MODUL 7
i Hidup Hemat MODUL 7
Modul Dinamis: Modul ini merupakan salah satu contoh bahan ajar pendidikan kesetaraan yang berbasis pada kompetensi inti dan kompetensi dasar dan didesain sesuai kurikulum 2013. Sehingga modul ini merupakan dokumen yang bersifat dinamis dan terbuka lebar sesuai dengan kebutuhan dan kondisi daerah masing-masing, namun merujuk pada tercapainya standar kompetensi dasar. Matematika Paket B Setara SMP/MTs Kelas VIII Modul Tema 7 : Hidup Hemat Penulis: Budiharjo Diterbitkan oleh: Direktorat Pembinaan Pendidikan Keaksaraan dan Kesetaraan- Ditjen Pendidikan Anak Usia Dini dan Pendidikan Masyarakat-Kementerian Pendidikan dan Kebudayaan, 2018 iv+ 56 hlm + illustrasi + foto; 21 x 28,5 cm Hak Cipta © 2018 pada Kementerian Pendidikan dan Kebudayaan Dilindungi Undang-Undang ii MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
Kata Pengantar P endidikan kesetaraan sebagai pendidikan alternatif memberikan layanan kepada mayarakat yang karena kondisi geografi s, sosial budaya, ekonomi dan psikologis tidak berkesempatan mengikuti pendidikan dasar dan menengah di jalur pendidikan formal. Kurikulum pendidikan kesetaraan dikembangkan mengacu pada kurikulum 2013 pendidikan dasar dan menengah hasil revisi berdasarkan peraturan Mendikbud No.24 tahun 2016. Proses adaptasi kurikulum 2013 ke dalam kurikulum pendidikan kesetaraan adalah melalui proses kontekstualisasi dan fungsionalisasi dari masing-masing kompetensi dasar, sehingga peserta didik memahami makna dari setiap kompetensi yang dipelajari. Pembelajaran pendidikan kesetaraan menggunakan prinsip fl exible learning sesuai dengan karakteristik peserta didik kesetaraan. Penerapan prinsip pembelajaran tersebut menggunakan sistem pembelajaran modular dimana peserta didik memiliki kebebasan dalam penyelesaian tiap modul yang di sajikan. Konsekuensi dari sistem tersebut adalah perlunya disusun modul pembelajaran pendidikan kesetaraan yang memungkinkan peserta didik untuk belajar dan melakukan evaluasi ketuntasan secara mandiri. Tahun 2017 Direktorat Pembinaan Pendidikan Keaksaraan dan Kesetaraan, Direktorat Jendral Pendidikan Anak Usia Dini dan Pendidikan Masyarakat mengembangkan modul pembelajaran pendidikan kesetaraan dengan melibatkan pusat kurikulum dan perbukuan kemdikbud, para akademisi, pamong belajar, guru dan tutor pendidikan kesetaraan. Modul pendidikan kesetaraan disediakan mulai paket A tingkat kompetensi 2 (kelas 4 Paket A). Sedangkan untuk peserta didik Paket A usia sekolah, modul tingkat kompetensi 1 (Paket A setara SD kelas 1-3) menggunakan buku pelajaran Sekolah Dasar kelas 1-3, karena mereka masih memerlukan banyak bimbingan guru/tutor dan belum bisa belajar secara mandiri. Kami mengucapkan terimakasih atas partisipasi dari Pusat Kurikulum dan Perbukuan Kemdikbud, para akademisi, pamong belajar, guru, tutor pendidikan kesetaraan dan semua pihak yang telah berpartisipasi dalam penyusunan modul ini. Jakarta, Desember 2018 Direktur Jenderal Harris Iskandar iii Hidup Hemat
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,ĂůĂŵĂŶϳHIDUP HEMAT %LOD DQJJRWD GDHUDK DVDO EHUXSD ELODQJDQ EXODW VHSHUWL SDGD WDEHO PDND JDPEDU IXQJVL WHUVHEXW EHUXSD WLWLN ± WLWLN ELUX ELOD GLQ\DWDNDQ VHEDJDL KLPSXQDQGLWXOLV^[\|\ [[\∈%`1DPXQELODGDHUDKDVDOELODQJDQUHDO VHKLQJJD GRPDLQ ^[ | ± [ [∈5` PDND JDPEDUQ\D EHUXSD JDULV FRNODWELODGLQ\DWDNDQVHEDJDLKLPSXQDQGLWXOLV^[\|\ [[\∈5` &RQWRKODLQSDGDLOXVWUDVLWHUVHEXWDGDODKIXQJVLKDUJDPLQ\DN\GDQKDUJD NHFDS[GHQJDQGHQJDQSHUVDPDDQ\ [&REDLVLODKWDEHOGLEDZDKLQLff [ ± [ \ I[ NRRUGLQDW 6HKLQJJDJDPEDUSDGDELGDQJNRRUGLQDWNDUWHVLXVDGDODKVHEDJDLEHULNXWff *DPEDU*DPEDUIXQJVL\ffl[→[ 'DSDWNDK $QGD PHPEXDW WDEHO XQWXN PHQJJDPEDU WLWLN ± WLWLN PHUDK ELOD GLQ\DWDNDQVHEDJDLKLPSXQDQGLWXOLV^[\|\ [[\∈%` GDQJDULVELUXELOD GLQ\DWDNDQVHEDJDLKLPSXQDQGLWXOLV^[\|\ [[\∈5` D3HQJHUWLDQ3HUUVDPDDQ*DULV/XUXV 3HQJHUWLDQSHUVDPDDQJDULVOXUXV %LOD VHEXDK IXQJVL I GLJDPEDU GDODP ELGDQJ NDUWHVLXV GHQJDQ \ I[ EHUXSD JDULV OXUXVPDND UXPXVIXQJVLWHUVHEXWPHUXSDNDQ SHUVDPDDQ JDULVOXUXV 3HQXOLVDQ IXQJVL OLQHDU VHEDJDL SHUVDPDDQ JDULV OXUXV DGD PRGHO \DLWXff 9 SHUVDPDDQJDULV \DQJGLQ\DWDNDQ VHFDUDexplisit\ P[FPLVDOffl \ [±\ [\ ଵ ଶ [\ [GDQODLQ±ODLQ 9 SHUVDPDDQJDULV\DQJGLQ\DWDNDQVHFDUDimplisit\DLWXD[E\F FRQWRK[\± [±\ [\ GDQODLQ±ODLQ [ \ I[ • • • • • Hidup Hemat 7
,ĂůĂŵĂŶϴHIDUP HEMAT 0HQJJDPEDU3HUVDPDDQ*DULV/XUXVGHQJDQ7DEHO D *DPEDUJDULV\ P[F &RQWRKff *DPEDUODKSDGDELGDQJNRRUGLQDWNDUWHVLXV\ [ %LODNLWDDNDQPHQJJDPEDUJDULVWHUVHEXWGLNDUHQDNDQNRHILVLHQ ³[´ DGDODK NLWD SLOLK GRPDLQ ELODQJDQ JHQDS VHKLQJJD OHELK PHPXGDKNDQVDDWPHODNXNDQSHUKLWXQJDQ [ (domain) ± ± ± ଵ ଶ [ ± ± ± \ I[ (range) NRRUGLQDW ± *DPEDU*DULV\ ଵ ଶ [ E *DPEDUJDULVD[E\F 3HUKDWLNDQJDPEDUJDULV\ [GDQJDPEDUJDULV\ ଵ ଶ [ SDGD NHGXD JDULV LWX PDVLQJ ± PDVLQJ PHPLOLNL WLWLN LVWLPHZD \DLWX$GDQ%SDGDJDULV\ [3GDQ4SDGDJDULV\ ଵ ଶ [ .HLVWLPHZDDQ WLWLN WHUVHEXW DGDODK PDVLQJ ± PDVLQJ WLWLN EHUDGD GL VXPEXNRRUGLQDW6HWLDSWLWLN[\SDGDVXPEX;PDND\ XQWXN NHGXD JDULV WHUVHEXW DGDODK WLWLN ± WLWLN %± GDQ 3± • • • • [ \ I[ • • • P Q 8 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϵHIDUP HEMAT 6HGDQJNDQVHWLDSWLWLN[\SDGDVXPEX<PDND[ SDGDNHGXD JDULVWHUVHEXWDGDODKWLWLN±WLWLN$±GDQ4 • 'HQJDQGHPLNLDQPDNDVHWLDSWLWLN[\SDGDVXPEX<PDND [ GDQVHWLDSWLWLN[\SDGDVXPEX;PDND\ • 0HODOXL GXD WLWLN WHUWHQWX KDQ\D GDSDW GLEXDW VHEXDK JDULV OXUXV +DOLQLODK\DQJNLWDJXQDNDQVHEDJDLFDUDXQWXNPHQJJDPEDUJUDILN SHUVDPDDQJDULVOXUXVD[E\F &RQWRK *DPEDUJDULVGHQJDQSHUVDPDDQ[\ 7LWLNSRWRQJGHQJDQ VXPEX;PDND\ [ ⇔[ ⇔[± ± ⇔[ ± ⇔ [ ± MDGL JDULV WHUVHEXWPHODOXL± 7LWLNSRWRQJGHQJDQ VXPEX<PDND[ \ ⇔\ ⇔\± ± ⇔\ ± ⇔ \ ± MDGL JDULV WHUVHEXWPHODOXL± 0DNDJDULV[\ PHODOXL±GDQ± Y X *DPEDU*DULV[\ &RQWRK *DPEDUJDULVGHQJDQSHUVDPDDQ[±\ 0RGHOWDEHOWLWLNSRWRQJWHUKDGDSVXPEXNRRUGLQDWff [ « \ « [\ « « .HPXGLDQVHWHODKGLKLWXQJNRRUGLQDWNHGXDWLWLNQ\Dff [ [± ⇔[ ⇔[ \ ±\ ⇔±\ ⇔\ ± [\ ± ± ± • • ± ± Hidup Hemat 9
