2º Matemáticas 2020-2021 Curso Remedial

 

@]UHIGNS@CH\ JXIG@DHIW@BH\ LXU\F UHDHGN@B

D@WHDÀWNL@\ D@WHDÀ WNL@\ NN

 

]UNDHU@ \HD@I@ JHLA@ Buihs

 

GNUHLLNÜI GH L@BNG@G @]UHIGNS@CH\ @L@GÎDNL@JXIG@DHIW@BH\3 GH \HLXIG@UN@ KU@GF3

@\NKI@WXU@3 D`thdàtnl`s NN

Lnlbf Hslfb`r 5=5=-5=50

5gf.

\nsthd` ghlnd`b y jr`llnfihs hi b` rhlt` iudîrnl`

WNHD]F3 Afr` lb`sh

 

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]rfpüsntf Bfs `budifs `prhighrài b`s prfpnhg`ghs ghb snsthd` gh iudhr`lnüi ghlnd`b y b` rhprhshit`lnüi gh jr`llnfihs hi b` rhlt` iudîrnl`.

D`ifs ` b` fer` Hb shr aud`if snhdprh a` thingf b` ihlhsng`g gh lfit`r y, lfdf lfishluhiln`, sh vnf hi b` ihlhsng`g gh lrh`r ui snsthd` gh iudhr`lnüi. Hi b` `ltu`bng`g sh ubnz` hb snsthd` ghlnd`b. Hb snsthd` gh iudhr`lnüi ghlnd`b ubnz` lfdf e`sh gnhz gäkntfs gnjhrhiths3 =, 0,5, . Hi hsth snsthd`, lu`bqunhr iódhrf sh hslrneh lfdf ui` sulhsnüi gh hstfs gnhz gäkntfs, gfigh b` pfsnlnüi gh l`g` gäkntf hih ndpfrt`iln`. ]fr hsth dfvf, hs ui snsthd` gh iudhr`lnüi pfsnlnfi`b. pfsnlnfi`b. ]fr hchdpbf hi hb iódhrf 87, hb 8 flup` hb ghlhi` hi`ss (8 x 0=) y hb 7 hb buk`r uing`ghs `ghs (7 x 0). Lnilf ghl ghlhi` hi`ss dàs lu`trf uing`ghs, hs ghlnr, buk`r buk `r gh b`s ghl buk`r gh b`s uing lniluhit` y lu`trf. Hi b` lnjr` 1:; hb 1 flup` b` lhithi` (1==), hb : b` ghlhi` (:=) y hb ; b` uing`g. \h bhh flaflnhitfs shshit` y snhth .

Hchrlnlnf3 Gh `luhrgf lfi b` t`eb` hslrneh lfdf sh bhhi b`s snkunhiths l`ig`ghs. 0 0= 0== 0 === 0= === 0== === 0 === ===

Xing`g Ghlhi` Lhithi` Dnbb`r Ghlhi` gh dnbb`r Lhithi` gh dnbb`r dnbbüi

78: VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV > 5 8;: 58< VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV

B`s lnjr`s sh puhghi hslrnenr hi ui` jfrd` dàs lfdp`lt`3 bf quh sh lfiflh lfdf ift`lnüi hxpfihiln`b . B`s uing`ghs, ghlhi`s, lhithi`s, htlîthr`, sh rhprhshit`i hslrnenhigf hb gnhz y hbhvàigfbf ` ui` pfthiln` shkói b`s vhlhs quh sh dubtnpbnquh hb gnhz.

0 4 0== 0= 4 0=0 0== 4 0= Û 0= 4 0= 5 0 === 4 0= Û 0= Û 0= 40= <         0

 

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0= === 4 0= Û 0= Û 0= Û 0= 40= 7 0== === 4 0= Û 0= Û 0= Û 0= Û 0= 40= 8 0 === === 4 0= Û 0= Û 0= Û 0= Û 0= Û 0= 40= : Gh `luhrgf lfi b` t`eb` `ithrnfr hslrneh hi jfrd` hxpfihiln`b b`s snkunhiths l`itng`ghs. === VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV  ;= === VVVVVVVVVVVVVVVVVVVVVVVVVVVVVV  8== === VVVVVVVVVVVVVVVVVVVVVVVVVVVVV  > === === VVVVVVVVVVVVVVVVVVVVVVVVVVVV  5= === === VVVVVVVVVVVVVVVVVVVVVVVVVVVV 

JHLA@ D`rths

@\NKI@WXU@3 D`thdàtnl`s NN

KU@GF3 5gf.

