRQXVHVFRRUGLQDWHJHRPHWU\7HDPVL]H VWXGHQWV'XUDWLRQ ZHHN/HDUQLQJ2EMHFWLYH 7R XQGHUVWDQG DQG DSSUHFLDWH WKH XVH RI FRRUGLQDWHJHRPHWU\LQQDYLJDWLRQ+LQWVDQG6XJJHVWLRQV $LUSODQHVDQG1DYDOVKLSVUHO\RQWKHYDVWFRRUGLQDWHRIWKHHDUWKVPDJQHWLFILHOGIRUFRPPXQLFDWLRQ





106

Introduction to Trigonometry Formative Assessment Manual for Teachers

CHAPTER-8Introduction to Trigonometry

1. ,Q)LJ VLQ& "

2. 7KHZRUGWULJRQRPHWU\LVGHVLUHGIURPWKH*UHHNZRUGVDQG 3. ,IVLQ$ VLQ$)LJWKHQILQG%&

Task-1: Do as directed7RSLF ,QWURGXFWLRQWR7ULJRQRPHWU\1DWXUHRI WDVN &RQWHQW&RQWHQW&RYHUDJH %DVLFVRIWULJRQRPHWU\75DWLRVRI/HDUQLQJ2EMHFWLYHV 7RUHFDOOGHILQLWLRQRIEDVLFUDWLRV

7RUHFDOODQGILQGYDOXHRI75DWLRRIVSHFLDODQJOHV([HFXWLRQRIWDVN 7KH WHDFKHU PD\ SURYLGH SULQWHG ZRUNVKHHW WR WKHVWXGHQWV'XUDWLRQ 3HULRG&ULWHULDIRU$VVHVVPHQW PDUN IRU HDFK FRUUHFW DQVZHU FDQEH DZDUGHG





108


MCQ Worksheet

Q.1. 9DOXHRI IRU6LQ ZKHUH LV $ % & '

Q.2. 9DOXH RI 6HF &RW LV $ % & '

Q.3. 3URGXFW WDQ WDQ WDQ WDQ LV $ % & '

Q.4. WDQ + LVHTXDO WR $ &RW % &RV & &RVHF ' 6HF

Q.5. ,I$% &RW% WKHQ WDQ$ LV HTXDO WR $ % & '

Task-2: MCQ Worksheet7RSLF ,QWURGXFWLRQWR7ULJRQRPHWU\1DWXUHRI WDVN &RQWHQW&RQWHQW&RYHUDJH &RPSOHWH&KDSWHU/HDUQLQJ2EMHFWLYHV 75DWLRVRIVSHFLDODQJOHV

7ULJRQRPHWU\,GHQWLWLHV([HFXWLRQRIWDVN 7KHWHDFKHUPD\JLYHSULQWHGZRUNVKHHWWRWKHVWXGHQWV'XUDWLRQ 3HULRG&ULWHULDIRU$VVHVVPHQW )RUHDFKFRUUHFWDQVZHUPDUNPD\EHDOORWHG

,QFDVH0&4LVXVHGDVSUDFWLVHZRUNVKHHWWKHPLWLVQRWQHFHVVDU\WRDVVLJQPDUNV)ROORZXS &ODVVURRP'LVFXVVLRQ

$QVZHUV WR WKHTXHVWLRQVDQGFRPPRQHUURUVPD\EHGLVFXVVHGLQWKHFODVV

s

s c

c c c s

c

-





109

Formative Assessment Manual for Teachers Introduction to Trigonometry

Q.6. 0D[LPXPYDOXHRI &RVHF LV$ % & '

Q.7. ,I &RV 6LQ = = WKHQYDOXHRI +$ % & '

Q.8. ,I 6LQ $% &RV $% WKHQ$ $ % % $ % & $ % ' $ %

Task-3: Remedial Worksheet7RSLF ,QWURGXFWLRQWR7ULJRQRPHWU\1DWXUHRI WDVN 1HHG EDVHG&RQWHQW&RYHUDJH 1HHG EDVHG([HFXWLRQRIWDVN &RPPRQSUREOHPVFDQEHWDNHQXSLQWKHFODVV