,ĂůĂŵĂŶϭϬHIDUP HEMAT *DPEDUJUDILNSHUVDPDDQ[±\ *DPEDU*DULV[±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fl ± • • ± ; < $OWHUQDWLI $OWHUQDWLI -DZDEDQ 0DVDODKD 10 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϭϭHIDUP HEMAT *UDILNMDUDN\DQJGLWHPSXKPRWRUD\DK *DPEDU*DULV\ ͶͲ[ D *UDILNWHUVHEXWPHPEHQWXNJDULVOXUXV E 3HUVDPDDQJDULVOXUXVWHUVHEXW\ [ F 8QWXNPHQHPSXKMDUDNNPGLSHUOXNDQòOLWHUEDKDQEDNDU G %DKDQEDNDUòOLWHUGDSDWPHQHPSXKMDUDNNLORPHWHU ,EX PHPEHOL PLQ\DN JRUHQJ OLWHU GDODP MHULJHQ+DOLQLGLODNXNDQNDUHQDKDUJDQ\D OHELKPXUDKGLEDQGLQJEHOLHFHUDQ-HULJHQ WHUVHEXWGLOHWDNNDQGLEDJDVLPRELONDUHQD VHVXDWX KDO MHULJHQ WHUVHEXW UHWDN GL EDJLDQ EDZDK VHKLQJJD PLQ\DN JRUHQJ UHPEHVóOLWHUWLDSMDPQ\D D *DPEDUODKJUDILN\DQJPHQ\DWDNDQVLVDPLQ\DNGDODPMHULJHQ E $SDNDKJUDILNWHUVHEXWPHPEHQWXNJDULVOXUXV" F %LODPHPEHQWXNJDULVOXUXVWXOLVSHUVDPDDQJDULVWHUVHEXW G %HUDSD OLWHU VLVD PLQ\DN GDODP MHULJHQ ELOD ,EX PHQJHWDKXL NHERFRUDQMHULJHQVHWHODKMDP" 7DEHOVLVDPLQ\DNJRUHQJGDODPMHULJHQGDODPOLWHU :DNWX [ fl ,VLDZDO 0LQ\DNWXPSDK ±ó[ ±ò ± ±ò ± 6LVD I[ ò ò .RRUGLQDW • • •ò •ò fl ; < I[ $OWHUQDWLI $OWHUQDWLI -DZDEDQ • 0DVDODKD 'ĂŵďĂƌϬϬ͗DŝŶLJĂŬ'ŽƌĞŶŐ ^ƵŵďĞƌ͗ŚƚƚƉƐ͗ͬͬǁǁǁ͘ŵĞĚŝĐĂůĚĂŝůLJ͘ĐŽŵ Hidup Hemat 11
,ĂůĂŵĂŶϭϮHIDUP HEMAT D *UDILN\DQJPHQ\DWDNDQVLVDPLQ\DNGDODPMHULJHQ *DPEDUfl*DULV\ െͳ Ͷ [ E *UDILNWHUVHEXWPHPEHQWXNJDULVOXUXV F 3HUVDPDDQJDULVOXUXVWHUVHEXW\ ±ó[ G 6LVDPLQ\DNJRUHQJGDODPMHULJHQVHWHODKMDPDGDODKòOLWHU 'LVNXVLNDQ GHQJDQ NHORPSRN $QGD FRQWRK ± FRQWRK ODLQ GDODP NHKLGXSDQ VHKDUL ± KDUL ELOD KDO WHUVHEXW GLQ\DWDNDQ GDODP JUDILN NDUWHVLXVGDSDWPHPEHQWXNJDULVOXUXV E *UDGLHQ *DPEDU GL VDPSLQJ PHQXQMXNNDQ NHMDGLDQ RUDQJ SXODQJ GDUL EHUEHODQMD GHQJDQ PHQJHQGDUDL PRELO GDQ VHGDQJ PHOHZDWL MDODQ QDLN DWDX PHQDQMDN %LOD MDODQ LWX NLWD DQJJDS VHEDJDL JDULV PDND NHPLULQJDQJDULVDGDODKVDODKVDWX IDNWRU \DQJ PHQHQWXNDQ NHODMXDQ NHQGDUDDQ DJDU Q\DPDQ GDQ VHODPDW %HULNXW LQL NLWD DNDQ EDKDV WHQWDQJ NHPLULQJDQ JDULV *DPEDUffi-DODQQDLNFXUDP WHUVHEXWGDODPPDWHPDWLND 6XPEHUffKWWSVfflZZZDXWRELOGHVQRWLFLDV • • •ò fl ; < I[ • • ffi Ayo Diskusikan 12 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϭϯHIDUP HEMAT 3HQJHUWLDQ*UDGLHQ *UDGLHQ JDULV GDSDW MXJD GLVHEXW NHPLULQJDQ NHFRQGRQJDQ DWDX NHFHQGHUXQJDQ VXDWX JDULV /DPEDQJ DWDX YDULDEHO JUDGLHQ \DQJ ELDVD GLJXQDNDQDGDODK³m´ *UDGLHQDGDODKSHUEDQGLQJDQDQWDUDNRPSRQHQ\DWDXMDUDNYHUWLNDO ± VLVL WHJDNGLEDQGLQJ GHQJDQ NRPSRQHQ [DWDX MDUDN KRUL]RQWDO ± VLVLGDWDUSDGDJDULVWHUVHEXWKDOLQLGDSDWGLWXOLVff ݉ ൌ ݕ݊݁݊݉݇ ݔ݊݁݊݉݇ *UDGLHQJDULV D *DULV$%³miring´NHNDQDQ B A C .RPSRQHQ[ $& (ke kanan, +6) .RPSRQHQ\ &% (ke atas, +3) -DGLJUDGLHQJDULV$%DWDXP$% ࢋ࢟ ൌ ࢞ࢋ ൌ *DULV$%³miring´NHNDQDQJUDGLHQQ\D³ELODQJDQSRVLWLI´ E *DULV34³miring´NHNLUL P R Q .RPSRQHQ[ 35 NHNDQDQ .RPSRQHQ\ 54 ±NHEDZDK± ࢟ࢋ P34DGL- ି ൌ ࢞ࢋ ൌെ ൌ െ *DULV$%³miring´NHNLULJUDGLHQQ\D³ELODQJDQQHJDWLI´ F *DULV./YHUWLNDODWDXWHJDN K L .RPSRQHQ[ WLGDNNHNDQDQDWDXNHNLUL .RPSRQHQ\ ./ ± NHEDZDK± -DGLP./ ௬ ௫ ൌ ିସ SHPEDJLDQGHQJDQQRO³WLGDNWHUGLILQLVLNDQ´ VHKLQJJDJDULVYHUWLNDOJUDGLQQ\DWLGDNWHUGLILQLVLNDQ Hidup Hemat 13
,ĂůĂŵĂŶϭϰHIDUP HEMAT G *DULV01KRUL]RQWDODWDXPHQGDWDU M N .RPSRQHQ[ 01 NHNDQDQ .RPSRQHQ\ WLGDNNHDWDVDWDXNHEDZDK -DGLP01 ௬ ௫ ൌ ൌ Ͳ VHKLQJJDJDULVKRUL]RQWDODWDXPHQGDWDUJUDGLHQQ\D *UDGLHQJDULV\DQJPHODOXLWLWLNSDGDELGDQJNDUWHVLXV 3HUKDWLNDQJDULV$%GDQJDULV&'EHULNXW *DPEDU*UDGLHQJDULVPHODOXLWLWLN 1LODLJUDGLHQGDULPDVLQJ±PDVLQJJDULV \DLWXJDULV$%GDQ&'GDSDW GLSHUROHKGHQJDQFDUDVHEDJDLEHULNXWff • $%PHODOXL$GDQ%±±VHKLQJJDff .RPSRQHQ[ [%±[$ ±± ±ffi .RPSRQHQ\ \%±\$ ±± ± -DGLJUDGLHQJDULV$%DWDXP$% ࢋ࢟ ࢟ି࢟ ൌ ࢞ࢋ ࢞ି࢞ ൌ ି ିૢ ൌ ૢ • *DULV&'PHODOXL&±GDQ'±VHKLQJJDff .RPSRQHQ[ ['±[& ±± .RPSRQHQ\ \'±\& ±± ± -DGLJUDGLHQJDULV&'DWDXP&' ࢋ࢟ ࢟ିࡰ࢟ ൌ ࢞ࢋ ࢞ିࡰ࢞ ൌ ି ଵଶ ൌȂ ଵଶ %LODNRRUGLQDW$[\GDQ%[\PDNDJUDGLHQJDULV$% ܡିܡ %$P ܠିܠ •%±± '± • ; < $ • •&± 14 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϭϱHIDUP HEMAT 7HQWXNDQJUDGLHQPDVLQJ±PDVLQJJDULVGLEDZDKLQL ;ŝͿ ;ŝŝͿ ;ŝŝŝͿ ;ŝǀͿ $PELODK WDQJJD NHPXGLDQ VDQGDUNDQ NH WHPERN +LWXQJODK JUDGLHQ WDQJJD WHUVHEXW $JDU GDSDW PHUDLK WHPSDW \DQJ OHELK WLQJJLEDJDLPDQDQLODLJUDGLHQWDQJJDWHUVHEXW" LP ௬ ௫ ൌ ଶ ହ LLP ௬ ௫ ൌ ିସ ଶ ൌ െʹ LLLP ௬ ௫ ൌ ସ JUDGLHQWLGDNWHUGLILQLLVLNDQ LYP ௬ ௫ ൌ ସ ൌ Ͳ 3HUKDWLNDQVNHWVDJDPEDUEHULNXW L LL 3DGDJDPEDU LXQWXNPHQHQWXNDQJUDGLHQWDQJJDPDNDGDSDW GLXNXU GDQ GLWHQWXNDQ EDKZD NRPSRQHQ [ FP GDQ NRPSRQHQ\ FP-DGLPWDQJJD ݇݉݊݁݊ݕ Ͳͳ ൌ ݔ݊݁݊݉݇ ͳʹͲ ൌ ͳǡ͵͵ $JDUGDSDWPHUDLKOHELKWLQJJLPDNDNRPSRQHQ\WDQJJDWHUVHEXW MXJDKDUXVGLQDLNNDQSDGDJDPEDUflFPVHKLQJJDNRPSRQHQ [ NXUDQJ GDUL VHPXOD SDGD JDPEDU fl FP 6HKLQJJD JUDGLHQ ݕ݊݁݊݉݇ PWDQJJDff PHQMDGL WDQJJD ͵ͳͺ ൌ ݔ݊݁݊݉݇ ͺͲ ൌ ʹǡʹͻ 'HQJDQ GHPLNLDQGDSDWGLVLPSXONDQELODWDQJJDLQJLQPHUDLKOHELKWLQJJL PDNDJUDGLHQQ\DKDUXVOHELKGDULJUDGLHQVHEHOXPQ\D ƚĞŵďŽŬ ůĂŶƚĂŝ ϭϮϬĐŵ ϴϬĐŵ ϭϲϬĐŵ ƚĞŵďŽŬ ůĂŶƚĂŝ ϭϴϯĐŵ $OWHUQDWLI $OWHUQDWLI -DZDEDQ 0DVDODKE Hidup Hemat 15
,ĂůĂŵĂŶϭϲHIDUP HEMAT &RED DPDWL EHQGD GL VHNLWDU $QGD DSDNDK DGD EHQGD \DQJ PHPLOLNL XQVXUNHPLULQJDQ"7HPXNDQVHEDQ\DNPXQJNLQEHQGD±EHQGDWHUVHEXW GDQ GLVNXVLNDQ DSD IXQJVL NHPLULQJDQ EHQGD DWDX EDJLDQ GDUL EHQGD WHUVHEXW" F 3HUVDPDDQ*DULV 3HUVDPDDQJDULV\ P[ 3HUKDWLNDQJDPEDUgaris bGDQgaris gEHULNXW *DPEDU*DULV\ P[ L 3HUVDPDDQJDULVEDGDODK\ [ *DULVWHUVHEXWPHODOXL$SHUKDWLNDQVHJLWLJD2$$PDNDff NRPSRQHQ[ 2$ GDQNRPSRQHQ\ $$ JUDGLHQJDULVE PJUE ௬ ௫ ൌ ଶ ଵ ൌ ʹ 7HUQ\DWDJDULVWHUVHEXWMXJDPHODOXL%WHQWXNDQNRPSRQHQ[ NRPSRQHQ\GDQJUDGLHQJDULVE$SDNDKP$% " LL 3HUVDPDDQJDULVJDGDODK\ െ [ *DULVWHUVHEXWPHODOXL3±SHUKDWLNDQVHJLWLJD233PDNDff NRPSRQHQ[ 23 GDQNRPSRQHQ\ 33 ± JUDGLHQJDULVJ PJUJ ࢋ࢟ ࢞ࢋ ൌ ି ൌ െ *DULV WHUVHEXW MXJD PHODOXL 4 ± WHQWXNDQ NRPSRQHQ [ NRPSRQHQ\GDQJUDGLHQJDULVJ$SDNDKPJUJ െ " 6L,ODKNDQPHQ\HOLGLNL JUDGLHQ JDULV ODLQ \DQJ MXJDPHODOXL SDQJNDO NRRUGLQDWDSDNHVLPSXODQQ\D" 2 • $ • 3 ± $ • 3 • 4 • ; < • % Ayo Diskusikan 16 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϭϳHIDUP HEMAT 'HQJDQGHPLNLDQJDULV\DQJPHODOXLSDQJNDONRRUGLQDW2GDQ 7DEPDNDJUDGLHQQ\D³P ࢈ ࢇ ´GDSDWGLWXOLVGHQJDQSHUVDPDDQ \ P[DWDX\ ࢈ ࢇ [ 3HUVDPDDQJDULV\ P[F 3HUKDWLNDQJDULV±JDULVEHULNXW *DPEDU*DULV\ P[F 0DVLKLQJDWNDQEDJDLPDQDPHQJJDPEDUJDULV\ ͵ Ͷ [" %XDWODKWDEHOVHEDJDLEHULNXWff ; ± < \ ଷ ସ [ ⇔ \ ଷ ସ ⇔\ \ ଷ ସ [ ⇔ \ ଷ ସ ⇔\ ± [\ ± 3HUKDWLNDQWDEHOEHULNXW *DULV1RPRU 3HUVDPDDQ *UDGLHQ 7LWLNSRWRQJSDGDVXPEX< \ ଷ ସ [ ͵ Ͷ \ ଵ ଶ [ ͳ ʹ \ ʹ[± ± \ ±[± ± ± \ െ ଵ ଶ [± െ ͳ ʹ ± \ െ ଵ ଷ [ െ ͳ ͵ 2 1 3 4 5 6 ; < Hidup Hemat 17
,ĂůĂŵĂŶϭϴHIDUP HEMAT %HUGDVDU WDEHO WHUVHEXW GDSDW GLVLPSXONDQ EDKZD SHUVDPDDQ JDULV \ P[ F DGDODK JDULV \DQJ PHODOXL F GHQJDQ JUDGLHQ ³P´ 3HUVDPDDQJDULV\DQJPHODOXLWLWLN[\GHQJDQJUDGLHQ³P´ 0LVDO JDULV WHUVHEXW PHODOXL $[\ JUDGLHQ P GDQ SHUVDPDDQ JDULVWHUVHEXWDGDODK\ P[F7LWLN$[\PHODOXLJDULVWHUVHEXW PDNDff\ P[F⇔ F \ ±P[ 6HKLQJJDff\ P[F ⇔\ P[ \ ±P[ ⇔\±\ P[\±P[±\ ⇔\±\ P[±P[ ⇔\±\ P[±[ 'HQJDQGHPLNLDQPDNDSHUVDPDDQJDULV\DQJPHODOXL[\GDQ JUDGLHQ PDGDODK\±\ P[±[ &RQWRKff 7HQWXNDQSHUVDPDDQJDULV\DQJPHODOXL%±GHQJDQJUDGLHQ -DZDEffl \±\ P[±[ ⇔\± [±± ⇔\± [ ⇔\± [fl ⇔\ [ 3HUVDPDDQJDULVPHODOXLGXDWLWLN$[\GDQ%[\ *DULVWHUVHEXWPHODOXL$[\GDQ%[\PDNDP$% ܡିܡ ܠିܠ *DULVWHUVHEXWPHODOXL$[\PDNDSHUVDPDDQJDULVQ\DDGDODKff \±\ P$%[±[ ܡିܡ \±\⇔ ܠିܠ [±[ ܡିܡ ⇔\± \]±] ]± ]\±\⇔ ܡିܡ ܠିܠ ൌ ܠିܠ 'HQJDQGHPLNLDQPDNDSHUVDPDDQJDULV\DQJPHODOXLGXDWLWLN ܡିܡ DGDODK[\GDQ[\ ܡିܡ ܠିܠ ൌ ܠିܠ &RQWRKff 7HQWXNDQSHUVDPDDQJDULV\DQJPHODOXL$±GDQ%±± 'LNHWDKXLffl$±GDQ%±± 6RDOffl3HUVDPDDQJDULV\DQJPHODOXL$GDQ% -DZDEffl ܡെܡ ܡ െ ܡ ܠെܠ ൌ ܠ െ ܠ ିܡ ⇔ ିି ൌ ܠିሺିሻ ିૠିሺିሻ⇔ ܡି ିି ൌ ܠା ିૠା ⇔ ିܡ ି ൌ ܠା ି ⇔ ିܡ ൌ ܠା ⇔\± [⇔\± [fl ⇔[±\ 18 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϭϵHIDUP HEMAT 3RVLVLWLWLNWHUKDGDSJDULV 3HUKDWLNDQJDPEDUJDULV\ െ [ EHULNXW *DPEDU*DULV\ െ [ 3RVLVLWLWLNWHUVHEXWWHUKDGDSJDULVGDSDWGLWXQMXNNDQVHSHUWLWDEHOEHULNXWff dŝƚŝŬ 'ĂƌŝƐ\ െ [ WŽƐŝƐŝƚŝƚŝŬƚĞƌŚĂĚĂƉŐĂƌŝƐ $± \ െ [ ⇔±fiെ ⇔±fi± ⇔±fi dŝƚŝŬĚŝďĂǁĂŚŐĂƌŝƐ % \ െ [ ⇔ െ ⇔ ± ⇔ dŝƚŝŬƉĂĚĂŐĂƌŝƐ & \ െ [ ⇔!െ ⇔!െ ⇔! dŝƚŝŬĚŝĂƚĂƐŐĂƌŝƐ '± « « (±± « « )± « « 3RVLVL WLWLN 7[\ WHUKDGDS JDULV \ P[ F GDSDW GLNHWDKXL GHQJDQ FDUD PHQVWXEVWLWXVL [\ NH SHUVDPDDQ JDULV %LOD KXEXQJDQ SHUQ\DWDDQQ\D VDPD GHQJDQ PDNDWLWLNWHUVHEXW EHUDGDSDGDJDULV%LODKXEXQJDQSHUQ\DWDDQQ\D³OHELKGDUL´! PDND WLWLN WHUVHEXW EHUDGD GL DWDV JDULV %LOD KXEXQJDQ SHUQ\DWDDQQ\D ³NXUDQJ GDUL´ fi PDND WLWLN WHUVHEXW EHUDGD GL EDZDKJDULV • % • $± • (±± • F(± ; < • '± • & Hidup Hemat 19
,ĂůĂŵĂŶϮϬHIDUP HEMAT 'LNHWDKXL$±GDQ%±WHQWXNDQff D 3HUVDPDDQJDULV\DQJPHODOXL$GDQ% E *UDGLHQJDULV$% F 7LWLNSRWRQJJDULVWHUVHEXWGHQJDQVXPEX< ܡିܡ D ܡିܡ ܠିܠ ൌ ܠିܠ ⇔ ܡିሺିሻ ିሺିሻ ൌ ܠି ାܡ⇔ିି ૠ ൌ ܠି ିૠ ⇔ܡା ିܠ ൌ ି ⇔±\ [±⇔±\± [± ⇔±\ [±⇔±\ [⇔[\ ⇔\ ±[± E *UDGLHQJDULVP$% ± F 7LWLNSRWRQJGHQJDQVXPEX<± G *UDGLHQGDQ*DULV *UDGLHQJDULVVHMDMDU *DPEDU*DULVVHMDMDU 3HUKDWLNDQ JDULV D PD ଷ ଶ WHQWXNDQ JUDGLHQ JDULV E F G GDQ H %DJDLPDQD NHGXGXNDQ NHOLPD JDULV WHUVHEXW" %HQDU NHOLPD JDULV WHUVHEXWVHMDMDU%XDWODKWLJDEXDKJDULVVHMDMDUGDQWHQWXNDQJUDGLHQ PDVLQJ±PDVLQJJDULVWHUVHEXW$SDNDKJUDGLHQQ\DMXJDVDPD" %LOD JDULV g VHMDMDU GHQJDQ JDULV l PDND JUDGLHQ NHGXD JDULV WHUVHEXWVDPDDWDXJDULVglPDNDPg Pl a b c d e 0DVDODKF ; < $OWHUQDWLI $OWHUQDWLI -DZDEDQ 20 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϮϭHIDUP HEMAT *UDGLHQJDULVWHJDNOXUXV *DPEDU*DULVWHJDNOXUXV 3HUKDWLNDQJDULV±JDULVSDGDJDPEDUGLDWDVJDULVWHJDNOXUXVJDULV GDQJDULVWHJDNOXUXVJDULV*DPEDUODKJDULVGDQVHUWDJDULV GDQfl\DQJMXJDVDOLQJWHJDNOXUXV,VLODKWLWLN±WLWLNEHULNXW ୟ୰୧ୱ ଵ ൌ െ ͵ ͷ ୟ୰୧ୱ ଶ ൌ ͷ ͵ ୟ୰୧ୱ ଵ ୟ୰୧ୱଶ ൌ െ ͵ ͷ Ǥ ͷ ͵ ൌ െͳ ୟ୰୧ୱ ଷ ൌ െ ʹ ͳ ୟ୰୧ୱ ସ ൌ ڮ ୟ୰୧ୱ ଷ ୟ୰୧ୱସ ൌ െ ʹ ͳ Ǥǥൌڮ ୟ୰୧ୱହ ൌ ڮ ୟ୰୧ୱ ൌ ڮ ୟ୰୧ୱ ହ ୟ୰୧ୱ ൌڮSǥൌڮ ୟ୰୧ୱ ൌ ڮ ୟ୰୧ୱ ଼ ൌ ڮ ୟ୰୧ୱ ୟ୰୧ୱ଼ ൌڮSǥൌڮ %LODGXDJDULVVDOLQJWHJDNOXUXVPDNDKDVLOSHUNDOLDQJUDGLHQQ\D DGDODK±+DOWHUVHEXWGDSDWGLWXOLVff %LODJDULVg ⊥ lPDNDPgPl ± D *DPEDUODKVHEXDKJDULVJNHPXGLDQWHQWXNDQJUDGLHQQ\D E *DPEDUODKJDULVE\DQJVHMDMDUGHQJDQJDULVJWHQWXNDQPE F *DPEDUODKJDULVU\DQJWHJDNOXUXVGHQJDQJDULVJWHQWXNDQPU 0DVDODKG ; < Hidup Hemat 21
