Programa Tn Matematica 2007


   






  
     

       
  


  
 I.

STATUTUL DISCIPLINEI

Matematica DUH vQ FDGUXO WHVWULL QDLRQDOH SHQWUX DQXO úFRODU 2006 / 2007, statut de GLVFLSOLQ obligatorie. II.

OBIECTIVELE DE EVALUARE

&DQGLGDLL WUHEXLH V GHPRQVWUH]H XUPWRDUHOH FRPSHWHQH 1. V FXQRDVF úL V vQHOHDJ FRQFHSWHOH WHUPLQRORJLD úL SURFHGXULOH GH FDOFXO VSHFLILFH PDWHPDWLFLL 2. V GH]YROWH FDSDFLWL GH H[SORUDUH  LQYHVWLJDUH úL UH]ROYDUH GH SUREOHPH 3. V GH]YROWH FDSDFLWDWHD GH D FRPXQLFD XWLOL]kQG OLPEDMXO PDWHPDWLF 4. V XWLOL]H]H FRQFHSWH úL PHWRGH PDWHPDWLFH VWXGLDWH vQ FRQWH[WH YDULDWH III.

&21,18785,

$5,70(7,& ù, $/*(%5

0XO LPL 0XOLPL UHODLL DSDUWHQHQ HJDOLWDWH LQFOX]LXQH  VXEPXOLPH RSHUDLL FX PXOLPL UHXQLXQHD LQWHUVHFLD GLIHUHQD SURGXVXO FDUWH]LDQ  0XOLPL ILQLWH PXOLPL LQILQLWH 0XOLPLOH N, Z, Q, R, R-Q. N ⊂ Z ⊂ Q ⊂ R. Scrierea numerelor naturale în baza zece.

3URSR]LLL DGHYUDWH úL SURSR]LLL IDOVH ÌPSULUHD FX UHVW D QXPHUHORU QDWXUDOH 'LYL]LELOLWDWHD vQ N GHILQLLH GLYL]RU PXOWLSOX SURSULHWL DOH UHODLHL GH GLYL]LELOLWDWH FULWHULLOH GH GLYL]LELOLWDWH FX     QXPHUH SULPH úL QXPHUH FRPSXVH QXPHUH SDUH úL QXPHUH LPSDUH QXPHUH SULPH vQWUH HOH GHVFRPSXQHUHD XQXL QXPU QDWXUDO vQ SURGXV GH SXWHUL GH QXPHUH SULPH FHO PDL PDUH GLYL]RU FRPXQ úL FHO PDL PLF PXOWLSOX FRPXQ Divizibilitatea în Z GHILQLLH GLYL]RU PXOWLSOX )UDFLH IUDFLL VXEXQLWDUH HFKLXQLWDUH VXSUDXQLWDUH UHSUH]HQWUL HFKLYDOHQWH DOH IUDFLLORU IUDFLL LUHGXFWLELOH 6FULHUHD XQXL QXPU UDLRQDO VXE IRUP ]HFLPDO VDX IUDFLRQDU 5HSUH]HQWDUHD SH D[ D QXPHUHORU UHDOH &RPSDUDUHD úL RUGRQDUHD QXPHUHORU UHDOH 9DORDUHD DEVROXW PRGXO  RSXV LQYHUV SDUWH vQWUHDJ SDUWH IUDFLRQDU 5RWXQMLUHD úL DSUR[LPDUHD XQXL QXPU UHDO Intervale în R GHILQLLH UHSUH]HQWDUH SH D[ 2SHUDLL FX QXPHUH UHDOH DGXQDUHD VFGHUHD vQPXOLUHD ULGLFDUHD OD SXWHUH FX H[SRQHQW QXPU vQWUHJ 5GFLQD SWUDW D XQXL QXPU QDWXUDO SWUDW SHUIHFW H[WUDJHUHD UGFLQLL SWUDWH GLQWUXQ QXPU UDLRQDO SR]LWLY DOJRULWPXO GH H[WUDJHUH D UGFLQLL SWUDWH VFULHUHD XQXL QXPU UHDO SR]LWLY FD UDGLFDO GLQ SWUDWXO VX 2UGLQHD HIHFWXULL RSHUDLLORU úL IRORVLUHD SDUDQWH]HORU )DFWRUXO FRPXQ Reguli de calcul cu radicali. Introducerea factorilor sub radical. Scoaterea factorilor de sub radical.

