,ĂůĂŵĂŶϰϰHIDUP HEMAT *UDGLHQJDULV\DQJPHODOXLWLWLN$±GDQ%±±DGDODK« $ % ଵ ସ & ±ଵ ସ ' ± 'LNHWDKXLJDULVJGHQJDQSHUVDPDDQ[±\ 7LWLN±WLWLNEHULNXWWHUOHWDN SDGDJDULVJkecuali« $ % ±± & ± ' ± 3HUKDWLNDQSHUQ\DWDDQEHULNXWff L JDULVg VHMDMDUJDULVhPDNDPJ PK LL JDULVg VHMDMDUJDULVhPDNDPJ[PK ± LLL JDULVg WHJDNOXUXVJDULVhPDNDPJ PK LY JDULVg WHJDNOXUXVhPDNDPJ[PK ± 3HUQ\DWDDQGLDWDV\DQJEHQDUDGDODK« $ LGDQLLL % LLGDQLY & LGDQLY ' LLGDQLLL fl ,EX%XGLLQJLQPHQGDSDWWDPEDKDQSHQJKDVLODQLDPHPEXNDZDUXQJPDNDQ GL UXPDKQ\D" 0RGDO DZDO ,EX %XGL 5S GLD EHUKDVLO PHQDEXQJ 5S WLDS EXODQQ\D %XNX WDEXQJDQ ,EX %XGL SDGD DZDO PHPEXND ZDUXQJ 5S %LOD VDOGR DNKLU \ WDEXQJDQ ,EX %XGL GLQ\DWDNDQ VHEDJDLIXQJVLZDNWXGDODP[EXODQPDNDSHUVDPDDQQ\DDGDODK« $ \ [ % \ [ & \ [ ' \ [ ffi 'LNHWDKXLSHUVDPDDQJDULVgGDQJDULVlEHUWXUXW±WXUXWDGDODK[\ GDQ\ ò[±.RRUGLQDWWLWLNSRWRQJJDULVJGDQJDULVl DGDODK « $ ± % ±± & ± ' Hidup Hemat 45
,ĂůĂŵĂŶϰϱHIDUP HEMAT 3HUVDPDDQJDULV\DQJPHODOXL±GDQJUDGLHQQ\Dെ DGDODK« $ [\ % [±\ & ±[\ ' [\ ± 3HUVDPDDQJDULV\DQJPHODOXL±flGDQ±±DGDODK« $ [\± % [±\ & ±[\ ' [\ 'LNHWDKXLSHUVDPDDQJDULVJDGDODK[±\ *DPEDUJDULV\DQJVHMDMDU JDULVJGDQPHODOXLDGDODK« %HULNXW LQL DGDODK FRQWRK ± FRQWRK VLVWHP SHUVDPDDQ OLQHDU GXD YDULDEHO kecuali« $ DE D ±E % D ±E± DE & \ [± [\ ' [ ±\ \ [ $ & % ' 46 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϰϲHIDUP HEMAT +DVLOSHQMXPODKDQELODQJDQDGDODKGDQVHOLVLKGXDELODQJDQWHUVHEXW %HUDSDKDVLONDOLNHGXDELODQJDQWHUVHEXW" $ % & ' ,EX PHPEHOL NJ VDODN GDQ NJ UDPEXWDQ KDUXV PHPED\DU 5S +DUJDNJVDODNGDQNJUDPEXWDDGDODK5S3DN'RQLPHPEHOLNJ VDODNGDQNJUDPEXWDQPHQ\HUDKNDQVHOHPEDUXDQJVHUDWXVULEXDQEHUDSD XDQJNHPEDOLDQ3DN'RQL" $ 5S % 5S & 5S ' 5S 8DQJ $OL GLWDPEDK GXD NDOL XDQJ %XGL GLWDPEDK WLJD NDOL XDQJ &KLFD VDPD GHQJDQ5S7LJDNDOLXDQJ$OLGLWDPEDKGXDNDOLXDQJ%XGLGLWDPEDK XDQJ &KLFD VDPD GHQJDQ 5S fl%HUDSD XDQJ$OL GLWDPEDK XDQJ%XGL GLWDPEDKXDQJ&KLFD" $ 5S % 5S & 5S ' 5S 6HRUDQJMXUXSDUNLUPHPXQJXWUHVWULEXVLNHQGDUDDQ\DQJWHUGLULGDULPRWRU GDQPRELO8DQJSDUNLUXQWXNPRELO5SGDQXQWXNPRWRU5SXDQJ SDUNLUVHOXUXKQ\DVHOXUXKQ\D5S%HUDSDEDQ\DNPRELO\DQJWHUSDUNLU