,ĂůĂŵĂŶϮϮHIDUP HEMAT D *UDGLHQJDULVJ E *UEJUJPE F *UU⊥JUJPU ± • %DJDLPDQDJUDGLHQJDULV\DQJVHMDMDUGHQJDQJDULVYHUWLNDO" • %DJDLPDQDJUDGLHQJDULV\DQJWHJDNOXUXVGHQJDQJDULVYHUWLNDO" 3HQXJDVDQ 3DGD NHJLDWDQ 8QLW ³7LS +LGXS +HPDW´PHOLSXWL EHEHUDSD NDMLDQPDWHUL \DLWXffl D 7XMXDQ 3DGDSHPEHODMDUDQLQLPHPLOLNLWXMXDQSHQXJDVDQDJDUSHVHUWDGLGLNGDSDWff • PHPDKDPL SHQJHUWLDQ SHUVDPDDQ JDULV OXUXV GDQ PHQJJDPEDU SHUVDPDDQJDULV • PHPDKDPLSHQJHUWLDQJUDGLHQNHPLULQJDQJDULV • PHQHQWXNDQ SHUVDPDDQ JDULV \ P[ \ P[ F D[ E\ F SHUVDPDDQJDULVPHODOXLGXDWLWLN $OWHUQDWLI $OWHUQDWLI -DZDEDQ ; < Ayo Diskusikan 22 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϮϯHIDUP HEMAT • PHPDKDPLVLIDWVLIDWJUDGLHQJUDGLHQJDULV\DQJVHMDMDUGHQJDQVXPEX [JUDGLHQJDULV\DQJ VHMDMDUVXPEX\JUDGLHQGXDJDULV\DQJVHMDMDU JUDGLHQGXDJDULV\DQJWHJDNOXUXV E 0HGLD$ODW%DKDQGDQ6XPEHU%HODMDU/DLQQ\D $ODWGDQ%DKDQ\DQJGLJXQDNDQNHUWDVEHUSHWDNEXNXWXJDVGDQDODW±DODW WXOLV F /DQJNDK/DQJNDK.HJLDWDQ3HPEHODMDUDQ3HVHUWD'LGLNffl .HJLDWDQ 3HPEHODMDUDQ Dffl PHPDKDPL SHQJHUWLDQ SHUVDPDDQ JDULV OXUXVGDQPHQJJDPEDUSHUVDPDDQJDULVSDGDELGDQJNDUWHVLXV 7HQHQWXNDQSHUVDPDDQJDULVNHPXGLDQJDPEDUODKSDGDELGDQJNDUWHVLXV \DQJPHQJJJDPEDUNDQNRQGLVLEHULNXWff D +DUJDOLWHU3HUWDPD[7XUERDGDODKGXDNDOLKDUJDOLWHU%LR6RODU E 6HPXOD OLOLQ SDQMDQJQ\D FP VDDW PHQ\DOD VHWLDS MDP OLOLQ LWX EHUNXUDQJ͵ Ͷ FP F 'HZLOHELKWXDWDKXQGDUL'LQGD .HJLDWDQ3HPEHODMDUDQEfflSHQJHUWLDQJUDGLHQNHPLULQJDQJDULV 7HQWXNDQJUDGLHQJDULV\DQJ$QGDJDPEDUSDGD.HJLDWDQD 7HQWXNDQJUDGLHQJDULV\DQJPHODOXL3±GDQ4±± .HJLDWDQ3HPEHODMDUDQFfflWHUDPSLOPHQHQWXNDQSHUVDPDDQJDULV\ P[\ P[FD[E\F SHUVDPDDQJDULVPHODOXLGXDWLWLN *DPEDUGDQEHULSHQMHODVDQSHUVDPDDQJDULV\ [GDQ\ ±[ *DPEDUGDQEHULSHQMHODVDQSHUVDPDDQJDULV\ ଵ ଶ [± GDQ\ ±ͳ ʹ [ 7HQWXNDQSHUVDPDDQJDULV\DQJPHODOXLGHQJDQJUDGLHQ± 7HQWXNDQSHUVDPDDQJDULV\DQJPHODOXL.±±GDQ4± .HJLDWDQ3HPEHODMDUDQGfflPHPDKDPLVLIDWVLIDWJUDGLHQJUDGLHQJDULV \DQJVHMDMDUGHQJDQVXPEX[JUDGLHQJDULV\DQJVHMDMDUVXPEX\JUDGLHQ GXDJDULV\DQJVHMDMDUJUDGLHQGXDJDULV\DQJWHJDNOXUXV *DPEDUODKJDULV[ GDQ\ NHPXGLDQWHQWXNDQJUDGLHQQ\D 'LNHWDKXLJDULVJGHQJDQSHUVDPDDQ[\± D 7HQWXNDQSHUVDPDDQJDULV\DQJVHMDMDUJDULVJGDQPHODOXL± E 7HQWXNDQSHUVDPDDQJDULV\DQJWHJDNOXUXVJDULVJGDQPHODOXL .HJLDWDQE .HJLDWDQF .HJLDWDQG .HJLDWDQD Hidup Hemat 23
,ĂůĂŵĂŶϮϰHIDUP HEMAT 6RDO/DWLKDQ7XJDV *DPEDUGDQWHQWXNDQSHUVDPDDQJDULV\DQJPHQJJJDPEDUNDQ NRQGLVLVHEDJDLEHULNXWff D6HEHOXPQ\D NXRWD LQWHUQHW VD\D PDVLK JLJDE\WH QDPXQ VDDW QRQWRQ VLDUDQ ODQJVXQJ OHZDW WHOHSRQ JHQJJDP WLDS MDP NXRWD LQWHUQHWVD\DEHUNXUDQJͳ ʹ JLJDE\WH E*DMLD\DKVHWHODKGLWDEXQJ5SGLVHUDKNDQNHSDGDLEX XQWXNEHODQMD F 8VLD%XGLVHNDUDQJWDKXQOHELKWXDGDUL$QQD G0RELOLWXVHWLDSEDKDQEDNDUOLWHUKDQ\DGDSDWPHQHPSXKMDUDN NLORPHWHU 7HQWXNDQJUDGLHQJDULV\DQJ$QGDJDPEDUSDGDVRDOQRPRU 7HQWXNDQJUDGLHQJDULV\DQJPHODOXL$±±GDQ4± 8VLD%XGLWDKXQOHELKPXGDGDULXVLD,GD D 1\DWDNDQIXQJVLXVLD%XGLVHNDUDQJWHUKDGDSXVLD,GD E *DPEDUODKIXQJVLWHUVHEXWGDODPELGDQJNDUWHVLXV F $SDNDKEHUXSDJDULVOXUXV"7XOLVSHUVDPDDQQ\D G %HUGDVDUNDQJDPEDUWHUVHEXWEHUDSDXVLD%XGLSDGDVDDWXVLD,GD EHUXVLDflWDKXQ" *DPEDUODKSHUVDPDDQJDULV\ ଷ ସ [GDQ\ ±ଷ ସ [SDGDVDWXJDPEDU *DPEDUODKJDULV\ [±GDQ\ ±[SDGDVDWXJDPEDU 7HQWXNDQSHUVDPDDQJDULV\DQJPHODOXL±GHQJDQJUDGLHQ± fl 7HQWXNDQSHUVDPDDQJDULV\DQJPHODOXL.±±GDQ4± ffi 'LNHWDKXL JDULV J GHQJDQ SHUVDPDDQ [ ± \ ± ffi 7HQWXNDQ SHUVDPDDQJDULVff D VHMDMDUJDULVJGDQPHODOXL± E WHJDNOXUXVJDULVJGDQPHODOXL± 24 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϮϱHIDUP HEMAT 8UDLDQ0DWHUL 0DVDODK WHUNDLW SHQJKHPDWDQ DLU GDSDW GLVHOHVDLNDQ GHQJDQ SHUVDPDDQ ODQJNDKSHUWDPD\DQJKDUXVGLODNXNDQDGDODKPHQJXEDKNDOLPDW FHULWDDWDX IDNWDWHUVHEXW NHGDODP NDOLPDWPDWHPDWLND 7HQWX VDMD GDODP KDO LQL DGDODK SHUVDPDDQ 0DVDODK\DQJWHUNDLWSHUVDPDDQJDULVOXUXV 0DVDODK \DQJ WHUNDLW GHQJDQ SHUVDPDDQ GDODP SHQJKHPDWDQ DLU FXNXS EDQ\DNGLDQWDUDQ\Dffl D 3HQJKHPDWDQSHQJJXQDDQDLU E 0HQJHWDKXLSHUVHGLDDQDLUPLQXP D .HEXWXKDQ SRNRN DLU GDODP VDWX NHOXDUJD $UPDQ XQWXN PDQGL PDVDN GDQ FXFL SHUKDUL OHELK GDUL P 6HODLQ LWX SHQJJXQDDQ DLU ELDVDQ\DXQWXNFXFLPRWRUPHQ\LUDPKDODPDQDWDXNHSHUOXDQODLQ 0XODL KDUL LQL GDODP UDQJND KLGXS KHPDW D\DK PHQJDWXU GDQ PHPEDWDVLWLDSKDULKDQ\Dଷ ସ P L 7HQWXNDQ SHUVDPDDQ JDULV \DQJ PHQ\DWDNDQ NHEXWXKDQ DLU GLNDLWNDQGHQJDQZDNWXKDUL LL %HUDSD ZDNWX \DQJ GLEXWXKNDQ MLND DLU WHODK GLJXQDNDQ VHEDQ\DNP" LLL %HUDSDPHWHUNXELNDLU\DQJWHODKGLJXQDNDQSDGDKDULNH" E 6HNDUDQJ NHOXDUJD 1DQGD PHPLOLNL VLPSDQDQ DLU PLQXP GL UXPDK VHEDQ\DNOLWHU5DWD±UDWDWLDSMDPNHOXDUJDWHUVHEXWEXWXK ଷ ସ OLWHU DLUPLQXP L 7HQWXNDQ SHUVDPDDQ JDULV \DQJ PHQ\DWDNDQ SHUVHGLDDQ DLU PLQXPELODGLNDLWNDQGHQJDQZDNWXSHUMDPQ\D LL %HUDSDVLVDDLUPLQXPVHWHODKGLJXQDNDQflMDP" LLL .DSDQVLPSDQDQDLUPLQXPGLUXPDK1DQGDKDELV" 8QLW+HPDW3HQJJXQDDQ$LU Modul 2 $LUPHUXSDNDQVDODKVDWXNHEXWXKDQSRNRNVHKDUL± KDUL \DQJ WLGDN ELVD GLWLQJJDONDQ ROHK NHOXDUJD 0LVDOQ\D XQWXNPDQGL FXFL SDNDLDQPHPDVDN GDQ ODLQ±ODLQ1DPXQWLGDNMDUDQJNLWDPHQJJXQDNDQDLU \DQJ NXUDQJ VHVXDL GHQJDQ NHEXWXKDQ NDUHQD NHOXSDDQ PHQXWXS NUDQ NHERFRUDQ SLSD DWDX PHQJJXQDNDQ DLU \DQJ NXUDQJ EHUPDQIDDW 1DPXQ ELOD KDO WHUVHEXW GDSDW GLFHJDK DNDQ PHQJKHPDW SHQJHOXDUDQUXPDKWDQJJD 0DVDODK 'ĂŵďĂƌϬϬ͗WĞŶŐŐƵŶĂĂŶŝƌ 6XPEHUfflKWWSfflSNPFLNXQGXOEORJVSRWFRP Hidup Hemat 25