,QGLYLGXDO UHPHGLDOZRUNVKHHWVFDQEHJLYHQ WRVWXGHQWVDVSHUQHHG'XUDWLRQ ,QGLYLGXDOOHDUQHUVQHHGEDVHG

1. )LOOXS$ WDQ % WDQ

WDQ WDQ & &RV ' 6LQ

&RV 6LQ ( 6HF ) &RVHF

6HF &RVHF * 6LQ + 6HF

6LQ 6HF , WDQ , 6HF

WDQ 6HF

c

c s

s c

cc

ss

ss

ss

s

s

ss

cc





110


2. ([SUHVV&RW WDQ LQ WHUPVRI $ WULJRQRPHWULFUDWLRVRIDQJOHVEHWZHHQDQG

&RW WDQ &RW WDQ

% ([SUHVV&RV6LQLQWHUPVRIWULJRQRPHWULFUDWLRVRIDQJOHVEHWZHHQDQG &RV 6LQ &RV 6LQ

3. )LQGWKHHUURUVLIDQ\DQGFRUUHFWLW$ 6LQ 6LQ &RV &RV %

6LQ 6LQ &RV &RV 6LQ 6LQ &RV &RV

6LQ 6LQ &RV &RV + 6LQ 6LQ &RV &RV

& 6LQ 6LQ &RV &RV '

6LQ 6LQ &RV &RV 6LQ 6LQ &RV &RV

6LQ &RV 6LQ &RV &RV 6LQ

( 6LQ 6LQ &RV &RV 6LQ 6LQ &RV &RV 6LQ &RV &RV 6LQ

c

c

c

c s

c s

c s

cs s

c

cs s

c

cs s

c

cs s

c

cs s

c

cs s

c

cs

cs s

c

cs s

c

cs s

c

cs c

s

cs c

s

s sc c





111

Formative Assessment Manual for Teachers Some Applications of Trigonometry

CHAPTER-9Some Applications of Trigonometry

Suggested Formative Assessment Tasks

Task-1: Recognize & Fill7RSLF $SSOLFDWLRQRI7ULJRQRPHWU\1DWXUHRI WDVN 3UHFRQWHQW&RQWHQW&RYHUDJH $QJOHRIHOHYDWLRQGHSUHVVLRQOLQHRIVLJKW7DVN :RUNVKHHW([HFXWLRQRIWDVN 3ULQWHGZRUNVKHHWPD\EHJLYHQWRWKHVWXGHQWV'XUDWLRQ PLQXWHV&ULWHULDIRUDVVHVVPHQW 7HDFKHUPD\GLVFXVVWKHZRUNVKHHWDQGREVHUYHWKHOHYHORIXQGHUVWDQGLQJ,WLVQRWQHFHVVDU\WRJLYHPDUNVIRUWKLVDVVHVVPHQW,WPD\EHXVHGIRUGLDJQRVWLFSXUSRVH

Worksheet)LJXUH $QJOHRI $QJOHRI /LQHRI(OHYDWLRQ GHSUHVVLRQ 6LJKW

s





112

Some Applications of Trigonometry Formative Assessment Manual for Teachers

)LJXUH $QJOHRI $QJOHRI /LQHRI(OHYDWLRQ GHSUHVVLRQ 6LJKW





113


Task-2: Class Worksheet7RSLF $SSOLFDWLRQRIWULJRQRPHWU\1DWXUHRI WDVN &RQWHQW&RQWHQW&RYHUDJH )LJXUHIRUPDWLRQIURPZRUGSUREOHPV/HDUQLQJ2EMHFWLYHV 7R UHDG DQG DQDO\]H ZRUG SUREOHP DQG WR GUDZ WKHFRUUHVSRQGLQJILJXUH7DVN &ODVV:RUNVKHHW([HFXWLRQRIWDVN :RUNVKHHWFRQWDLQLQJTXHVWLRQVDQGEODQNVSDFHWRGUDZILJXUHPD\EHJLYHQWRHDFKFKLOG7KH\ZRXOGEHWKHQDVNHGWRGUDZWKHFRUUHVSRQGLQJILJXUHVIRUHDFKTXHVWLRQ

$OWHUQDWLYHO\7HDFKHUPD\ZULWHWKHTXHVWLRQRQERDUG

'XUDWLRQ SHULRG&ULWHULDIRUDVVHVVPHQW 7HDFKHUPD\SUHSDUHDUDWLQJVFDOHDFFRUGLQJWRPDUNVDVVLJQHGWRWKLVWDVN)ROORZXS :RUNVKHHWIRUSUDFWLFLQJPD\EHJLYHQ

Worksheet)RUHDFKSUREOHPJLYHQEHORZGUDZDILJXUHWRLOOXVWUDWHWKHVLWXDWLRQ7KHILUVWRQHLVGRQHIRU\RX$ WRZHU VWDQGV YHUWLFDOO\ RQ WKHJURXQG)URPDSRLQWRQWKHJURXQGZKLFKLVPDZD\IURPWKHIRRWRIWKHWRZHUWKHDQJOHRIHOHYDWLRQRIWKHWRSRI WKH WRZHU LV IRXQG WREH