GLDUHDMXUXSDUNLUWHUVHEXW" $ % & ' fl3DGD SHQLODLDQ DNKLU PRGXO WHUGDSDW VRDO SLOLKDQ JDQGD GDQ LVLDQ VLQJNDW 6D\D PHQJHUMDNDQ EHQDU VRDO SLOLKDQ JDQGD GDQ VRDO LVLDQ PHQGDSDW QLODLVHGDQJNDQ'HZLPHQJHUMDNDQEHQDUflVRDOSLOLKDQJDQGDGDQVRDO LVLDQPHQGDSDW QLODL %HUDSD QLODL \DQJ GLSHUROHK 'L\DK ELODPHQJHUMDNDQ EHQDUVRDOSLOLKDQJDQGDGDQVRDOLVLDQ" $ fl % fl & fl ' Hidup Hemat 47
,ĂůĂŵĂŶϰϳHIDUP HEMAT ffi8PXU 5LWD VHNDUDQJ VDPD GHQJDQ GXD NDOL XPXU 1HQL VHWDKXQ \DQJ ODOX 6HOLVLKXPXUPHUHNDWDKXQ%HUDSDMXPODKXPXUPHUHNDVHNDUDQJ" $ WDKXQ % ffiWDKXQ & WDKXQ ' WDKXQ 3DGDVHJLWLJD$%&GLNHWDKXLEHVDUVXGXW$ 6HOLVLKVXGXW%GDQVXGXW &DGDODK6XGXWWHUNHFLOSDGDVHLWLJD$%&EHVDUQ\DDGDODK $ fl % & ' ,, .HUMDNDQVHEDJDLPDQDPHVWLQ\DLWHP 6HJLWLJD $%& VLNX ± VLNX GL VXGXW $ GLJDPEDU SDGD NRRUGLQDW NDUWHVLXV .RRUGLQDW$±GDQ%±7HQWXNDQSHUVDPDDQJDULV \DQJPHODOXL VLVL$&SDGDVHJLWLJD$%&WHUVHEXW 6HEXDK UXPDK PHQJJXQDNDQ JHQHUDWRU JHQVHW PHPEXWXKDNDQ fl OLWHU EDKDQEDNDUWLDSMDPQ\D3HPLOLNUXPDKPHQ\LDSNDQOLWHUEDKDQEDNDUXQWXN PHQJKLGXSNDQJHQVHWQ\D D *DPEDUODKGDODPJUDILNNDUWHVLXV\DQJPHQ\DWDNDQIXQJVLZDNWXSDGDVLVD EDKDQEDNDU E 3DGD JUDILN WHUVHEXW GLPDQD $QGD PHQJHWDKXL NDSDQ EDKDQ EDNDU WHODK KDELV"6HWHODKEHUDSDODPDEDKDQEDNDUWHUVHEXWKDELV" 6HOLVLKXVLDNDNDNGDQDGLNDGDODKflWDKXQ8VLDNDNDNVHNDUDQJWLJDNDOLXVLD DGLNGXDWDKXQ\DQJODOX%HUDSDXVLDNDNDNVHNDUDQJ" *XQDNDQPHWRGHJUDILNXQWXNPHQ\HOHVDLNDQVLVWHPSHUVDPDDQGXDYDULDEHO EHULNXW[\ GDQ\ ±[ <XGKDPHPEHOLNJVDODNGDQNJPDQJJDVHKDUJD5SVHGDQJNDQ )LNDPHPEHOLNJVDODNGDQNJPDQJJDVHSHUWL\DQJGLEHOL<XGKDVHKDUJD 5S %LOD 1LQLN LQJLQ PHPEHOL NJ VDODN GDQ NJ PDQJJD WHUVHEXW EHUDSDGLDKDUXVPHPED\DU" 48 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϰϴHIDUP HEMAT H. Rubrik penilaian, Kunci Jawaban, dan Pembahasan Modul 2 .XQFL-DZDEDQGDQ5XEULN3HQLODLDQ 3LOLKDQ*DQGD ««««««««««WLDSLWHPVNRU 1R -DZDEDQ 1R -DZDEDQ ' ' $ % & $ ' & % & ' % & & fl ' fl & ffi $ ffi % $ % %62$/85$,$1 ««VNRUPD[ 'LNHWDKXLffl6HJLWLJD$%&VLNX±VLNXGLVXGXW$ $±GDQ%± 6RDOffl3HUVDPDDQJDULV\DQJPHODOXLVLVL$& -DZDEffl6HJLWLJD$%&VLNX±VLNXGLVXGXW$PDND$%⊥$& ࢟ࢋ %$P ࢟ି࢟ ൌ ࢞ࢋ ࢞ି࢞ ൌ ି ିିሺିሻ ൌ ି ିା ൌ ି ି ൌ «««««« .DUHQD$%⊥$&PDNDP$%[P$& ± «««««« ⇔[P$& ± ⇔P$& ± «««««« 3HUVDPDDQJDULV\DQJPHODOXLVLVL$&DUWLQ\DJDULVWHUVHEXWPHODOXL$± GDQP$& ± -DGLSHUVDPDDQJDULVWHUVHEXWDGDODKff \±\$ P[±[$ «««««« ⇔\± ± [±± ⇔\± ± [ ⇔\± ± [± ⇔\ ± [ «««««« ⇔\ ±[ffi⇔[\±ffi «««««« Hidup Hemat 49
,ĂůĂŵĂŶϰϵHIDUP HEMAT 'LNHWDKXLffl%%0JHQVHW flOLWHUMDP %%0\DQJDGDOLWHU 6RDOff D *DPEDUODKGDODPJUDILNNDUWHVLXV\DQJPHQ\DWDNDQIXQJVLZDNWXSDGDVLVD EDKDQEDNDU E 3DGD JUDILN NDSDQ EDKDQ EDNDUWHODK KDELV"6HWHODK EHUDSD ODPD EDKDQ EDNDUWHUVHEXWKDELV" -DZDEff «««««« X D *DULV WHUVHEXW SDGD SRVLVL [ JHQVHW EHOXP PHQJJXQDNDQ %%0 PDND %%0 PDVLK OLWHU \DLWX SDGD VHGDQJNDQ NHEXWXKDQ%%0SHUMDP\DLWXEHUNXUDQJflOLWHUSHUMDPDWDXP ± PHUXSDNDQJUDGLHQJDULVVHKLQJJDSHUVDPDDQJDULVWHUVHEXWDGDODK \ ± [ «««««« E %DKDQ EDNDU WHUVHEXW KDELV NHWLND JDULV PHPRWRQJ VXPEX [ DWDX QLODL\ \DLWXSDGDWLWLNP DUWLQ\DVHWHODK MDP%%0 WHUVHEXWKDELV «««««« 'LNHWDKXLffl0LVDOXVLDNDNDNVHNDUDQJ D XVLDDGLNVHNDUDQJ E 6HOLVLKXVLDNDNDNGDQDGLNDGDODKflWDKXQ D±E fl 8VLDNDNDNVHNDUDQJWLJDNDOLXVLDDGLNGXDWDKXQ\DQJODOX D E± 6RDOffl8VLDNDNDNVHNDUDQJ -DZDEffl3HUKDWLNDQ63/'9EHULNXWff D±E fl D E± «««««« Y I[ P ; 50 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϱϬHIDUP HEMAT 'HQJDQPHWRGHVXEVWLWXVLPDND D±E fl ⇔ E±±E fl ⇔ E±±E fl ⇔ E±±E fl ⇔ E ⇔ E «««««« -DGLD±E fl⇔D± fl ⇔D «««««« 8VLDNDNDNVHNDUDQJWDKXQ «««««« *XQDNDQPHWRGHJUDILNXQWXNPHQ\HOHVDLNDQVLVWHPSHUVDPDDQGXDYDULDEHO EHULNXW[\ GDQ\ ±[ -DZDEffl [\ JDULVWHUVHEXWPHODXLGDQ «««««« \ ±[JDULVWHUVHEXWPHODXLGDQ «««««« *DPEDUJUDILN «««««« X 7LWLNSRWRQJQ\D7 ;͕± «««««« 'LNHWDKXLfflPLVDOKDUJDVDODN [UXSLDKNJ KDUJDPDQJD \UXSLDKNJ <XGKDffl[\ )LND ffl[\ 6RDOffl+DUJDNJVDODNGDQNJPDQJD -DZDEffl3HUKDWLNDQ63/'9EHULNXWff [\ [\ «««««« ; Y I[ 7 ;͕± Hidup Hemat 51
,ĂůĂŵĂŶϱϭHIDUP HEMAT 'HQJDQPHWRGHHOLPLQDVLff [\ GLNDOL [ffi\ [\ GLNDOL [\ fl±GLNXUDQJ \ ⇔ \ «««««« [\ ⇔[ ⇔[ ⇔[± ± ⇔[ ⇔[ «««««« +DUJDNJVDODNGDQNJPDQJD 5S5S 5S «««««« 1LODL$NKLU 6NRU3HUROHKDQ6RDO3LOLKDQ*DQGD6NRU3HUROHKDQ6RDO8UDLDQ 52 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