,ĂůĂŵĂŶϮϲHIDUP HEMAT D 3HUKDWLNDQSHUQ\DWDDQff³tiap hari hanya m3´ L 'DUL SHUQ\DWDDQff ³tiap hari hanya m3´ 'DSDW GLQ\DWDNDQ VHEDJDL SHUVDPDDQ \ [ ³\´ DGDODK EDQ\DNQ\D DLU VHGDQJNDQ³[´DGDODKZDNWXGDODPKDUL LL \ [⇔ [⇔ [⇔[ $LUWHODKGLJXQDNDQPVHODPDKDUL LLL \ [⇔\ ⇔\ ffi 3DGDKDULNHDLUWHODKGLJXQDNDQVHEDQ\DNffiP E 3HUKDWLNDQ SHUQ\DWDDQffl ³Nanda PHPLOLNL VLPSDQDQ DLU PLQXP GL UXPDKVHEDQ\DNOLWHU´GDQ³rata – rataWLDSMDPNHOXDUJDWHUVHEXW EXWXKଷ ସ OLWHUDLUPLQXP´ L 'DUL SHUQ\DWDDQ WHUVHEXW GDSDW GLQ\DWDNDQ VHEDJDL SHUVDPDDQ\ െ [³\´DGDODKVLVDVLPSDQDQDLUPLQXP GLUXPDKVHGDQJNDQ³[´DGDODKVDWXDQZDNWXGDODPMDP LL 6LVDDLUPLQXPVHWHODKGLJXQDNDQflMDPDUWLQ\D[ flPDNDffl \ െ [⇔\ െ fl⇔\ ± fl 6LVDDLUPLQXPVHWHODKGLJXQDNDQflMDPDGDODKflOLWHU LLL 6LPSDQDQ DLU PLQXP GL UXPDK 1DQGD KDELV DUWLQ\D \ PDNDff \ െ [⇔ െ [⇔ [ െ [ [ ⇔ [ ⇔[ ffi⇔[ 6LPSDQDQDLUPLQXPGLUXPDK1DQGDKDELVVHWHODKMDP %XDWODK FRQWRK ODLQ GDODP NHKLGXSDQ VHKDUL ± KDUL \DQJ GDSDW GLQ\DWDNDQ VHEDJDL SHUVDPDDQ OLQHDU GXD YDULDEHO VHKLQJJD GDSDW GLJDPEDUGDODPELGDQJNDUWHVLXVPHUXSDNDQJDULVOXUXV $OWHUQDWLI $OWHUQDWLI -DZDEDQ Ayo Diskusikan 26 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϮϳHIDUP HEMAT 3HQXJDVDQ 3DGDNHJLDWDQ8QLW³+LGXS+HPDW´PHOLSXWLEHEHUDSDNDMLDQPDWHULPHOLSXWLffl D 7XMXDQ 3DGDSHPEHODMDUDQLQLPHPLOLNLWXMXDQSHQXJDVDQDJDUSHVHUWDGLGLNGDSDW PHQ\HOHVDLNDQ PDVDODK GDODP NHKLGXSDQ VHKDUL ± KDUL \DQJ WHUNDLW GHQJDQSHUVDPDDQJDULVOXUXV E 0HGLD$ODW%DKDQGDQ6XPEHU%HODMDU/DLQQ\D $ODW GDQ %DKDQ \DQJ GLJXQDNDQ NHUWDV EHUSHWDN EXNX WXJDV GDQ DODW ± DODWWXOLV F /DQJNDK/DQJNDK .HJLDWDQ DGDODK PHQ\HOHVDLNDQ PDVDODK GDODP NHKLGXSDQVHKDUL±KDUL\DQJWHUNDLWGHQJDQSHUVDPDDQJDULVOXUXV 'DODP UDQJND PHPHQXKL EHUEDJDL NHSHUOXDQ VHWLDS KDUL ,EX PHPEXWXKNDQPDLUEHUVLK D *DPEDUODK JUDILN KDO WHUVHEXW GDODP ELGDQJ NRRUGLQDW NDUWHVLXV GHQJDQ VXPEX; VHEDJDL VDWXDQ ZDNWX KDUL GDQ VXPEX< VHEDJDL VDWXDQNHEXWXKDQDLUP E %HUGDVDUNDQ³JUDILN´WHUVHEXWWHQWXNDQNHEXWXKDQDLUVHODPDKDUL F %LOD,EXPHPEXWXKNDQDLUVHEDQ\DNPEHUDSDODPDDLUWHUVHEXW GLJXQDNDQ" 6RDO/DWLKDQ 8VLD NDNDN WDKXQ LQL VDPD GHQJDQ VHSHUWLJD XVLD D\DK SDGD WDKXQ GHSDQ L 1\DWDNDQ SHUQ\DWDDQ WHUVHEXW VHEDJDL SHUVDPDDQ \DQJ PHQ\DWDNDQXVLDNDNDNWHUKDGDSXVLDD\DKVHNDUDQJ LL %LODXVLDNDNDNWDKXQEHUDSDXVLDD\DKVHNDUDQJ" LLL %LODXVLDD\DKVHNDUDQJWDKXQEHUDSDXVLDNDNDN" 3HQJHOXDUDQ,EXEXODQLQL5SOHELKKHPDWGDULEXODQ\DQJODOX L 1\DWDNDQ SHUQ\DWDDQ WHUVHEXW VHEDJDL SHUVDPDDQ \DQJ PHQ\DWDNDQ SHQJHOXDUDQ LEX WHUKDGDS SHQJHOXDUDQ LEX EXODQ \DQJODOX LL %LODSHQJHOXDUDQLEXEXODQLQL5SEHUDSDSHQJHOXDUDQ LEXEXODQ\DQJODOX .HJLDWDQ Hidup Hemat 27
+DUJDSHUNJEXDKGXULDQ VHWHODKQDLN5SDGDODKWLJDNDOLKDUJD PDQJJDPDQDODJL L 1\DWDNDQ SHUQ\DWDDQ WHUVHEXW VHEDJDL SHUVDPDDQ \DQJ PHQ\DWDNDQ KDUJD GXULDQ VHEHOXP QDLN WHUKDGDS KDUJD PDQJJD SHUNJ LL %LODKDUJDGXULDQVHEHOXPQDLNSHUNJDGDODK5SEHUDSD KDUJDPDQJJDSHUNJ" LLL %LOD KDUJD PDQJJD 5S SHUNJ EHUDSD KDUJD GXULDQ VHWHODKQDLN" +DUJD NHPHMD LWX OHELK PDKDO 5S GLEDQGLQJ KDUJD NDRV PHVNLSXQKDUJDNDRVWHODKGLGLVNRQ L 1\DWDNDQ SHUQ\DWDDQ WHUVHEXW VHEDJDL SHUVDPDDQ \DQJ PHQ\DWDNDQ KDUJD NHPHMD WHUKDGDS KDUJD NDRV VHEHOXP GLGLVNRQ LL %LODKDUJDNHPHMDDGDODK5SEHUDSDKDUJDNDRV" LLL %LOD KDUJD NDRV VHEHOXP GLGLVNRQ 5S EHUDSD KDUJD NHPHMD" Modul 2 ,ĂůĂŵĂŶϮϴHIDUP HEMAT %DJLNHOXDUJD\DQJLQJLQKLGXSKHPDW PDND NHEXWXKDQ DODW ± DODW UXPDK WDQJJDPHUXSDNDQ VDUDQD \DQJ KDUXV GLPLOLNL 7HQWX VDMD VDDW PHPEHOL EDUDQJ ± EDUDQJ WHUVHEXW KDUXV GLVHVXDLNDQ GHQJDQ NHEXWXKDQ GDQ GDQD \DQJ DGD 7DN KDUXV SHUDODWDQ UXPDK WDQJJD PRGHUQ \DQJ SDOLQJ SHQWLQJ DGDODK NLWD ELVD PHPDQIDDWNDQ 6DODK VDWX \DQJ GLSHUWLPEDQJNDQ WHQWDQJ EDUDQJ NHEXWXKDQ DGDODK PDVDODK KDUJD 6HODLQ KDUJD MXJDIUHTXHQVL NHJXQDDQ EDUDQJWHUVHEXW 8UDLDQ0DWHUL 3HUVDPDDQ/LQHDU 6HEHOXP NLWDPHPEDKDV VLVWHP SHUVDPDDQ OLQHDU GXD YDULDEHOPDULODK NLWD PHQJLQJDWNHPEDOLSHUVDPDDQ\DQJWHODKGLSHODMDULGLDQWDUDQ\Dff L SHUVDPDDQOLQHDUVDWXYDULDEHOOLQHDUGLVLQLDUWLQ\DSDQJNDWWHUWLQJJL GDULYDULDEHOQ\DDGDODKVDWXGDQKDQ\DWHUGDSDWVDWXYDULDEHO &RQWRKff D YDULDEHOQ\D³D´GDQ³DSDQJNDW´ ±[ [YDULDEHOQ\D³[´GDQ³[SDQJNDW´ %XNDQFRQWRKffl D NDUHQDYDULDEHO³D´SDQJNDWGXD D±E NDUHQDDGDYDULDEHO\DLWX³D´GDQ³E´ *DPEDU3HUDERW5XPDK7DQJJD 6XPEHUfflKWWSVfflELVQLVXNPFRPXSORDGV 8QLW+DUJD'XD%DUDQJ .HEXWXKDQ Modul 2 28 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϮϵHIDUP HEMAT LL SHUVDPDDQ OLQHDU GXD YDULDEHO \DLWX VHEXDK SHUVDPDDQ \DQJ PHPLOLNLGXDYDULDEHO\DQJPDVLQJ±PDVLQJEHUSDQJNDWVDWX &RQWRKffl[\ YDULDEHOffl³[´GDQ³\´PDVLQJ±PDVLQJSDQJNDW D±E YDULDEHOffl³D´GDQ³E´PDVLQJ±PDVLQJSDQJNDW %XNDQFRQWRKffl [\ NDUHQDYDULDEHO³[´SDQJNDWGXD D±EF ffiNDUHQDDGDYDULDEHO\DLWXDEGDQF D 3HQJHUWLDQ63/'9 .RSHUDVL'HVDPHQMXDONHEXWXKDQVHKDUL±KDULGLDQWDUDQ\DNHFDSPLQ\DN JRUHQJ WHSXQJ JDQGXP EHUDV GDQ ODLQ ± ODLQ ,EX $QQD PHPEHOL VHERWRO NHFDSGDQNJEHUDVVHKDUJD5SVHGDQJNDQ,EX(QGDQJPHPEHOL ERWRONHFDSGDQNJEHUDVVHKDUJD5S.HFDSGDQEHUDV\DQJGLEHOL ,EX$QQDGDQ,EX(QGDQJDGDODKVHMHQLV 3DGDLOXVWUDVLFHULWDWHUVHEXWPLVDOKDUJDNHFDSSHUERWRO³[´GDQKDUJDEHUDV SHUNJ³\´SHPEHOLDQ,EX$QQDGDSDWGLQ\DWDNDQff[\ VHGDQJNDQ SHPEHOLDQ,EX(QGDQJGDSDWGLQ\DWDNDQGDODPPRGHO[\ 'XD SHUVDPDDQWHUVHEXWYDULDEHOQ\DVDPDGDQWHUNDLW\DQJVDWXGHQJDQ\DQJODLQ \DLWXffl [\ [\ %LODSHUVDPDDQ\DQJVDWXWHUNDLWGHQJDQSHUVDPDDQ\DQJODLQGDQSDGD PDVLQJPDVLQJ SHUVDPDDQ PHUXSDNDQ SHUVDPDDQ OLQHDU GHQJDQ GXD YDULDEHO PDND VLVWHP SHUVDPDDQ WHUVHEXW GLVHEXW VLVWHP SHUVDPDDQ OLQHDUGXDYDULDEHO $QGL GDQ%XGLWLDS KDULPHQ\LVLKNDQ XDQJQ\D XQWXN GLWDEXQJ6HWLDS KDUL %XGL PHQDEXQJ 5S OHELK EDQ\DN GDUL XDQJ \DQJ GLWDEXQJ $QGL 8DQJ WDEXQJDQ $QGL GDQ %XGL VHODPD KDUL WHUNXPSXO 5S 1\DWDNDQXDQJWDEXQJDQ$QGLGDQ%XGLWHUVHEXWGDODPVLVWHPSHUVDPDDQ GXDYDULDEHO 0LVDO XDQJWDEXQJDQ$QGLWLDS KDUL ³D´ GDQ XDQJWDEXQJDQ%XGLWLDS KDUL ³E´PDNDffl • Setiap hari Budi menabung Rp3.000,- lebih banyak dari uang yang ditabung Andi.+DOLQLGDSDWGLQ\DWDNDQGHQJDQE D • Uang tabungan Andi dan Budi selama 5 hari terkumpul Rp45.000,-+DO LQLGDSDWGLQ\DWDNDQGHQJDQDE 'HQJDQGHPLNLDQ63/'9SDGDFHULWDWHUVHEXWffff 0DVDODKD E D DE $OWHUQDWLI $OWHUQDWLI -DZDEDQ Hidup Hemat 29
