Matematicas-PRIMER PERIODO
September 30, 2022 | Author: Anonymous | Category: N/A
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BGQFPFABA N. ?2. GLYYMW_LNAM BJ MKM QMEÂQFGL; Glngmptubjfzbgf÷n 2. Mngumntrb mj alefnfl, glalefnfl, rbndl y drb`l am gbab `ungf÷n. (smbn als `ungflnms af`mrmntms, c y d)
Ale c 5 {-=, ?, =} Gla c 5 {9, 7 , 1} Ybn c 5 {7} Drb`l c 5 {(-=,7)8(?,7)8(=,7)}
Ale d 5 {Bnb, _btty, Klbn} Gla d 5 {29, 27, 21, 2= ,20} Ybn d 5 {21, 2=} Drb`l d 5 {(Bnb,21)8(_btty,2=),(Klbn,2=)}
9. Amtmrefnb sf jbs rmjbgflnms sln l nl sln `ungflnms am`fnfabs amj glnkuntl B 5 {?, 2, 9, 7, 1, =} mn mj glnkuntl I 5 {?, 2, 9, 7, 1, =, 0, 4, 3, 6, 2?}. - B gbab mjmemntl am B jm glrrmsplnam su alijm mn I. ?
?
2
2
9
9
7
7
1
1
=
= 0 4 3 6 2?
Ms unb `ungf÷n, yb qum gbab vbjlr am mntrbab tfmnm un s÷jl vbjlr am sbjfab.
- Gbab mjmemntl am B sm rmjbgflnb gln su gubarbal mn I.
?
?
2
2
9
9
7
7
1
1
=
= 0 4 3 6 2?
Nl ms `ungf÷n, yb qum mj vbjlr 1 y = nl tfmnmn un vbjlr am sbjfab.
- Gbab mjmemntl am B sm rmjbgflnb gln = mn I.
?
?
2
2
9
9
7
7
1
1
=
= 0 4 3 6 2?
Nl ms `ungf÷n, yb qum gbab vbjlr am mntrbab s÷jl pumam tmnmr un vbjlr am sbjfab.
7. Gjbsf`fgb jb drâ`fgb am gbab `ungf÷n glel jfnmbj l b`ån. 2)
9)
2) Ms unb `ungfln jfnmbj, plrqum pbsb plr mj puntl am lrfdmn. y 5 ex 9) Ms unb `ungfln b`fn, plrqum nl pbsb plr mj puntl am lrfdmn. y 5 ex + i
1. Cbjjb jb pmnafmntm am jbs rmgtbs qum pbsbn plr jls p puntls untls abals y drb`ågbjls mn mj pjbnl p jbnl gbrtmsfbnl. x2, y2
x9, y9
- Ymgtb p, qum pbsb plr jls puntls B5(-1, -2) y I5(2, 7)
5 5
∙ ∙
7∙(∙) ∙(∙)
5
Jb pmnafmntm am jb rmgtb ms p
Drb`fgb;
y
x
-x
-y
x2, y2
x9, y9
- Ymgtb q, qum pbsb plr jls puntls B5(?, -7) y I5(0, ?)
5 5
∙ ∙
∙( ∙ (∙7) ∙7)
7
0∙
0
5 7
Jb pmnafmntm am jb rmgtb q ms 0
Drb`fgb; y
x
- x
- y
x2, y2
x9, y9
- Ymgtb r, qum pbsb plr jls puntls B5 (-1, 1) y I5 (?, ?)
5 5
∙ ∙
∙ ∙(∙)
5
∙
Jb pmnafmntm am jb rmgtb r ms
Drb`fgb;
∙
y
x
- x
- y
x2, y2
x9, y9
- Ymgtb s, qum pbsb plr jls puntls B5(-=, -=) y I5(=, -=)
5 5
∙ ∙
∙∙((∙) ∙∙ ∙)
∙ ∙((∙) ∙)
5
5 ?
Jb pmnafmntm am jb rmgtb s ms ?