5DLRQDOL]DUHD QXPLWRUXOXL GH IRUPD a b , a ± b cu a ∈ Z*, b ∈ N . 0HGLD DULWPHWLF úL PHGLD DULWPHWLF SRQGHUDW 0HGLD JHRPHWULF D GRX QXPHUH UHDOH SR]LWLYH 5DSRDUWH úL SURSRULL UDSRUW SURSULHWDWHD IXQGDPHQWDO D SURSRULLORU SURSRULL GHULYDWH DIODUHD XQXL WHUPHQ QHFXQRVFXW GLQWUR SURSRULH úLU GH UDSRDUWH HJDOH PULPL GLUHFW SURSRULRQDOH úL PULPL LQYHUV SURSRULRQDOH UHJXOD GH WUHL VLPSO Procente: S GLQWUXQ QXPU UHDO DIODUHD XQXL QXPU UDLRQDO FkQG FXQRDúWHP p% din el; aflarea raportului procentual. Rezolvarea problemelor în care intervin procente.

&DOFXOXO SUREDELOLWLL GH UHDOL]DUH D XQXL HYHQLPHQW XWLOL]kQG UDSRUWXO QXPUXO FD]XULORU IDYRUDELOH  QXPUXO cazurilor posibile. Calcul algebric

&DOFXOXO FX QXPHUH UHSUH]HQWDWH SULQ OLWHUH DGXQDUHD VFGHUHD vQPXOLUHD vPSULUHD ULGLFDUHD OD SXWHUH FX H[SRQHQW QXPU vQWUHJ



  Programa pentru Testarea     

1

Formulele de calcul prescurtat:

(a ± b )2 = a 2 ± 2ab + b 2 ; (a + b )(a − b ) = a 2 − b 2 (a + b + c )2 = a 2 + b 2 + c 2 + 2ab + 2ac + 2bc

Descompunerea în factori: metoda factorului comun; utilizarea formulelor de calcul prescurtat; gruparea

WHUPHQLORU úL PHWRGH FRPELQDWH 5DSRDUWH GH QXPHUH UHDOH UHSUH]HQWDWH SULQ OLWHUH 6LPSOLILFDUH 2SHUDLL FX UDSRDUWH DGXQDUH VFGHUH vQPXOLUH vPSULUH ULGLFDUH OD SXWHUH FX H[SRQHQW QXPU vQWUHJ  )XQF LL

6LVWHP GH D[H RUWRJRQDOH UHSUH]HQWDUHD SXQFWHORU vQ SODQ UH]ROYDUHD XQRU SUREOHPH GH JHRPHWULH SODQ pornind de la reprezentarea punctelor într-un sistem de axe ortogonale. 1RLXQHD GH IXQFLH IXQFLL GH WLSXO f : A → R , f (x ) = ax + b, unde a, b ∈ R úL

A LQWHUYDO PXOLPH ILQLW

sau A = R  UHSUH]HQWDUHD JUDILF D DFHVWRU IXQFLL $IODUHD PXOLPLL YDORULORU tipul f : A → R , f ( x) = ax + b, a, b ∈ R úL A PXOLPH ILQLW 'HWHUPLQDUHD XQHL