@]UHIGNS@CH\ JXIG@DHIW@BH\3 \nsthd` ghlnd`b y jr`llnfihs hi b` rhlt` iudîrnl`

WNHD]F3 Afr` lb`sh

]`r` hxprhs`r iódhrfs if hithrfs, sh us`i gäkntfs ` b` ghrhla` ghb puitf. L`g` gnkntf ` b` ghrhla` ghb puitf rhprhshit` hb lflnhith gh îsh gäkntf y gh ui` pfthiln` gh 0=3

=.: 4

 

 : 0=

\h bhh3 ‒shns gîlnd`s—  78

 

=.78 4

0==

\h bhh3 lu`trf gîlnd`s y lnilf lhitîsnd`s f, gnrhlt`dhith, lu`rhit` y lnilf lhitîsnd`s.

4

=.=:5

  :5 0===

\h bhh3 shns lhitîsnd`s y gfs dnbîsnd`s f, gnrhlt`dhith, shshit` y gfs dnbîsnd`s   ;< =.==;<

4 0====

\h bhh3 snhth dnbîsnd`s y trhs gnhz dnbîsnd`s f, gnrhlt`dhith, shthit` y trhs gnhz dnbîsnd`s.         0

 

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 NUHLLNÜI   H L@BN @

@L@ ÎDNL@  H \HLXI @UN@

Hchrlnlnf3 gh `luhrgf lfi b` t`eb` =.0 =.=0 =.==0 =.===0

Gîlnd` Lhitîsnd` Dnbîsnd` Gnhzdnbîsnd`

=.====0 Lnhidnbîsnd` =.=====0 Dnbbfiîsnd` Hslrneh lfdf sh bhhi b`s snkunhiths l`itng`ghs. l`itng`ghs. =.=: VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV  V  =.=7 VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV  V  =.=81 VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV  V  =.==78 VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV  V  =.===>8 VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV  V  =.====:< VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV  V  @ift` bfs snkunhiths iódhrfs hi b` t`eb` gh `e`cf lfbfl`igf l`g` gäkntf hi hb buk`r quh bh lfrrhspfigh. 8 1=:.5 >:.==8 ; =80.=1 0 ===.==; 7 :==.0 8=5.= Dnbb`rhs 0 ===

Lhithi`s 0==

Ghlhi`s 0=

Xing`g 0

.

Ghlnd`s .=0

lhitîsnd`s .=0

Dnbîsnd`s .==0

Uhluhrg` quh b` pfsnlnüi hi gfigh sh hiluhitr` hb puitf ghphigh gh güigh sh hslrnenrài b`s l`itng`ghs. @afr` hslrneh lfdf sh bhhi hst`s l`itng`ghs. 8 1=:.5 VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV  >:.==8 VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV  ; =80.=1 VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV  0 ===.==; VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV  7 :==.0 VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV 

        0

 

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 NUHLLNÜI   H L@BN @

@L@ ÎDNL@  H \HLXI @UN@

8=5.= VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV 

JHLA@ Dnîrlfbhs

@\NKI@WXU@3 D`thdàtnl`s NN

KU@GF3 5gf.

@]UHIGNS@CH\ JXIG@DHIW@BH\ JXIG@DHIW@BH\33 \nsthd` ghlnd`b y jr`llnfihs hi b` rhlt` iudîrnl`

WNHD]F3 Afr` lb`sh

Bfs iódhrfs ghlnd`bhs sh puhghi rhprhshit`r hi b` rhlt` iudîrnl` y sh puhghi hslrnenr y` sh` gh jfrd` ghlnd`b f hi jfrd` gh jr`llnüi.

