1 Planeación Recta Númerica

 

KTD[KHF TKD[IEF]BF @KIK]FH ¨DFI[UL F]FIEF HL]F¨ _HFIKFDBLI EBEFDUBDF

FTB@IFU[]F:

@]FEL R @][_L:

ILAM]K EKH AFKTU]L:

Aftkaætbdfs

6¿ F

Aôibdf Hbzkt @frdáf Tæidckz

MHLV[K:

_K]BLEL:

ALE[HLT:

]k`uhfrbzfdbôi

; aôeuhls

UKAF:

6.- Iúakrls ik`ftbvls ik`ftbvls y rkdtf iua iuaârbdf ârbdf _]L_LTBUL EKH MHLV[K:

-

_rlpbd _rlpbdbfr bfr bistfid bist fidbfs bfs pfrf kh rkdli rkdlildba ldbabkit bkitl, l, ek usl fiæhbsb fiæhbsbs s ek hls iúak iúakrls rls kitk kitkrls rls y sus lpkrfdb lpkrfdblik liks s pfrf alekhbzfr sbtufdbliks prlmhkaætbdfs f trfvâs hf yAftkaætbdf.

F_]KIEBZFJKT KT_K]FELT:

Dlal rksuhtfel ekh kstuebl ek âstk tkaf tkaætbdl sk kspkrf quk hls fhuails:

-

]kdlilzdfi iúakrls kitkrls. Bekitbnbquki hls iúakrls plsbtbvls y ik`ftbvls. Lrekiki iúakrls kitkrls ek afikrf fsdkiekitk y eksdkiekitk cfdbkiel usl ek hf rkdtf iuaârbdf.

 Fphbquki kitkrls. prlpbkefeks pfrf hf rkslhudbôi ek sbtufdbliks prlmhkaætbdfs quk baphbquki dæhduhls dli iúakrls - Knkdtúki lpkrfdbliks kitrk iúakrls kitkrls

]KHFDBLI DLI KH _K]NBH EK K@]KTL:

Kh fhuail eksfrrlhhfrf dlildbabkitls, dlildbabkitls, dlapktkidbfs, cfmbhbefeks nuiefakitfhks y prldksls ek rfzlifabkitls supkrblrks, quk hls prkpfrki pfrf fsuabr rksplisfmhkakitk hfs tfrkfs ek pfrtbdbpfdbôi sldbfh, kirbqukdkr su vbef pkrslifh, fprkiebkiel aæs fhhæ sk su nlrafdbôi ksdlhfr, y tkibkiel nhkxbmbhbefe ek fefptfdbôi f hls dfambls.

 

DLA_KUKIDBF F EKTF]]LHHF]:

-

Dlapktkidbfs pfrf kh fprkiebzfjk pkrafikitk Dlapktkidbfs pfrf kh afikjl ek hf binlrafdbôi Dlapktkidbfs pfrf kh afikjl ek sbtufdbliks

 

 

 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\  _rlnkslrf Aôibdf Hbzkt @frdáf Tæidckz

KTD[KHF TKD[IEF]BF @KIK]FH ¨DFI[UL F]FIEF HL]F¨

 

_HFIKFDBLI EBEFDUBDF Kjk: Nlraf, Kspfdbl y Akebf Ukaf: Iúakrls ik`ftbvls y rkdtf iuaârbdf Dlildbabkitls y cfmbhbefeks:

]kdlildbabkitl ]kdlildbabkit l y usl ek iúakrls plsbtbvls y ik`ftbvls y sus lpkrfdbliks pfrf rkslhvkr prlmhkafs. Bitkrprktfdbôi ek rkhfdbliks kitrk iúakrls kitkrls, plsbtbvls y ik`ftbvls, fsá dlal su lreki y rkprkskitfdbôi ki hf rkdtf iuaârbdf pfrf rkslhvkr prlmhkafs ki ebnkrkitks dlitkxtls. FDUB^BEFEKT FDUB^BEFEKT EK BIBDBL:

-

-

-

Kh eldkitk dlapfrtk dli hf dhfsk kh bibdbl ek ui iukvl dlitkibel, fitbdbpfiel quk vfi f rks rkslhv lhvkr kr prl prlmhk mhkafs afs rkf rkfhks hks dla dlal l hls quk sk prks prkski kitf tfi i ki kh au auie iel l ek hl hls s ik`l ik`ldb dbls ls,, hf dbkidbf y hf vbef ebfrbf. _rkskitf f hls fhuails kh sb`ubkitk prlmhkaf: Tk cfdk uif kxdfvfdbôi ek 3 a ek prlnuiebefe fh hfel ek ui aurl ek 3 a ek fhturf. ¼Vuâ ebnkrkidbf kxbstk kitrk hls 3 a ek fhturf ekh aurl y hls 3 a ek prlnu prlnuieb iebefe efe ek hf kxdfv kxdfvfdb fdbôi< ôi< ¼Kxbstk fh`uif ebnkrkidbf kitrk hls 5 a slmrk kh ibvk ibvkhh ekh ekh tk tkrr rrki kil l y hls hls 5 a mfjl mfjl kh ibvk ibvkhh ekh ekh tkrrkil< ¼Dôal ebstbi`ubrhls< ¼Dôal sfmkr duæiel sli ; a slmrk kh ibvkh ekh

K^FH[FDBLI

]KD[]TLT EBEFDUBDLT

-

_bzfrrôi _bitfrrli Hbmrktf Hæpbz @laf

- Bitkrâs - _frtbdbpfdbôi - ]kspktl -  Fsbstkidbf -  Fr`uakitfdbôi - Ebsplsbdbôi -

Lreki  Kjkrdbdbls

-

_frtbdbpfdbôi Bitkrâs Lreki

tkrrkil l4a mfjl kh ibvkh ekhkh tkrrkil sbitkrrkil‑ tkikr quk ksdrbmbr hfs nrfsks ‘slmrk ibvkh ekh l ‘mfjl ibvkh ekh tkrrkil< ¼_leráfs dlhldfr f hls iúakrls ek frrbmf y fmfjl fh`uif sköf l sb`il pfrf ebnkrkidbfrhls< FDUB^BEFEKT EK EKTF]]LHHL:

-

Hls kstuebfitks rksplieki hfs prk`uitfs y

-

_bzfrrôi _bitfrrli Hfabifs

 

-

-

-

-

-

-

huk`l rkprkskitfi hf sbtufdbôi akebfitk ui dæhduhl, dli su rksuhtfel. [i pkz quk ifefmf f = a ek hf supkrnbdbk sk suakr`k 5 aktrls. ¼F quâ prlnuiebefe sk kidukitrf< m. Ki hf prbakrf afil ek ui juk`l pkrebô 0 nbdcfs y ki hf sk`uief `fiô 64. ¼Duæh ks su mfhfidk< d. [i fsdkislr kstfmf ki kh qubitl pbsl y mfjô ldcl pbsls. ¼Eôiek sk kidukitrf< e. ¼Duæitls iúakrls kitkrls cfy kitrk -4 y ;< k. [i muzl kstæ ifefiel f 0 a ek prlnuiebefe abkitrfs uif `fvbltf vukhf f 3 a ek fhturf slmrk âh. ¼Vubâi kstæ aæs dkrdf ek hf supkrnbdbk< n. F y M sli iúakrls ik`ftbvls. Tb M kstæ aæs dkrdf ekh dkrl, ¼duæh ek hls els ks akilr< ¼Duæh tbkik afylr aôeuhl< `. Lrekif kstfs tkapkrfturfs ek hf aæs mfjf f hf aæs fhtf. Huk`l, rlekf hf ek afylr  aôeuhl: ;¿ D 4¿ mfjl dkrl ?¿ D -0¿ D 3¿ D _fsfel ui tbkapl sk rk`bstrfi ki kh pbzfrrôi hfs dlidhusbliks dlistrubefs plr dfef uil.

-

Hbmrktf Hæpbz Cljfs ek dlhlrks Afrdfelrks ]k`hf Ubjkrfs

-

Urfmfjl biebvbeufh Ebsplsbdbôi ]kspktl

 

FDUB^BEFEKT EK DBK]]K:

-

_fsfel ui tbkapl sk rk`bstrfi ki kh pbzfrrôi hfs dlidhusbliks dlistrubefs plr dfef uil.

-

Hbmrktf _bzfrrôi _bitfrrli Hæpbz @laf Hæpbz

- Urfmfjl ki kqubpl - _frtbdbpfdbôi - Bitkrâs - Lreki - Ebsplsbdbôi - ]kspktl -  Fr`uakitfdbôi

Fdtbvbefeks kxtrf dhfsk: LMTK]^FDBLIKT:

- Tk rknlrzfrf kstk tkaf ekjfiel fdtbvbefeks pfrf rkfhbzfr ki dfsf.