$SDNDK ELOD NLWD PHPLOLNL SHUVDPDDQ GHQJDQ GXD YDULDEHO DNDQ VHODOX PHPEHQWXN VLVWHP SHUVDPDDQ OLQHDU GXD YDULDEHO" %HULNDQ FRQWRK SHUVDPDDQ GDODP NHKLGXSDQ VHKDUL ± KDUL \DQJ PHPEHQWXN VLVWHP SHUVDPDDQ GXD YDULDEHO GDQ \DQJEXNDQPHPEHQWXN VLVWHP SHUVDPDDQ GXDYDULDEHO E 3HQ\HOHVDLDQ63/'9 6LVWHPSHUVDPDDQOLQHDUGXDYDULDEHO63/'9GDSDWGLVHOHVDLNDQGHQJDQ FDUD\DLWXff • 0HWRGHHOLPLQDVL\DLWXPHQ\HOHVDLNDQ63/'9GHQJDQFDUDPHQJHOLPLQLU DWDX³PHQJKLODQJNDQ´VDODKVDWXYDULDEHO • 0HWRGH JUDILN \DLWX PHQ\HOHVDLNDQ 63/'9 GHQJDQ FDUD PHQJJDPEDU PDVLQJ ± PDVLQJ SHUVDPDDQ GDQ PHQHQWXNDQ WLWLN SRWRQJ JUDILN SHUVDPDDQWHUVHEXW • 0HWRGH VXEVWLWXVL \DLWX PHQ\HOHVDLNDQ 63/'9 GHQJDQ FDUD PHQVXEVWLWXVLDWDX³PHQJJDQWL´VDODKVDWXYDULDEHO &RQWRKff 3HUKDWLNDQ VLVWHP SHUVDPDDQ EHULNXW NHPXGLDQ WHQWXNDQ SHQ\HOHVDLDQQ\D GHQJDQPHWRGHHOLPLQDVLVXEVWLWXVLGDQJUDILN -DZDEff • 0HWRGHHOLPLQDVL [\ ⇔[\ GLNDOL[\ \ [± ⇔±[\ ± GLNDOL±[\ ± ±NXUDQJNDQ [ ⇔[ 0HQJDSDGLNXUDQJNDQ"$JDUQLODL\WHUHOLPLQDVL DWDXPHQMDGLQRODWDX³KLODQJ´ [\ ⇔[\ GLNDOL[\ \ [± ⇔±[\ ± GLNDOL±[ \ ± MXPODKNDQ \ ⇔\ 0HQJDSDGLMXPODKNDQ"$JDUQLODL[WHUHOLPLQDVL DWDXPHQMDGLQRODWDX³KLODQJ´ -DGLKLPSXQDQSHQ\HOHVDLDQQ\D ^` [\ \ [± Ayo Diskusikan 30 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϯϭHIDUP HEMAT [\ \ [± .HGXD SHUVDPDDQ WHUVHEXW ELOD GLJDPEDU EHUXSD JDULV OXUXV +LPSXQDQ SHQ\HOHVDLDQQ\DDGDODKWLWLNSRWRQJNHGXDJDULVWHUVHEXW 3HUVDPDDQJDULVL[\ PHODOXLGDQ 3HUVDPDDQJDULVLL\ [±PHODOXL±GHQJDQP Y X 7LWLNSRWRQJQ\D3-DGLKLPSXQDQSHQ\HOHVDLDQQ\D ^` • 0HWRGHVXEVWLWXVL [\ L \ [± LL 1LODL\SDGDSHUVDPDDQLLdisubstitusikanNHSHUVDPDDQLVHKLQJJDff [\ ⇔[[± ⇔[[± ⇔[± ⇔[ ⇔[ \ [±⇔\ ± ± ⇔\ -DGLKLPSXQDQSHQ\HOHVDLDQQ\D ^` 3HUKDWLNDQ63/'9EHULNXWffl D 6HOHVDLNDQ63/'9WHUVHEXWGHQJDQPHWRGHHOLPLQDVL E 6HOHVDLNDQ63/'9WHUVHEXWGHQJDQPHWRGHJUDILN F 6HOHVDLNDQ63/'9WHUVHEXWGHQJDQPHWRGHVXEVWLWXVL ± 0DVDODKE [\ [±\ P ; • 0HWRGHJUDILN Hidup Hemat 31
,ĂůĂŵĂŶϯϮHIDUP HEMAT D 0HWRGHHOLPLQDVL [\ GLNDOL [\ [±\ GLNDOL [±\ ± \ ⇔\ [\ GLNDOL [\ [±\ GLNDOL [±\ [ ⇔[ ൌ -DGLKLPSXQDQSHQ\HOHVDLDQQ\D ^ ` E 0HWRGHJUDILN 3HUVDPDDQJDULVLff[\ PHODOXLGDQ 3HUVDPDDQJDULVLff[±\ PHODOXL±GDQ Y X -DGLKLPSXQDQSHQ\HOHVDLDQQ\D ^ ` F 0HWRGHVXEVWLWXVL [\ L [±\ LL [±\ ⇔±\ ±[⇔\ ±[ [\ ⇔[\ ⇔[±[ • • • • (3 , 0) (0 , – 1) ( , 0) •(0 , 4) $OWHUQDWLI $OWHUQDWLI -DZDEDQ 32 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϯϯHIDUP HEMAT ⇔[±[ ⇔[± ⇔[± ⇔[ ⇔[ ൌ \ ±[ ⇔ \ ± ሻ ⇔ \ ± ⇔\ -DGLKLPSXQDQSHQ\HOHVDLDQQ\D ^ ` • 'LVNXVLNDQGHQJDQWHPDQ±WHPDQ$QGDGDULNHWLJDPHWRGHWHUVHEXW DSDNDKDGDPHWRGH\DQJ$QGDDQJJDSSDOLQJPXGDK" • %DJDLPDQDKLPSXQDQSHQ\HOHVDLDQQ\DELODSDGDPHWRGHJUDILNJDULV GDULNHGXDSHUVDPDDQWHUVHEXWVHMDMDU" • %DJDLPDQDKLPSXQDQSHQ\HOHVDLDQQ\DELODSDGDPHWRGHJUDILNJDULV GDULNHGXDSHUVDPDDQWHUVHEXWEHULPSLW" F 0DVDODK\DQJ7HUNDLW63/'9 0DVDODKGDODPNHKLGXSDQVHKDUL±KDUL\DQJWHUNDLWGHQJDQ63/'9FXNXS EDQ\DN \DLWX VHWLDS PDVDODK \DQJ GDSDW PHPEHQWXN GXD SHUVDPDDQ GHQJDQGXDYDULDEHO0LVDOQ\DVHSHUWLNLVDKEHULNXWLQL 6HWLDS KDUL VD\D NH VHNRODK QDLN DQJNXWDQ NRWD VHGDQJNDQ NDNDN NH VHNRODK QDLN EXV NRWD6HWLDS KDUL LEX ELDVDPHPEHULXDQJNHSDGDVD\DGDQ NDNDN XQWXN WUDQVSRUW NH VHNRODK SXODQJSHUJLVHEHVDU5S'DODP VHPLQJJXKDULPDVXNVHNRODKNDNDN NH VHNRODK KDQ\D KDUL NDUHQD DGD NHJLDWDQ ³:LVDWD -DNDUWD´ 8DQJ WUDQVSRUW NH VHNRODK \DQJGLNHOXDUNDQ LEX GDODP VHPLQJJX WHUVHEXW VHEHVDU 5S 7HQWXNDQ RQJNRV WUDQVSRUW NH VHNRODK \DQJ GLKHPDW LEX VHODPD NDNDN³:LVDWD-DNDUWD´" 3HQ\HOHVDLDQffl 0LVDOffXDQJWUDQVSRUWVD\DSHUKDUL D XDQJWUDQVSRUWNDNDNSHUKDUL E 63/'9GDULFHULWDWHUVHEXWff DE DE ffi .DUHQD \DQJ GLWDQ\DNDQ RQJNRV WUDQVSRUW NH VHNRODK \DQJ GLKHPDW LEX VHODPDNDNDN³:LVDWD.H-DNDUWD´PDND\DQJDNDQGLFDULDGDODKQLODL³E´ Ayo Diskusikan 'ĂŵďĂƌϬϬ͗ƵƐ<ŽƚĂĚĂŶŶŐŬŽƚ ^ƵŵďĞƌ͗ŚƚƚƉƐ͗ͬͬǁǁǁ͘ŵĞƌĚĞŬĂ͘ĐŽŵͬũĂŬĂƌƚĂ Hidup Hemat 33
,ĂůĂŵĂŶϯϰHIDUP HEMAT 8QWXNLWXDNDQGLHOLPLQDVLQLODLµD´Q\D DE [ DE DE ffi [ DE ffi± E ⇔ E 6HODPDKDUL [ -DGLLEXPHQJKHPDW5S 'DODP UDQJND PHQJKHPDW SHQJHOXDUDQ VDDW %XGL DNDQ PHPEHOL EXNX WXOLV GDQ EROSRLQ PHQJDPDWL SHPEHOLDQ GL GXD WRNRDODWWXOLV\DLWXWRNR³0XUDK´GDQWRNR ³/DULV´ +DVLO SHQJDPDWDQ GL WRNR ³0XUDK´$QGLPHPEHOL EXNXWXOLV GDQ EROSLQVHKDUJD5SVHGDQJNDQ %HQL PHPEHOL VHEXDK EXNX GDQ VHEXDK EROSRLQKDUXVPHPED\DU5S +DVLO SHQJDPDWDQ GL WRNR ³/DULV´ &LWUD PHPEHOL EXNX GDQ VHEXDK EROSRLQ VHKDUJD 5Sfl VHGDQJNDQ 'LQDU PHPEHOL VHEXDK EXNX GDQ VHEXDK ERSRLQ KDUXVPHPED\DU 5S0HUN GDQ NXDOLWDV EXNX GDQ EROSRLQ \DQJ GLDPDWL %XGL GDQ GLEHOL WHPDQ WHPDQQ\D GL NHGXD WRNR WHUVHEXWDGDODKVDPDGDQVHVXDLGHQJDQ\DQJELDVDGLSDNDLQ\D6HODPD VHPHVWHU %XGL PHPHUOXNDQ EXNX GDQ EROSRLQ EHUDSD XDQJ \DQJ GLSHUOXNDQXQWXNPHPEHOLNHSHUOXDQWHUVHEXWVHKHPDW±KHPDWQ\D" 3DGD VRDO LQL DGD 63/'9 \DLWX \DQJ WHUMDGL GL WRNR ³/DULV´ GDQ WRNR ³0XUDK´ 63/'9\DQJWHUMDGLGLWRNR³0XUDK´ 0LVDOKDUJDEXNX DGDQKDUJDEROSRLQ E DE DE ⇔D ±E 'HQJDQPHWRGHVXEVWLWXVLPDNDffl DE ⇔±EE ⇔±EE ⇔±±EE ± ⇔±E ±⇔E D ±E ⇔D ±⇔D -DGLGLWRNR³0XUDK´KDUJDEXNX D 5SGDQ KDUJDEROSRLQ E 5S $OWHUQDWLI $OWHUQDWLI -DZDEDQ 0DVDODKF 'ĂŵďĂƌϬϬ͗ƵŬƵdƵůŝƐ ^ƵŵďĞƌ͗ŚƚƚƉƐ͗ͬͬďĞůĂŶũĂďŚŝŶĞŬĂ͘ŝĚͬďĞƐƚƐĞůůĞƌƐ 34 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϯϱHIDUP HEMAT 63/'9\DQJWHUMDGLGLWRNR³/DULV´ 0LVDOKDUJDEXNX FGDQKDUJDEROSRLQ G FG FG 'HQJDQPHWRGHHOLPLQDVLPDNDff FG FG ± F ⇔F FG ⇔ G ⇔G -DGLGLWRNR³/DULV´KDUJDEXNX F 5SGDQ KDUJDEROSRLQ G 5S .HVLPSXODQKDUJD\DQJOHELKPXUDKff KDUJDEXNX\DQJOHELKPXUDKGLWRNR³/DULV´\DLWX5S KDUJDEROSRLQ\DQJOHELKPXUDKGLWRNR³0XUDK´\DLWX5S 6HODPDVHPHVWHU%XGLPHPHUOXNDQEXNXGDQEROSRLQ -DGLGLSHUOXNDQXDQJ [5S[5S 5Sfl5S 5Sffi 3HUKDWLNDQ DOWHUQDWLYH SHQ\HOHVDLDQ 0DVDODK F WHUVHEXW +DUXVNDK GLVHOHVDLNDQGHQJDQPHWRGHVXEVWLWXVLGDQHOLPLQDVL"0XQJNLQNDKGHQJDQ PHWRGHODLQDWDXKDQ\DPHQJJXQDNDQVHEXDKPHWRGHVDMD" 3HQXJDVDQ 3DGDNHJLDWDQ8QLW³63/'9´PHOLSXWLEHEHUDSDNDMLDQPDWHUL\DLWXffl D 7XMXDQ 3DGDSHPEHODMDUDQLQLPHPLOLNLWXMXDQSHQXJDVDQDJDUSHVHUWDGLGLNff • PHPDKDPLSHQJHUWLDQ63/'9 • WHUDPSLOPHQ\HOHVDLNDQ63/'9GDQ • WHUDPSLOPHQ\HOHVDLNDQPDVDODKWHUNDLW63/'9 E 0HGLD$ODW%DKDQGDQ6XPEHU%HODMDU/DLQQ\D $ODWGDQ%DKDQ\DQJGLJXQDNDQDODWWXOLVEXNXEHUSHWDNGDQEXNXWXJDV F /DQJNDK/DQJNDK.HJLDWDQ7XMXDQSHPEHODMDUDQSHVHUWDGLGLNGDSDWffl Ayo Diskusikan Hidup Hemat 35