XQHL IXQFLL GH IXQFLL GH WLSXO

f : R → R, f (x ) = ax + b , unde a, b ∈ R  DO FUHL JUDILF FRQLQH GRX SXQFWH ([HUFLLL GH LQYHVWLJDUH D FROLQLDULWLL XQRU SXQFWH FXQRVFkQG FRRUGRQDWHOH DFHVWRUD,QWHUVHFLLOH JUDILFXOXL XQHL IXQFLL OLQLDUH FX D[HOH GH FRRUGRQDWH ,QWHUVHFLD JUDILFHORU D GRX IXQFLL OLQLDUH (FXD LL úL LQHFXD LL

ax + b = 0, a ∈ R *, b ∈ R  (FXDLL HFKLYDOHQWH 2 Rezolvarea în R D HFXDLLORU GH IRUPD ax + bx + c = 0, a, b, c ∈ R, a ≠ 0 .

Rezolvarea în R D HFXDLLORU GH IRUPD

(FXDLL GH IRUPD ax + by + c = 0 cu a, b, c ∈ R. Rezolvarea în R x R D VLVWHPHORU GH HFXDLL GH IRUPD

 a1 x + b1 y = c1 , a1 , a 2 , b1 , b2 , c1 , c 2 ∈ R .  a 2 x + b2 y = c 2 Rezolvarea în R D LQHFXDLLORU GH IRUPD ax + b ≤ 0 (<, ≥, > ) , a ∈ R *, b ∈ R .

3UREOHPH FX FDUDFWHU DSOLFDWLY FDUH VH UH]ROY FX DMXWRUXO HFXDLLORU LQHFXDLLORU úL DO VLVWHPHORU GH HFXDLL 8WLOL]DUHD PHWRGHORU DULWPHWLF VDX DOJHEULF SHQWUX UH]ROYDUHD XQHL SUREOHPH GEOMETRIE

0VXUDUH úL PVXUL OXQJLPH XQJKL DULH YROXP   WUDQVIRUPUL LQFOXVLY GP3 = 1 litru). )LJXUL úL FRUSXUL JHRPHWULFH 1. 3XQFWXO GUHDSWD SODQXO VHPLSODQXO VHPLGUHDSWD VHJPHQWXO GH GUHDSW XQJKLXO -

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SR]LLL UHODWLYH FODVLILFDUH SDUDOHOLVP úL SHUSHQGLFXODULWDWH vQ SODQ úL vQ VSDLX D[LRPD SDUDOHOHORU XQJKLXUL FX ODWXULOH UHVSHFWLY SDUDOHOH XQJKLXO D GRX GUHSWH vQ VSDLX GUHSWH SHUSHQGLFXODUH GUHDSWD SHUSHQGLFXODU SH XQ SODQ GLVWDQD GH OD XQ SXQFW OD XQ SODQ SODQH SDUDOHOH GLVWDQD GLQWUH GRX SODQH SDUDOHOH WHRUHPD FHORU GRX SHUSHQGLFXODUH GLVWDQD GH OD XQ SXQFW OD R GUHDSW SURLHFLD RUWRJRQDO D XQXL SXQFW VHJPHQW VDX D XQHL GUHSWH SH XQ SODQ XQJKLXO XQHL GUHSWH FX XQ SODQ OXQJLPHD SURLHFLHL XQXL VHJPHQW XQJKL GLHGUX XQJKLXO SODQ FRUHVSXQ]WRU XQXL XQJKL GLHGUX PVXUD XQJKLXOXL D GRX SODQH SODQH perpendiculare;

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VLPHWULD ID GH XQ SXQFW vQ SODQ VLPHWULD ID GH R GUHDSW vQ SODQ

2. Triunghiul -

SHULPHWUXO úL DULD VXPD PVXULORU XQJKLXULORU XQXL WULXQJKL unghi exterior unui triunghi;



  Programa pentru Testarea     

2

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OLQLL LPSRUWDQWH vQ WULXQJKL úL FRQFXUHQD ORU linia mijlocie în triunghi;