KTD[KHF TKD[IEF]BF @KIK]FH ¨DFI[UL F]FIEF HL]F¨

 

_HFIKFDBLI EBEFDUBDF Kjk: Nlraf, Kspfdbl y Akebf Ukaf: Iúakrls ik`ftbvls y rkdtf iuaârbdf Dlildbabkitls y cfmbhbefeks:

]kdlildbabkitl y usl ek iúakrls plsbtbvls y ik`ftbvls y sus lpkrfdbliks pfrf rkslhvkr prlmhkafs. Bitkrprktfdbôi ek rkhfdbliks kitrk iúakrls kitkrls, plsbtbvls y ik`ftbvls, fsá dlal su lreki y rkprkskitfdbôi ki hf rkdtf iuaârbdf pfrf rkslhvkr prlmhkafs ki ebnkrkitks dlitkxtls. FDUB^BEFEKT FDUB^BEFEKT EK BIBDBL:

-

K^FH[FDBLI

]KD[]TLT EBEFDUBDLT

-

Kh eldk eldkit itk k rktl rktlaf af hl tr trfm fmfj fjfe fel l ki hf dhfs dhfsk k fitkrblr.

_bzfrrôi _bitfrrli Hbmrktf Hæpbz @laf @klphfil

- Bitkrâs - _frtbdbpfdbôi - ]kspktl -  Fsbstkidbf -  Fr`uakitfdbôi - Ebsplsbdbôi -

Lreki  Kjkrdbdbls

-

_frtbdbpfdbôi Bitkrâs Lreki Urfmfjl biebvbeufh Ebsplsbdbôi ]kspktl

-

Urfmfjl ki kqubpl _frtbdbpfdbôi Bitkrâs Lreki

FDUB^BEFEKT EK EKTF]]LHHL:

-

_hfitkf hf sb`ubkitk sbtufdbôi prlmhkaætbdf:

FDUB^BEFEKT EK DBK]]K:

-

Kh eldkitk kvfhufrf biebvbeufhakitk fh fhuail y kxphbdfrf kxph bdfrf ek afikrf afikrf pkrslifhbz pkrslifhbzfef fef hfs euefs rknkrkitks fh tkaf.

 

-

_bzfrrôi _bitfrrli Hfabifs Hbmrktf Hæpbz Cljfs ek dlhlrks

--

Afrdfelrks ]k`hf Ubjkrfs

-

Hbmrktf _bzfrrôi _bitfrrli Hæpbz

UBKA_L

 

-

-

Ek af afik ikrf rf `k `kik ikrf rfhh hls hls fh fhua uail ils s fplr fplrtf tfræ ræi i akebfitk sus prlpbfs pfhfmrfs, ek quk hks sbrvk hl fprkiebel ki hf dhfsk. Tk hks ekjfræ uif fdtbvbefe ki dfsf, ki eôiek kh fhuail rknukrdk hls dlildbabkitls fequbrbels ki kh eáf.

-

@laf Hæpbz

- Ebsplsbdbôi - ]kspktl -  Fr`uakitfdbôi

LMTK]^FDBLIKT:

- Kh fhuail trfmfjfræ ki dfsf, ek afikrf biebvbeufh ki hfs fdtbvbefeks ek hf dlisb`if.

KTD[KHF TKD[IEF]BF @KIK]FH ¨DFI[UL F]FIEF HL]F¨

 

_HFIKFDBLI EBEFDUBDF Kjk: Nlraf, Kspfdbl y Akebf Ukaf: Iúakrls ik`ftbvls y rkdtf iuaârbdf Dlildbabkitls y cfmbhbefeks:

]kdlildbabkitl y usl ek iúakrls plsbtbvls y ik`ftbvls y sus lpkrfdbliks pfrf rkslhvkr prlmhkafs. Bitkrprktfdbôi ek rkhfdbliks kitrk iúakrls kitkrls, plsbtbvls y ik`ftbvls, fsá dlal su lreki y rkprkskitfdbôi ki hf rkdtf iuaârbdf pfrf rkslhvkr prlmhkafs ki ebnkrkitks dlitkxtls. FDUB^BEFEKT FDUB^BEFEKT EK BIBDBL:

-

Tk rkpfsfi hls dlitkibels trfmfjfels eurfitk hfs els dhfsks. Kh prlnkslr prlnkslr vf phfit phfitkfiel kfiel prlmhka prlmhkafs fs hls quk, huk`l ek uif prbakrf rkspukstf biebvbeufh, sli fifh fifhbbzf zfel els s ki dlij lijuitl uitl,, dl dlis isbe bekr krf fiel iel prl prldkeb dkeba abk bki itl tls s dl dlrr rrkd kdttls y krrf krrfe els, ls, y ektkibâielsk ki kstls úhtbals pfrf bief`fr ki hls nfhhls ek rfzlifabkitl y phfitkfr fh`lrbtals dlrrkdtls.

K^FH[FDBLI

]KD[]TLT EBEFDUBDLT

-

_bzfrrôi _bitfrrli Hbmrktf Hæpbz @laf @klphfil

- Bitkrâs - _frtbdbpfdbôi - ]kspktl -  Fsbstkidbf -  Fr`uakitfdbôi - Ebsplsbdbôi --

Lreki  Kjkrdbdbls

-

_frtbdbpfdbôi Bitkrâs Lreki Urfmfjl biebvbeufh

--

Ebsplsbdbôi ]kspktl

UBKA_L

.6? Abiutls.

FDUB^BEFEKT EK EKTF]]LHHL:

-

Kh prbakr prlmhkaf ek hf dhfsk ks: ^fhkitái aukvk su nbdcf slmrk ui juk`l ek tfmhkrl ek hf sb`ubkitk afikrf: fvfizf ; dfsbhhfs eksek hf pfrtbef, rktrldkek 4, fvfizf 5, rktrldkek 6, rk rktr trld ldke kek k =, fvfi fvfizf zf 3, rktr rktrld ldke kek k > y fvfi fvfizf zf 5. ¼Ki ¼Ki quâ quâ dfsb dfsbhh hhf f kstæ kstæ< < _f _frf rf fv fvkr krb` b`uf ufrh rhl, l, pukek pukeks s br lp lpkr krfi fiel el dl dli i hl hls s iúakrls f akebef quk vfs hkyâielhl, l mbki suafr tlels hls fvfidks y rkstfr hf suaf ek hls rktrldksls. _rldkek ek hfs els afikrfs y dlaprukmf sb lmtbkiks kh absal rksuhtf.

-

_bzfrrôi _bitfrrli Hfabifs Hbmrktf

-

Hæpbz

5? abiutls

 

-

]kslhvkræi hls sb`ubkitks kjkrdbdbls: Dfhduhf: f. 3 — 6= — = + 2 — 6 — 2 + 65 — ; + > — 3 1 m. 6 — 5 - 0 + 2 — 4 — 6? + 5 + =? + 4 1

Tuprbak hls pfrâitksbs y dfhduhf. f. ( -2 +;) — (4- 0) + (-4+;) 1 m. 6? + (->+5) — (=-3) — (-6) 1 d. 65 — (-6-=) + (->+2) +; — (-4) 1 FDUB^BEFEKT EK DBK]]K:

-

-

-

Kh eldkitk kvfhufrf biebvbeufhakitk fh fhuail y kxphbdfrf kxph bdfrf ek afikrf afikrf pkrslifhbz pkrslifhbzfef fef hfs euefs rknkrkitks fh tkaf. Ek af afik ikrf rf `k `kik ikrf rfhh hls hls fh fhua uail ils s fplr fplrtf tfræ ræi i akebfitk sus prlpbfs pfhfmrfs, ek quk hks sbrvk hl fprkiebel ki hf dhfsk. Tk hks ekjfræ uif fdtbvbefe ki dfsf, ki eôiek kh fhuail rknukrdk hls dlildbabkitls fequbrbels ki kh eáf.

LMTK]^FDBLIKT:

-

Hbmrktf _bzfrrôi _bitfrrli Hæpbz

-

-

@laf Hæpbz

- Ebsplsbdbôi - ]kspktl -  Fr`uakitfdbôi

Urfmfjl ki kqubpl _frtbdbpfdbôi Bitkrâs Lreki

6? abiutls

 

- Kh fhuail trfmfjfræ ki dfsf, ek afikrf biebvbeufh ki hfs fdtbvbefeks ek hf dlisb`if.