Modul 2 I. Kriteria Pindah/ Lulus Modul .LULWHULDSLQGDKOXOXVPRGXOSHVHUWDGLGLNVHWHODKPHPHQXKLV\DUDWEHULNXW 0HQ\HOHVDLNDQVHOXUXKPDWHULSHPEHODMDUDQff 0HQJHUMDNDQVHOXUXKODWLKDQVRDOSHQXJDVDQff 0HQGDSDWQLODLNHWXQWDVDQEHODMDUGDULSHQLODLDQDNKLUPRGXOff $SDELOD QLODL PDVLK GL EDZDK NULWHULD NHWXQWDVDQ EHODMDU PDND GLODNXNDQ UHPHGLDO %DJLSHVHUWDGLGLN\DQJQLODLSHQLODLDQDNKLUPRGXOPDNDELVDPHODMXWNDQ NHPRGXOVHODQMXWQ\D %HUGDVDUNDQ KDVLO DQDOLVLV SHQLODLDQ DNKLU PRGXO SHVHUWD GLGLN \DQJ EHOXP PHQFDSDLNHWXQWDVDQEHODMDUGLEHULNHJLDWDQSHPEHODMDUDQUHPHGLDOGDODPEHQWXNff ELPELQJDQSHURUDQJDQMLNDSHVHUWDGLGLN\DQJWXQWDVEHODMDUff EHODMDU NHORPSRN MLND SHVHUWD GLGLN \DQJ WXQWDV EHODMDU DQWDUD VDPSDL GHQJDQGDQ SHPEHODMDUDQ XODQJ PDQGLUL MLND SHVHUWD GLGLN \DQJ WXQWDV EHODMDU OHELK GDUL WHWDSLNXUDQJGDUL 7XWRUPHPEHULNDQUHPHGLDONHSDGDSHVHUWDGLGLN\DQJEHOXPPHQFDSDLDWDXLQJLQ PHQLQJNDWNDQNRPSHWHQVLGDVDU%HULNXWDOWHUQDWLIUHPHGLDO\DQJELVDGLEHULNDQ 7XWRU DWDX WHPDQ GDODP WLQJNDWDQ \DQJ VDPD DWDX GL DWDVQ\D PHPELPELQJ NHPEDOL SHVHUWD GLGLN \DQJ PDVLK PHQJDODPL NHVXOLWDQ GDODP PHPDKDPL PHQHQWXNDQGDQPHQ\HOHVDLNDQPDVDODK\DQJEHUNDLWDQPDWHULPersamaan Garis Lurus 7XWRU DWDX WHPDQ GDODP WLQJNDWDQ \DQJ VDPD DWDX GL DWDVQ\D PHPELPELQJ NHPEDOL SHVHUWD GLGLN \DQJ PDVLK PHQJDODPL NHVXOLWDQ GDODP PHPDKDPL PHQHQWXNDQ GDQ PHQ\HOHVDLNDQ PDVDODK \DQJ EHUNDLWDQ PDWHUL Sistem Persamaan Linear Dua Variabel (SPLDV) Hidup Hemat 53
,ĂůĂŵĂŶϱϯHIDUP HEMAT Modul 2 J. Daftar Pustaka 1HJRUR67GDQ%+DUDKDSffiffiffiEnsiklopedia Matematika-DNDUWDffl*KDOLD,QGRQHVLD 3DQGXDQ 3HQLODLDQ ROHK 3HQGLGLN GDQ 6DWXDQ 3HQGLGLNDQ XQWXN 6HNRODK 0HQHQJDK 3HUWDPD 'LUHNWRUDW 3HPELQDDQ 6HNRODK 0HQHQJDK 3HUWDPD 'LUMHQGLNGDVPHQ .HPHQGLNEXG .RQWHNVWXDOLVDVL .XULNXOXP 3HQGLGLNDQ .HVHWDUDDQ 3URJUDP 3DNHW % 6HWDUD 60307V0DWD3HODMDUDQ0DWHPDWLND-DNDUWDffl.HPHQGLNEXG 0XDWDQ .XULNXOXP 0DWD 3HODMDUDQ 0DWHPDWLND 6HNRODK 0HQHQJDK 3HUWDPD0DGUDVDK 7VDQDZL\DK60307V-DNDUWDffl%DOLWEDQJ3XVNXUEXN.HPHQGLNEXG 