WULXQJKLXO LVRVFHO úL WULXQJKLXO HFKLODWHUDO ± SURSULHWL FULWHULLOH GH FRQJUXHQ D WULXQJKLXULORU WULXQJKLXO GUHSWXQJKLF ± WHRUHPD vQOLPLL WHRUHPD FDWHWHL WHRUHPD OXL 3LWDJRUD úL UHFLSURFD HL sin, cos, tg, ctg; rezolvarea triunghiului dreptunghic; teorema lui 7KDOHV úL UHFLSURFD HL

WHRUHPD IXQGDPHQWDO D DVHPQULL WULXQJKLXUL DVHPHQHD ± FULWHULLOH GH DVHPQDUH D WULXQJKLXULORU

3. Patrulaterul convex -

SHULPHWUXO úL DULD SDUDOHORJUDPXO GUHSWXQJKLXO URPEXO SWUDWXO WUDSH]XO  VXPD PVXULORU XQJKLXULORU XQXL SDWUXODWHU FRQYH[ SDUDOHORJUDPXO ± SURSULHWL UHIHULWRDUH OD ODWXUL XQJKLXUL GLDJRQDOH SDUDOHORJUDPH SDUWLFXODUH GUHSWXQJKL URPE SWUDW ± SURSULHWL trapezul; linia mijlocie în trapez;

WUDSH]H SDUWLFXODUH LVRVFHO úL GUHSWXQJKLF ± SURSULHWL

4. Cercul -

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FHQWUX UD] GLDPHWUX GLVF unghi la centru, sector de cerc;

FRDUGH úL DUFH vQ FHUF OD DUFH FRQJUXHQWH FRUHVSXQG FRDUGH FRQJUXHQWH úL UHFLSURF SURSULHWDWHD GLDPHWUXOXL SHUSHQGLFXODU SH R FRDUG SURSULHWDWHD DUFHORU FXSULQVH vQWUH GRX FRDUGH SDUDOHOH SURSULHWDWHD FRDUGHORU HJDO GHSUWDWH GH FHQWUX  PVXUD XQJKLXOXL vQVFULV vQ FHUF SR]LLLOH UHODWLYH DOH XQHL GUHSWH ID GH XQ FHUF cercul înscris într-un triunghi; cercul circumscris unui triunghi; lungimea cercului; lungimea arcului de cerc; aria discului; aria sectorului de cerc;

FDOFXOXO HOHPHQWHORU vQ SROLJRDQH UHJXODWH WULXQJKL HFKLODWHUDO SWUDW KH[DJRQ UHJXODW ODWXU DSRWHP SHULPHWUX DULH 

5. Corpuri geometrice Poliedre: 3ULVPD GUHDSW FX ED]D WULXQJKL HFKLODWHUDO GUHSWXQJKL SWUDW VDX KH[DJRQ UHJXODW FXEXO

SLUDPLGD UHJXODW úL WUXQFKLXO GH SLUDPLG UHJXODW ED]D WULXQJKL HFKLODWHUDO SWUDW VDX KH[DJRQ UHJXODW  - reprezentarea lor prin desen; - HOHPHQWHOH ORU YkUIXUL PXFKLL IHH ODWHUDOH ED]H GLDJRQDOH vQOLPL  - GHVIúXUUL - VHFLXQL SDUDOHOH FX ED]D - DULD ODWHUDO DULD WRWDO YROXPXO Corpuri rotunde: Cilindrul circular drept, conul circular drept, trunchiul de con circular drept, sfera. - reprezentarea lor prin desen; - HOHPHQWHOH ORU UD]H JHQHUDWRDUH ED]H vQOLPL  - GHVIúXUUL - VHFLXQL SDUDOHOH FX ED]D - VHFLXQL D[LDOH - DULD ODWHUDO DULD WRWDO YROXPXO

Not

   
 

 
 
    
    se vor realiza în conformitate cu prevederile prezentei programe  
     




 
   
    
 
   
 

     

 

   
 
 
      
     
  
  

  
     

  
 
  
  



  Programa pentru Testarea     

3