Sec 1-2 Math notes

/VNCFST /BUVSBMOVNCFST ʜʜ- 8IPMFOVNCFST ʜʜ- 1SJNFOVNCFST ʜʜ- 3BUJPOBMOVNCFSTOVNCFSTUIBUDBOCFFYQSFTTFEJOGSBDUJPOJODMVEJOH UFSNJOBUJOH FH BOESFDVSSJOHEFDJNBMT FH ʜ ʜ ʜ - *OUFHFSOVNCFSTXJUIPVUGSBDUJPO JTOFVUSBM - 'JOE)$'UBLFUIFQPXFSUIBUJTJODMVEFEJOBMMOVNCFST- 'JOE-$.UBLFUIFQPXFSUIBUJTUIFIJHINVTUNPTUCFGSPNBMMUIF OVNCFST - 1FSGFDUTRVBSFJOEJDFTPGQSJNFGBDUPSJTBUJPONVTUCFNVMUJQMFTPG- 1FSGFDUDVCFJOEJDFTPGQSJNFGBDUPSJTBUJPONVTUCNVMUJQMFTPG- Š Š - Š Š- Š Š- Š- Š- × = ÷- ÷ = ×- X²= ±√- X³= ±√- 3PVOEJOHTJHOJGJDBOUGJHVSFT "MMOPOBSFTJHOJGJDBOU- "MMJOCFUXFFOEJHJUTBSFTJHOJGJDBOU- &YQBOTJPO 9: BC 9B9C:B:C- B YZ BYBZ- ∗𝑎 3=1 3𝑎- #1 (𝑎+𝑏)!=𝑎!+2𝑎𝑏+𝑏!- #2 (𝑎−𝑏)!=𝑎!−2𝑎𝑏+𝑏!- #3 (𝑎+𝑏)(𝑎−𝑏)=𝑎!−𝑏!- 'BDUPSJTBUJPO 5BLFPVUDPNNPOGBDUPST−𝑥−𝑦=−(𝑥+𝑦)- GPVSUFSNTHSPVQJOH(𝑎−𝑏)=−(𝑏−𝑎)- UISFFUFSNTDSPTTNFUIPE- UXPUFSNT#3 (𝑎+𝑏)(𝑎−𝑏)=𝑎!−𝑏!- -JOFBSHSBQI TUSBJHIUMJOFHSBQI- -JOFBSGVODUJPOT𝑦=𝑚𝑥+𝑐- FH ZY YD Y- NHSBEJFOU"!#"$ %!#%$- DZJOUFSDFQU XIFSFMJOFDVUTZBYJT - NQPTJUJWF- NOFHBUJWF- 1BSBMMFMMJOFTIBWFUIFTBNFHSBEJFOU- )PSJ[POUBMMJOF (SBEJFOU- &RVBUJPOˠZDPOTUBOU- 7FSUJDBMMJOF (SBEJFOUVOEFGJOFE- &RVBUJPOˠYDPOTUBOU- DVUTYBYJT TVCZ DVUTZBYJT TVCY /VNCFSQBUUFSO &WFOOVNCFS5OO- 0EEOVNCFS5OO- 1FSGFDUTRVBSF5OO²- 1FSGFDUDVCF5OO³- JGBEEPSTVCUSBDUBOVNCFSUPHFUUIFOFYUUFSN- 5OB O E - BGJSTUUFSNPGUIFTFRVFODF- EUIFDPOTJTUFOUJODSFBTFPGEFDSFBTFJOUIFTFRVFODF- 1FSDFOUBHF 𝑥%=𝑥 100- YPG"% $&& × A- UPDPOWFSUUP𝑥× - FYQSFTT"BTBQFSDFOUBHFPG#! "× - QFSDFOUBHFDIBOHF#$%&'!(' *& +'%&'!(' *&#,#$!- × - JODSFBTFECZYQFSDFOU Y - EFDFBTFECZYQFSDFOU Y - JODSFBTFEFDSFBTFUPYQFSDFOUY- QSPGJU'()*+, -.//+01 '(+3. # 3)-, '(+3. × - MPTT /)-- 3)-, '(+3. # -.//+01 '(+3. × - EJTDPVOUQFSDFOUBHF4+-3)50, 67(8.4 '(+3. × - 1PMZHPOT USJBOHMF›- RVBESJMBUFSBM›- 4VNPGBOHMFTJOBOOTJEFEQPMZHPO O - 0OFJOUFSJPSBOHMF𝑛=(0#!)×$;&° 0- 0OFFYUFSJPSBOHMF=>&° 0- 0OFJOUFSJPSBOHMF0OFFYUFSJPSBOHMF›- 5SJBOHMFTJEFT EFHSFFT- 2VBESJMBUFSBMTJEFT EFHSFFT- 1FOUBHPOTJEFT EFHSFFT- )FYBHPOTJEFT EFHSFFT- )FQUBHPOTJEFT EFHSFFT- 0DUBHPOTJEFT EFHSFFT- /POBHPOTJEFT EFHSFFT- %FDBHPOTJEFT EFHSFFT- TJEFT EFHSFFT- 5SJBOHMFT TJEFTTBNFFRVJMBUFSBM- TJEFTTBNFJTPTDFMFT- BMUFSOBUFBOHMFT BMU㲃T - - DPSSFTQPOEJOHBOHMFT DPSS㲃T - BC›JOUFSJPSBOHMFT JOU㲃T - (FPNFUSZ 㲃MFTTUIBO›BDVUFBOHMF- 㲃SJHIUBOHMF- 㲃NPSFUIBO›CVUMFTTUIBO›PCUVTFBOHMF- 㲃NPSFUIBO›CVUMFTTUIBO›SFGMFYBOHMF- - "OHMFCJTFDUPS 1FSQFOEJDVMBSCJTFDUPS -JOFBSJOFRVBMJUJFT XIFONVMUJQMZJOHPSEJWJEJOHOFHBUJWFOVNCFST GMJQUIFJOFRVBMJUZTJHO FHY𝑥>$> #?Y - - 2VBESBUJDHSBQI GBDUPSJTBUJPO - HSBQIJDBMNFUIPETPMVUJPOYJOUFSDFQU- 4JNVMUBOFPVTFRVBUJPOT FMJNJOBUJPONFUIPE NBLFPOFBMQIBCFUUIFTBNF JGUIFTBNFTJHO TVCUSBDUFRVBUJPOT JGEJGGFSFOUTJHO BEEFRVBUJPOT FH4𝑥−5𝑦=17—(1) 2x−5y=8 —(2) YZ YZ

YY Y Y@ !=4.5 TVCYJOUP Z Z Z Z$ A Y Z$ A TVCTUJUVUJPONFUIPE NBLFPOFBMQIBCFUUIFTVCKFDU TVCUIJTBMQIBCFUJOUPUIFPUIFSFRVBUJPOT FHYZŠ YZŠ 'SPN YZ Y;B!" = —(3) 4VC JOUP ;B!" =)+3𝑦=5 =!B;" = +3𝑦=5 ZZ Z Z 4VCZJOUP Y ;B!(#$) = Y Y Z HSBQIJDBMNFUIPE QMPUUXPMJOFT TPMVUJPOQPJOUPGJOUFSTFDUJPO "MHFCSBJDGSBDUJPO GPSºBOE× GBDUPSJTFC