0RGHO6LODEXV0DWD3HODMDUDQ3HQGLGLNDQ.HVHWDUDDQ3DNHW%6HWDUD6HNRODK0HQHQJDK 3HUWDPD0DGUDVDK 7VDQDZL\DK 60307V 0DWD 3HODMDUDQ 0DWHPDWLND -DNDUWDffl.HPHQGLNEXG :DK\XGLQ GDQ 6XGUDMDWfl Referensi Matematika dalam Kehidupan Manusia 2 %DQGXQJffl&9,3$$ERQJ :DK\XGLQ GDQ 6XGUDMDWfl Referensi Matematika dalam Kehidupan Manusia 4 %DQGXQJffl&9,3$$ERQJ :DWVRQ *RHUJH fl 190 Kegiatan Siap Saji yang Membuat Matematika Menyenangkan%DQGXQJffl3DNDU5D\D 6XODLPDQ5>HWDO@flContextual Teaching and Learning Matematika: Sekolah Menengah Pertama/ Madrasah Tsanawiyah Kelas IX Edisi 4. -DNDUWDffl 3XVDW 3HUEXNXDQ'HSDUWHPHQ3HQGLGLNDQ1DVLRQDO 1XKDULQL 'HZL GDQ :DK\XQL 7ULfl Matematika Konsep dan Aplikasinya: untuk SMP/MTs Kelas VIII.-DNDUWDffl3XVDW3HUEXNXDQ'HSDUWHPHQ3HQGLGLNDQ1DVLRQDO 5DKDMX(QGDK%XGL«>HW DO@² fl Contextual Teaching and Learning Matematika: Sekolah Menengah Pertama/ Madrasah Tsanawiyah Kelas VIII Edisi 4. -DNDUWDffl 3XVDW3HUEXNXDQ'HSDUWHPHQ3HQGLGLNDQ1DVLRQDO 54 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϱϰHIDUP HEMAT %LRGDWD3HQXOLV 1DPD ffl%XGLKDUGMR .HODKLUDQ ffl.ODWHQffi)HEUXDULffi -DEDWDQ ffl3UDNWLVL (PDLO fflPDVEXG#\DKRRFRLG 7HOSRQ fflfl 3HQGLGLNDQ • %DFKHORURI$UW-XUXVDQ&LYLFV+XNXP ,.,39HWHUDQ±ffifl • 6WUDWD-XUXVDQ3HQGLGLNDQ0DWHPDWLND 811(6± 3HQJDODPDQ$NDGHPLV • *XUX6031HJHUL6HPDUDQJ 'LQDV3HQGLGLNDQ.RWD6HPDUDQJffi± • ,QVWUXNWXU3HODWLKDQ*XUX60307V 'LQDV3HQGLGLNDQ3URYLQVL-DZD7HQJDKffiffi± • 5HJXODU&RXUVHffl'LDJQRVWLF$VVHVVPHQW 6HDPHR5HFVDP±3HQDQJ0DOD\VLDffiffi • 7LP3HQJPEDQJ.XULNXOXP±3HODWLKDQ*XUX 'LQDV3HQGLGLNDQ3URYLQVL-DZD7HQJDKffiffifl± • 3HPELQD7LP2610DWHPDWLND3URYLQVL-DZD7HQJDK 'LQDV3HQGLGLNDQ3URYLQVL-DZD7HQJDK± • 3HPELQD7LP/RPRMDUL3URYLQVL-DZD7HQJDK 'LQDV3HQGLGLNDQ3URYLQVL-DZD7HQJDK± • 3HQDWDU*XUX%LQD6037HUEXND3URYLQVL-DZD7HQJDK 'LQDV3HQGLGLNDQ3URYLQVL-DZD7HQJDK± • 3HQDWDU7XWRU.HMDU3DNHW%3URYLQVL-DZD7HQJDK 'LQDV3HQGLGLNDQ3URYLQVL-DZD7HQJDKfl± • &RUH7HDP9LGHR6WXG\,GDQ,, 'HSGLNEXG±:RUOG%DQN± Hidup Hemat 55
56 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7