$Q REVHUYHU P WDOO LV PDZD\IURPDFKLPQH\7KHDQJOHRIHOHYDWLRQ RI WKH WRS RI WKH FKLPQH\IURPKHUH\HVLV





114


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





115


Task-3: Question Framing7RSLF $SSOLFDWLRQRIWULJRQRPHWU\1DWXUHRI WDVN &RQWHQW&RQWHQW&RYHUDJH )UDPLQJZRUGSUREOHPVIURPJLYHQILJXUH/HDUQLQJ2EMHFWLYHV 7RIUDPHDZRUGSUREOHPVIURPRQDJLYHQILJXUH7DVN :RUNVKHHW([HFXWLRQRIWDVN :RUNVKHHWFRQWDLQLQJILJXUHVDQGEODQNVSDFHWRZULWHTXHVWLRQPD\EHJLYHQWRHDFKFKLOG7KH\ZRXOGEHWKHQDVNHGWRIUDPHDWOHDVWRQHTXHVWLRQRQWKHJLYHQILJXUH'XUDWLRQ SHULRG&ULWHULDIRUDVVHVVPHQW 7HDFKHUPD\GLVFXVVWKHTXHVWLRQVIUDPHGE\VWXGHQWVDQGREVHUYHWKHLUOHYHORIWKLQNLQJLPDJLQDWLRQ,WLVQRWQHFHVVDU\WRJLYHPDUNVIRUWKLVDVVHVVPHQW

WorksheetFigure World Problem





116


Figure World Problem





117


Task-4: Home Assignment7RSLF $SSOLFDWLRQRIWULJRQRPHWU\1DWXUHRI WDVN 3RVW&RQWHQW&RQWHQW&RYHUDJH &RPSOHWH&KDSWHU/HDUQLQJ2EMHFWLYHV 7RDSSO\WKHNQRZOHGJHRIWULJRQRPHWU\LQVROYLQJUHDOOLIHSUREOHPV7DVN +RPH$VVLJQPHQW([HFXWLRQRIWDVN 3ULQWHGDVVLJQPHQWPD\EHJLYHQDIWHUFRPSOHWLQJWKHFKDSWHU'XUDWLRQ GD\V&ULWHULDIRUDVVHVVPHQW )ROORZ5XEULFIRU+:$VVLJQPHQWV)ROORZXS 5HIHUHQFHPDWHULDO LQ WKHIRUPRI LPSRUWDQWSRLQWV WRUHPHPEHUFDQEHJLYHQDVDVXSSRUWPDWHULDO

Figure World Problem





118


Home Assignment

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

VWUDLJKWOLQHZLWKLWDUHFRPSOHPHQWDU\3URYHWKDWWKHKHLJKWRIWKHWRZHULV DE





120


(QVXUHWKDWWKHZHLJKWDWWKHHQGRIWKHVWULQJKDQJVEHORZWKHSURWUDFWRU 0DUNGHJUHHVLQVH[DJHFLPDOVFDOHZLWKDW WKH ORZHVWDQG WRSURFHHGLQJERWKFORFNZLVHDQGDQWLFORFNZLVH>)LJ@

Fig. 1

(B) To determine the height of an object: )LUVWPHDVXUHWKHGLVWDQFHRIWKHREMHFWIURP\RX/HWWKHGLVWDQFHEHG /RRNWKURXJKWKHVWUDZRUSLSHDWWKHWRSRIWKHREMHFW0DNHVXUH\RXFDQFOHDUO\VHHWKH WRSRI WKHREMHFW +ROGWKHFOLQRPHWHUVWHDG\DQGOHW\RXUSDUWQHUUHFRUGWKHDQJOHWKHVWULQJPDNHVRQWKHVFDOHRIWKHFOLQRPHWHU/HWWKLVDQJOHEH"

Observations:

8VLQJWULJRQRPHWULFUDWLRWDQ q KHLJKWGLVWDQFH KG

K G WDQq,I IRUH[DPSOHG P DQGq

K WDQ PRemark:

6WXGHQWVPD\EHDVNHG WRFKDQJH WKHGLVWDQFHRI WKHREMHFW E\HLWKHUPRYLQJ WKHREMHFWRUE\FKDQJLQJWKHLUSRVLWLRQDQGQRWHKRZWKHDQJOHRIHOHYDWLRQYDULHV7KH\ZLOOQRWLFHWKDWWKRXJKGDQG qZLOOYDU\WKHSURGXFWK GWDQqZLOOEHFRQVWDQWZLWKLQPHDVXUHPHQWHUURU

coordinate geometry

Documents