Hi ui` rhlt` iudîrnl` bfs iódhrfs jr`llnfi`rnfs sh pfsnlnfi`i gh `luhrgf lfi hb iudhr`gfr y hb ghifdni`gfr. Hb ghifdni`gfr nignl` hi luàitfs shkdhitfs a`y quh gnvngnr hb shkdhitf uint`rnf. Hb iudhr`gfr nignl` b` pfsnlnüi quh flup` hb iódhrf jr`llnfi`rnf. ]fr hchdpbf, sn quhrhdfs hxprhs`r 58, hi b` rhlt`, thihdfs quh gnvngnr `b shkdhitf quh rhprhshit` b` uing`g hi 8 p`rths nku`bhs y bfl`bnz`r b` shkuig` gnvnsnüi gh b` uing`g.

Hchrlnlnf3 Hi b`s snkunhiths rhlt`s iudîrnl`s bfl`bnz` bfs puitfs quh sh dhilnfi`i.

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 NUHLLNÜI   H L@BN @

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JHLA@ Cuhvhs

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@L@ ÎDNL@  H \HLXI @UN@

0 8 05  7 08 , , , 0  y 1 1 1 1 1

@\NKI@WXU@3 D`thdàtnl`s NN

KU@GF3 5gf.

@]UHIGNS@CH\ JXIG@DHIW@BH\3 \nsthd` ghlnd`b y jr`llnfihs hi b` rhlt` iudîrnl`

WNHD]F3 Afr` lb`sh

Gnvngh Gnvn gh b` rhlt rhlt` ` y bfl`bn bfl`bnz` z` bfs bfs snkunhit snkunhiths hs puitfs. puitfs.

g) 0 <

,0

5 ;  5 : , , 5  y < < < <

h) Hi b` snkunhith snkunhith rhlt` rhlt` sh hiluhitr` hiluhitr` puitfs shð`b`gfs shð`b`gfs lfi bhtr`s, bhtr`s, Bbhi` Bbhi` b` t`eb` lfi b` jr`llnüi jr`llnüi lfrrhlt`, lfrrhlt`,

Bhtr` ` e l g

Jr`llnüi

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 5 :

h j  k a ZNHUIH\ 4444444444444444444 44444444444444444444444444444444444444444 44444444444444444444444444444444444444444444Uhtrf 4444444444444444444444Uhtrf`bndhit`lnüi `bndhit`lnüi

\HKXIG@ \HD@I@ JHLA@ Buihs

@\NKI@WXU@3 D`thdàtnl`s NN

KU@GF3 5gf.

@]UHIGNS@CH\ JXIG@DHIW@BH\3

\ulhsnfihs gh iódhrfs y jnkur`s

WNHD]F3 Afr` lb`sh

]rfpüsntf Bfs `budifs `prhighrài ` `i`bnz`r sulhsnfihs gh iódhrfs y jnkur`s. Hilfitr`rài b` rhkb` p`r` fethihr ui tîrdnif `rentr`rnf gh b` sulhsnüi.         0

 

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 NUHLLNÜI   H L@BN @

@L@ ÎDNL@  H \HLXI @UN@

]`r` hdphz`r  Xi` sulhsnüi hs ui lficuitf gh iódhrfs f jnkur`s lfi b` prfpnhg`g gh quh a`y ui p`trüi quh phrdnth fethihr tfgfs bfs iódhrfs b`s jnkur`s ghb lficuitf, hdphz`igf pfr ui prndhr buk`r gh b` sulhsnüi, buhkf b` quh flup` hb shkuigf, buhkf b` quh flup` hb thrlhrf y `sä sulhsnv`dhith. D`ifs ` b` fer` ¶Hxnsth ui` jfrd` gh s`ehr luàitfs lu`grfs ihkrfs a`y hi b` jnkur` quh flup` hb gîlndf buk`r hi b` shrnh sni lfit`r gh uif hi uif6

 @iths gh rhsfbvhr hsth prfebhd`, vh`dfs ftrfs hchdpbfs3 ]`r` lfdpbht`r hst` ftr` sulhsnüi sh ihlhsnt` vhr luàbhs sfi bfs iódhrfs quh flup`i bfs hsp`lnfs v`läfs. =,