,ĂůĂŵĂŶϯϲHIDUP HEMAT .HJLDWDQ 3HPEHODMDUDQ SHQJHUWLDQ 63/'9 FDUD PHQ\HOHVDLNDQ 63/'9GDQSHQ\HOHVDLDQPDVDODKWHUNDLW63/'9 .HJLDWDQ3HPEHODMDUDQDffl3HQJHUWLDQ63/'9 %XDWODK VHEXDK FHULWD GDODP NHKLGXSDQ VHKDULKDUL VHGHPLNLDQ KLQJJD FHULWD WHUVHEXW ELOD GLQ\DWDNDQ GDODP PRGHO PDWHPDWLND DNDQ PHQMDGL ³6LVWHP3HUVDPDDQ/LQHDU'HQJDQ'XD9DULDEHO´ .HJLDWDQ3HPEHODMDUDQEffl&DUDPHQ\HOHVDLNDQ63/'9 3HUKDWLNDQ63/'9EHULNXW 6HOHVDLNDQGHQJDQPHWRGHHOLPLQDVL 3HUKDWLNDQ63/'9EHULNXW 6HOHVDLNDQGHQJDQPHWRGHVXEVWLWXVL 3HUKDWLNDQ63/'9EHULNXW 6HOHVDLNDQGHQJDQPHWRGHJUDILN .HJLDWDQ3HPEHODMDUDQFffl3HQ\HOHVDLDQPDVDODKWHUNDLW63/'9 $QQDPHPEHOL NJ GXNX GDQ NJ VDODN VHKDUJD 5S VHGDQJNDQ %XGLPHPEHOLNJGXNXGDQNJVDODN\DQJVDPDVHKDUJD5S D 1\DWDNDQFHULWDGLDWDVGDODP63/'9 E 7HQWXNDQKDUJDSHUNJEXDKWHUVHEXWGHQJDQVHNXUDQJ±NXUDQJQ\D FDUDPHWRGHJUDILNHOLPLQDVLDWDXVXEVWLWXVL 6RDO/DWLKDQ7XJDV 1\DWDNDQFHULWDEHULNXWGDODP63/'9 D 8DQJVDNXNDNDN5SOHELKEDQ\DNGDULXDQJVDNXDGLNWLDS KDULGDQ 6HODPDKDULLEXKDUXVPHQ\LDSNDQXDQJ5SXQWXNXDQJ VDNXNDNDNGDQDGLN E 8DQJ EHODQMD ,EX XQWXN PDNDQ WLDS EXODQQ\D VHEHVDU VHWHQJDK GDULJDMLD\DKGDQ .HJLDWDQD .HJLDWDQF [±\ [\ [±\ [\ [±\ [\ ± .HJLDWDQE 36 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϯϳHIDUP HEMAT %LOD XDQJ EHODQMD LEX GLWDPEDK 5S VDPD GHQJDQWLJD SHUHPSDWJDMLD\DK F +DUJDWLDSNLORJUDPGDJLQJVDSLLPSRU5SOHELKPXUDKGDUL VDSLORNDOGDQ +DUJD NLODJUDP GDJLQJ VDSL LPSRU VDPD GHQJDQ KDUJD NLORJUDPGDJLQJVDSLORNDO 3HUKDWLNDQ63/'9EHULNXW 6HOHVDLNDQ 63/'9 WHUVHEXW GHQJDQ FDUD PHWRGH HOLPLQDVL PHWRGH VXEVWLWXVLGDQPHWRGHJUDILN 6HOHVDLNDQ 63/'9 EHULNXW VHNXUDQJ ± NXUDQJQ\D GHQJDQ FDUD PHWRGHHOLPLQDVLPHWRGHVXEVWLWXVLDWDXPHWRGHJUDILN 3DUGL PHPEHOL NHPHMD GDQ FHODQD SHQGHN VHKDUJD 5Sffi VHGDQJNDQ %DPEDQJ PHPEHOL NHPHMD GDQ FHODQD SHQGHN VHSHUWL \DQJ GLEHOL 3DUGL SDGD WRNR \DQJ VDPD VHKDUJD 5S %HUDSD VHOLVLKKDUJDNHPHMDGDQFHODQDSHQGHNSHUSRWRQJQ\D" 7HQWXNDQ QLODL ³S´ GDQ ³T´ VHKLQJJD VLVWHP SHUVDPDDQ OLQHDU GXD YDULDEHOEHULNXWSHQ\HOHVDLDQQ\D .HOLOLQJ VHEXDK ODSDQJDQ VHSDN EROD DGDODK PHWHU VHGDQJNDQ VHOLVLK SDQMDQJ GDQ OHEDU ODSDQJDQ PHWHU 7HQWXNDQ OXDV ODSDQJDQ VHSDNERODWHUVHEXW 'DODP UDQJND PHQJKHPDW SHQJHOXDUDQ VDDW ,EX DNDQ PHPEHOL D\DP GDQ LWLN PHQJDPDWL SHPEHOLDQ GL GXD RUDQJ SHGDJDQJ \DLWX 3DN 8GLQ GDQ 3DN 0DPDQ +DVLO SHQJDPDWDQ GL WHPSDW 3DN 8GLQ %X $QL PHPEHOLVHHNRUD\DPGDQHNRULWLNVHKDUJD5SffiVHGDQJNDQ%X %HQLPHPEHOLHNRUD\DPGDQVHHNRULWLNKDUXVPHPED\DU5Sffi +DVLO SHQJDPDWDQ GL WHPSDW 3DN 0DPDQ %X 1XQLN PHPEHOL HNRU D\DPGDQVHHNRULWLNVHKDUJD5SVHGDQJNDQ%X'LQDUPHPEHOL VHHNRU D\DP GDQ HNRU LWLN KDUXVPHPED\DU5S+DUJDSHU HNRU LWLN PDXSXQ D\DP \DQJ GLEHOL WHPDQ ± WHPDQ LEX GL PDVLQJ ± PDVLQJ NHGXD SHGDJDQJ WHUVHEXW DGDODK VDPD ,EX LQJLQ PHPEHOL HNRUD\DPGDQHNRULWLNEHUDSDXDQJ\DQJGLSHUOXNDQXQWXNPHPEHOL NHSHUOXDQWHUVHEXWVHKHPDW±KHPDWQ\D" fl %DSDN%XGLPHPLOLNL KDODPDQ UXPDK VHOXDV P EHUKXEXQJ UXPDK 3DN %XGL EHUGHNDWDQ GHQJDQ SDVDU PDND GLPDQIDDWNDQ XQWXN SDUNLU XPXP 3DGD VXDWX KDUL WHUGDSDW NHQGDUDDQ \DQJ WHUGLUL PRELO GDQ PRWRU$UHD\DQJGLEXWXKNDQXQWXNSDUNLUPRELOPVHGDQJNDQXQWXN PRWRU P %LOD XDQJ SDUNLU PRELO 5S GDQ PRWRU 5S [±\ fl [\ [±\ [\ S[T\ S[\ ± Hidup Hemat 37
,ĂůĂŵĂŶϯϴHIDUP HEMAT Modul 2 EHUDSDVHEDQ\DN±EDQ\DNQ\DXDQJ\DQJGLWHULPD3DN%XGLGDULWHPSDW SDUNLUWHUVHEXW" E. Rangkuman *DPEDU*UDILN)XQJVLGDODP%LGDQJ.DUWHVLXV *DPEDUIXQJVL\ffl[→[GDODPELGDQJNDUWHVLXV .LWDEXDWWDEHOGHQJDQGDHUDKDVDO^±±±` [ Domain ± ± ± [ ± ± ± \ I[ range ± : %LODDQJJRWDGDHUDKDVDOEHUXSDELODQJDQEXODWVHSHUWLSDGDWDEHOPDND JDPEDUIXQJVLWHUVHEXWEHUXSDWLWLN±WLWLN ELUXELODGLQ\DWDNDQVHEDJDL KLPSXQDQGLWXOLV^[\|\ [[\∈%`1DPXQELODGDHUDKDVDOELODQJDQ UHDOVHKLQJJDGRPDLQ^[|±[[∈5`PDNDJDPEDUQ\DEHUXSD JDULVFRNODWDWDXGDSDWGLWXOLV^[\|\ [[\∈5` 3HQJHUWLDQSHUVDPDDQJDULVOXUXV %LOD VHEXDK IXQJVL I GLJDPEDU GDODP ELGDQJ NDUWHVLXV GHQJDQ \ I[ EHUXSD JDULV OXUXVPDND UXPXVIXQJVLWHUVHEXWPHUXSDNDQ SHUVDPDDQ JDULVOXUXV 3HQXOLVDQSHUVDPDDQJDULVOXUXVDGDPRGHO\DLWXff [ \ I[ • • • • • • • A B 38 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϯϵHIDUP HEMAT 9 SHUVDPDDQJDULV\DQJGLQ\DWDNDQVHFDUDexplisit\ P[F 9 SHUVDPDDQJDULV\DQJGLQ\DWDNDQVHFDUDimplisit\DLWXD[E\F 3HUVDPDDQJDULV\ P[F &RQWRKff *DPEDUODKSDGDELGDQJNRRUGLQDWNDUWHVLXV\ ଵ ଶ [ 7DEHOXQWXNJDULV\ ଵ ଶ [ [ domain ± ± ± ଵ ଶ [ ± ± ± \ I[ range : 3HUVDPDDQJDULVD[E\F 3HUKDWLNDQJDPEDUGLDWDVJDULV\ ଵ ଶ [SDGDNHGXDJDULVLWXPDVLQJ ±PDVLQJPHPLOLNLWLWLNLVWLPHZD\DLWXWLWLN$GDQ%SDGDJDULV\ [ 3 GDQ 4 SDGD JDULV \ ଵ ଶ [ .HLVWLPHZDDQ WLWLN WHUVHEXW DGDODK PDVLQJ±PDVLQJWLWLNEHUDGDGLVXPEXNRRUGLQDW • 6HWLDSWLWLN[\SDGDVXPEX<PDND[ GDQVHWLDSWLWLN[\ SDGDVXPEX;PDND\ • 0HODOXLGXDWLWLNWHUWHQWXKDQ\DGDSDWGLEXDWVHEXDKJDULVOXUXV &RQWRK *DPEDUODKJDULVGHQJDQSHUVDPDDQ[\ 7LWLNSRWRQJGHQJDQVXPEX;PDND\ [ \ I[ • • • • • • • P Q Hidup Hemat 39