 

Fdtvbefeks kxrf dhfsk:

-

-

-

-

_fmhl tkiáf ui sfhel ek $ =2?? ki su dukitf mfidfrbf. Cbzl dbidl kxtrfddbliks ki kh dfjkrl futlaætbdl, tlefs ek $ >??. Fekaæs hk ekmbtfrli els dultfs ek $42?. ¼Duæitl tbkik quk ekplsbtfr pfrf quk hf dukitf qukek dli ui sfhel $ ;??< Ksdrbmk hls dæhduhls quk cfdks. Hf skafif pfsfef, ui abikrl trfmfjô f 5 aktrls mfjl kh ibvkh ekh afr y kstf skafif f 6= aktrls mfjl kh ibvkh ekh afr. f. Ksdrbmk ui dæhduhl quk rkprkskitk hf sbtufdbôi. m. ¼Duæh ks hf ebstfidbf kitrk famfs umbdfdbliks< d. ¼Dli quâ dæhduhl pukeks rkprkskitfr hf sbtufdbôi< e. ¼Kh abikrl fsdkiebô l eksdkiebô< Dufiel Jufi sk nuk f elrabr, hf tkapkrfturf krf ek = `rfels mfjl dkrl. Fh ekspkrtfr, cf fuakitfel 2¿ D. ¼Ek duæitls `rfels ks hf tkapkrfturf ki kstk alakitl ek ekspkrtfrsk<

[ils kxdursblibstfs quk sk kidukitrfi ki uif clielifef f 5> a mfjl kh ibvkh ekh afr, fh pbk ek uif alitföf, ksdfhfi 4=? a cfstf su dfapfakitl. ¼F quâ fhturf sk kidukitrfi< Hf tfmhf aukstrf f quâ tkapkrfturfs sk fhafdkifi fh`uils fhbakitls pfrf kvbtfr hf dlitfabifdbôi. Hædtkls 5¿D Nrutfs y vkreurfs 0¿D Dli`khfels druels -=?¿D Dfrik ek dkrel nrksdf -4¿D

- Dli`khfels dldbifels -3¿D ]kspliek: f. ¼Vuâ ebnkrkidbf ek tkapkrfturf cfy kitrk hls hædtkls y hf nrutf< m. ¼Vuâ ebnkrkidbf ek tkapkrfturf kitrk hfs nrutfs y hls dli`khfels dldbifels< d. ¼R kitrk hls hædtkls y hf h f dfrik ek dkrel< e. ¼Duæitls `rfels ek ebnkrkidbf cfy kitrk hf tkapkrfturf aæs fhtf y hf aæs mfjf<

 

Ki dfef dfsl, ekdbek sb hfs fnbrafdbliks sli vkrefekrfs l nfhsfs. Kxphbdf tus ekdbsbliks :

f. Kh sb`ubkitk ek -6?? ks -6?6. m. Kh fitkrblr ek 22 ks 6??. d. Kh sb`ubkitk ek -22 ks -6??. e. -4> ′ -4;. k. 50 › -6?6. Ki uif kstfdbôi ek ksquá hf tkapkrfturf aæs fhtf cf sbel ek =? D y hf aæs mfjf, ek -=4? D. ¼Duæh cf sbel hf ebnkrkidbf ek tkapkrfturf<

f. =;¿ m. =6¿ d. -=6 [i fvbôi vukhf f 66??? a y ui sumafrbil kstæ f -3;? a. ¼Duæh ks hf ebnkrkidbf ek fhturf kitrk famls < f. 6?.6;? m. 66.3;? d. 66.=;? Ck vbfjfel eksek ^bhhf Elhlrks eliek hf tkapkrfturf krf ek 66 `rfels cfdbf ^bhhf Afráf ki quk hf tkapkrfturf ks ek 4 `rfels.

¼Duæh cf sbel hf ebnkrkidbf ek tkapkrfturf< f. 3¿ m. 65¿ d. -65¿ Dlaprfals uif ckhfekrf. Dufiel hf kidcunfals f hf rke khâdtrbdf kstæ f hf tkapkrfturf fambkitk, quk ks ek =;? D. Tb dfef clrf mfjf hf tkapkrfturf ;? D, ¼f quâ tkapkrfturf kstfræ fh dfml ek > clrfs<

 

Fdtvbefeks kxrf dhfsk