,ĂůĂŵĂŶϮHIDUP HEMAT [ ⇔[ ⇔[± ±⇔[ ± ⇔ [ ±MDGLJDULVWHUVHEXWPHODOXL± 7LWLNSRWRQJGHQJDQVXPEX<PDND[ \ ⇔\ ⇔\± ±⇔\ ± ⇔ \ ±MDGLJDULVWHUVHEXWPHODOXL± 0DNDJDULV[\ PHODOXL±GDQ± Y X 3RVLVLWLWLNWHUKDGDSJDULV 3RVLVLWLWLN7[\WHUKDGDSJDULV\ P[FGDSDWGLNHWDKXLGHQJDQFDUD PHQVWXEVWLWXVL [\ NH SHUVDPDDQ JDULV%LOD KXEXQJDQ SHUQ\DWDDQQ\D VDPD GHQJDQ PDND WLWLN WHUVHEXW EHUDGD SDGD JDULV %LOD KXEXQJDQ SHUQ\DWDDQQ\D ³OHELK GDUL´ ! PDND WLWLN WHUVHEXW EHUDGD GL DWDV JDULV %LODKXEXQJDQSHUQ\DWDDQQ\D³NXUDQJGDUL´fiPDNDWLWLNWHUVHEXWEHUDGD GLEDZDKJDULV • 3HUVDPDDQJDULV\DQJPHODOXLWLWLNWHUWHQWXGHQJDQJUDGLHQ³P´ 3HUVDPDDQJDULV\DQJPHODOXL$[\GDQJUDGLHQ P \±\ P[±[ &RQWRKff 7HQWXNDQSHUVDPDDQJDULV\DQJPHODOXL%±GHQJDQJUDGLHQ -DZDEffl \±\ P[±[ ⇔\± [±± ⇔\± [ ⇔\± [fl 3HUVDPDDQJDULVPHODOXLGXDWLWLN$[\GDQ%[\ *DULVWHUVHEXWPHODOXL$[\GDQ%[\PDNDP$% ܡିܡ ܠିܠ ܡିܡ ܡିܡ ܠିܠ ൌ ܠିܠ &RQWRKff 7HQWXNDQSHUVDPDDQJDULV\DQJPHODOXL$±GDQ%±± -DZDEffl ܡെܡ ܡ െ ܡ ܠെܠ ൌ ܠ െ ܠ ± ± • • ± ± 40 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϰϬHIDUP HEMAT ିܡ ⇔ ିି ൌ ܠିሺିሻ ିૠିሺିሻ⇔ ܡି ିି ൌ ܠା ିૠା ⇔ ିܡ ି ൌ ܠା ି ⇔ ିܡ ൌ ܠା ⇔\± [ ⇔\± [fl ⇔[±\ *UDGLHQJDULVVHMDMDU %LODJDULVJVHMDMDUGHQJDQJDULVOPDNDJUDGLHQNHGXDJDULVWHUVHEXWVDPD DWDXJDULVglPDNDPg Pl *UDGLHQJDULVWHJDNOXUXV 'XDJDULV VDOLQJWHJDNOXUXVPDNDKDVLOSHUNDOLDQ JUDGLHQQ\DDGDODK ± +DOWHUVHEXWGDSDWGLWXOLVff%LODJDULVg ⊥ l,PDNDPgPl ± 63/'9 3HUVDPDDQOLQHDU 3HUVDPDDQOLQHDUVDWXYDULDEHOOLQHDUGLVLQLDUWLQ\DSDQJNDWWHUWLQJJLGDUL YDULDEHOQ\DDGDODKVDWXGDQKDQ\DWHUGDSDWVDWXYDULDEHO &RQWRKff D YDULDEHOQ\D³D´GDQ³DSDQJNDW´ ±[ [YDULDEHOQ\D³[´GDQ³[SDQJNDW´ %XNDQFRQWRKffl D NDUHQDYDULDEHO³D´SDQJNDWGXD D±E NDUHQDDGDYDULDEHO\DLWX³D´GDQ³E´ 3HUVDPDDQ OLQHDU GXD YDULDEHO \DLWX VHEXDK SHUVDPDDQ \DQJ PHPLOLNL GXDYDULDEHO\DQJPDVLQJ±PDVLQJEHUSDQJNDWVDWX &RQWRKffl[\ YDULDEHOffl³[´GDQ³\´PDVLQJ±PDVLQJSDQJNDW D±E YDULDEHOffl³D´GDQ³E´PDVLQJ±PDVLQJSDQJNDW %XNDQFRQWRKffl [\ NDUHQDYDULDEHO³[´SDQJNDWGXD D±EF ffiNDUHQDDGDYDULDEHO\DLWXDEGDQF 3HQJHUWLDQ6LVWHP3HUVDPDDQ/LQHDU'XD9DULDEHO %LODWHUGDSDWGXDSHUVDPDDQOLQHDUGXDYDULDEHOGLPDQDSHUVDPDDQ\DQJ VDWXWHUNDLWGHQJDQSHUVDPDDQ\DQJODLQ0DNDDNDQWHUEHQWXNVLVWHP SHUVDPDDQOLQHDUGXDYDULDEHO DE D±E 3HQ\HOHVDLDQ6LVWHP3HUVDPDDQ/LQHDU'XD9DULDEHO 9 0HWRGH HOLPLQDVL \DLWX GHQJDQ FDUD PHQJHOLPLQLU DWDX ³PHQJKLODQJNDQ´VDODKVDWXYDULDEHO 7HQWXNDQSHQ\HOHVDLDQQ\DGHQJDQPHWRGHHOLPLQDVL [\ \ [± [\ ⇔[\ GLNDOL [\ \ [± ⇔±[\ ±GLNDOL ±[\ ± ±NXUDQJNDQ [ ⇔[ \ [±⇔\ ± ± ⇔\ -DGLKLPSXQDQSHQ\HOHVDLDQQ\D ^` Hidup Hemat 41
,ĂůĂŵĂŶϰϭHIDUP HEMAT 9 0HWRGH VXEVWLWXVL \DLWX GHQJDQ FDUD PHQVXEVWLWXVL DWDX ³PHQJJDQWL´VDODKVDWXYDULDEHO 7HQWXNDQSHQ\HOHVDLDQQ\DGHQJDQPHWRGHHOLPLQDVLVXEVWLWXVLGDQ JUDILN [\ \ [± [\ L \ [± LL 1LODL\SDGDSHUVDPDDQLLdisubstitusikanDWDXGLJDQWLNDQNH SHUVDPDDQLVHKLQJJDff [\ ⇔[[± ⇔[[± ⇔[± ⇔[ ⇔[ \ [±⇔\ ± ± ⇔\ -DGLKLPSXQDQSHQ\HOHVDLDQQ\D ^` 9 0HWRGHJUDILN\DLWXGHQJDQFDUDPHQJJDPEDUPDVLQJ±PDVLQJ SHUVDPDDQ GDQ PHQHQWXNDQ WLWLN SRWRQJ JUDILN SHUVDPDDQ WHUVHEXW 7HQWXNDQSHQ\HOHVDLDQQ\DGHQJDQPHWRGHJUDILN [\ \ [± .HGXD SHUVDPDDQ WHUVHEXW ELOD GLJDPEDU EHUXSD JDULV OXUXV +LPSXQDQSHQ\HOHVDLDQQ\DDGDODKWLWLNSRWRQJNHGXDJDULVWHUVHEXW 3HUVDPDDQJDULVL[\ PHODOXLGDQ 3HUVDPDDQJDULVLL\ [±PHODOXL±GHQJDQP Y X 7LWLNSRWRQJQ\DDGDODK3 -DGLKLPSXQDQSHQ\HOHVDLDQQ\D ^` ± P ; 42 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7
,ĂůĂŵĂŶϰϮHIDUP HEMAT Modul 2 F. Saran Referensi 8QWXNPHQDPEDKZDZDVDQGDODPSHPDKDPDQWHUNDLW0RGXO\DQJPHOLSXWL PDWHUL persamaan garis lurus dan sistem persamaan linear dua variabel. PDND GLKDUDSNDQ PHQFDUL VXPEHU ODLQ DWDX UHIHUHQVL 6DUDQ UHIHUHQVL XQWXN PHQGXNXQJSHQDPEDKDQZDZDVDQWHUVHEXWDQWDUDODLQVHEDJDLEHULNXWffl -XGXO%XNXffl³(QVLNORSHGLD0DWHPDWLND7HUDSDQ´.DU\D6XH7KRPVKRQ GDQ,DQ)RUWVWHUGHQJDQMXGXOWHPDWHUMHPDKDQffl D 0DWHPDWLNDGDODP0DV\DUDNDW E 0DWHPDWLNDGDODP2ODKUDJD F 0DWHPDWLNDGDODP/LQJNXQJDQ G 0DWHPDWLNDGDODP7HPSDW.HUMD H 0DWHPDWLNDGDODP0DNDQDQ I 0DWHPDWLNDGDODP5DQFDQJ%DQJXQ J 0DWHPDWLNDGDODP7HOHYLVL K 0DWHPDWLNDGDODP6DLQV L 0DWHPDWLNDGDODP7HNQRORJL M 0DWHPDWLNDGDODP3HUMDODQDQ N 0DWHPDWLNDGDODP5XPDK O 0DWHPDWLNDGDODP7XEXK -XGXO%XNXffl³7LQJNDWNDQ.HPDPSXDQ2WDN$QGDImprove Your Brain Power´.DU\D-DFNLH*XWKULHGDQ7LP3UHVWRQ -XGXO%XNXffl³5HIHUHQVL0DWHPDWLNDGDODP.HKLGXSDQ0DQXVLD´.DU\D'U :DK\XGLQGDQ'UV6XGUDMDW03G -XGXO%XNXffl³0HQ\HODPDWNDQ/LQJNXQJDQ+LGXS´.DU\D$GULDQ5 1XJUDKD 6XPEHUPHGLDLQWHUQHWpencarian dengan kata kuncifflpersamaan garis lurus dan sistem persamaan linear dua variabel.SHQHUDSDQQ\DGDODP NHKLGXSDQVHKDULKDUL Hidup Hemat 43
,ĂůĂŵĂŶϰϯHIDUP HEMAT Modul 2 G. Penilaian Akhir Modul 2 3LOLKODKMDZDEDQ\DQJ$QGDDQJJDSEHQDUGHQJDQFDUDPHPEHUL WDQGDVLODQJSDGDKXUXI$%&DWDX'LWHP 3HUKDWLNDQKLPSXQDQEHULNXW L ^[\|\ ±[[\∈5` LL ^[\|[±\ [\∈5` LLL ^[\|\ [\∈5` LY ^[\|\ [[\∈5` +LPSXQDQWHUVHEXWELODGLJDPEDUEHUXSDJDULVOXUXVkecuali« $ L % LL & LLL ' LY 3HUKDWLNDQSHUQ\DWDDQEHULNXWff L JUDGLHQDGDODKNRPSRQHQ\GLEDQGLQJNRPSRQHQ[VXDWXJDULV LL JUDGLHQDGDODKNRPSRQHQ[GLEDQGLQJNRPSRQHQ\VXDWXJDULV LLL JUDGLHQDGDODKNRPSRQHQ\GLNDOLNRPSRQHQ[VXDWXJDULV LY JUDGLHQDGDODKNRPSRQHQ[GLNXUDQJNRPSRQHQ\VXDWXJDULV 3HUQ\DWDDQGLDWDV\DQJEHQDUDGDODK« $ L % LL & LLL ' LY *UDGLHQJDULVGHQJDQSHUVDPDDQ\ ±[DGDODK« $ % & ± ' ± *UDGLHQJDULVGHQJDQSHUVDPDDQ[ ±DGDODK« $ % & ± ' WDNWHUGLILQLVLNDQ 44 MatemaƟ ka Paket B Setara SMP/MTs Kelas VIII Modul Tema 7