Drb`fgb;
y
- x
x
- y
=. Famntf`fgb als puntls slirm jb rmgtb y mngumntrb mj vbjlr am jb pmnafmntm. 2)
7
9)
x2, y2
x9, y9
2) _untls; B5 (?,-2) y I5 (7,2) _mnafmntm;
5 5
∙ ∙
∙( ∙ (∙) ∙)
7∙
7
5
Jb pmnafmntm am jb rmgtb ms
x2, y2
7
x9, y9
9) _untls; B5 (7,-2) y I5 (7,2) _mnafmntm;
5 5
∙ ∙
∙( ∙ (∙) ∙)
7∙7
5
Jb pmnafmntm am jb rmgtb ms
x2, y2
(vbjlr fnamtmrefnbal)
x9, y9
7) _untls; B5 (-2,-9) y I5 (2,-9) _mnafmntm;
5
∙ ∙
∙∙((∙) ∙∙ ∙)
5
∙(∙) 5
Jb pmnafmntm am jb rmgtb ms
x2, y2
x9, y9
1) _untls; B5 (?,4) y I5 (9,?) _mnafmntm;
5 5
∙ ∙ ∙
5
∙
∙
Jb pmnafmntm am jb rmgtb ms
∙
1)
BGQFPFABA N. ?9. GLYYMW_LNAM BJ MKM QMEÂQFGL; Amsbrrljjl am mkmrgfgfls am bpjfgbgf÷n bpjfgbgf÷n 2. Gln ibsm mn jb drâ`fgb, amtmrefnb mj vbjlr am vmraba am gbab mnungfbal. Kustf`fgb tu rmspumstb.
(7,9) - Jb pmnafmntm am e ms fdubj b gmrl. ]sbrmels jls puntls B5 (-7,9) y I5 (7,9)
5 5
∙ ∙
∙
5 5 ?
7∙ 7∙((∙7) ∙7)
0
Ms vmraba, yb qum jb pmnafmntm am e5 ?.
- Jb jånmb rmgtb q ms amgrmgfmntm. ]sbrmels jls puntls B5 (-7,?) y I5 (?,-9)
5 5
∙ ∙
∙∙ ∙ ∙((∙7) ∙7)
5
∙ 7
Ms vmraba, yb qum jb pmnafmntm q 5
∙ 7
ms nmdbtfvb. nmdbtfvb.
- Jb `ungf÷n qum rmprmsmntb jb jånmb rmgtb r ms b`ån.
jfnmbj. Ms @bjsl, yb qum jb jånmb rmgtb r pbsb plr mj puntl am lrfdmn, ms jfnmbj. (7,-2) - Jb pmnafmntm am jb rmgtb l ms fdubj b gmrl. ]sbrmels jls puntls B5 (7,2) y I5 (7,-2)
5 5
∙ ∙
∙∙
∙
7∙7
5
Ms `bjsl, yb qum jb pmnafmntm am l ms fnamtmrefnbab.
- Jb `ungf÷n qum rmprmsmntb jb jånmb p ms jfnmbj.
Ms vmraba, yb qum jb jånmb rmgtb p pbsb plr mj puntl am lrfdmn.
9. Famntf`fgb als puntls slirm gbab rmgtb y mngumntrb mj vbjlr am jb pmnafmntm. pmnafmntm. x2, y2
x9, y9
2) _untls; B5 (?,-2) y I5 (7,2) _mnafmntm;
5
∙ ∙
∙ (∙) ∙) 5 ∙( 5 x2, y2 7∙
x9, y9
7
Jb pmnafmntm am jb rmgtb ms
x2, y2
7
x9, y9
9) _untls; B5 (7,-2) y I5 (7,2) _mnafmntm;
5 5
∙ ∙
∙( ∙ (∙) ∙)
7∙7
5
Jb pmnafmntm am jb rmgtb ms
(vbjlr fnamtmrefnbal)
x2, y2
x9, y9
7) _untls; B5 (-2,-9) y I5 (2,-9) _mnafmntm;
5 5
∙ ∙
∙∙((∙) ∙∙ ∙)
∙(∙)
5
Jb pmnafmntm am jb rmgtb ms
x2, y2
x9, y9
1) _untls; B5 (?,4) y I5 (9,?) _mnafmntm;
5 5
∙ ∙ ∙
5
∙
∙
Jb pmnafmntm am jb rmgtb ms
∙
BGQFPFABA N. ?7. GLYYMW_LNAM BJ MKM QMEÂQFGL; Wljugf÷n am prlijmebs
2. Fnafgb gubjms am jbs sfdufmntms sftubgflnms rmprmsmntbn `ungflnms jfnmbjms l b`fnms. b) Mn unb `bgturb tmjm`÷nfgb sm tfmnm un gbrdl `fkl am $9.??? $9.?? ? y gbab efnutl gumstb $2??. Qmnmels qum mj pbdl am jb `bgturb mjmgtr÷nfgb smrâ mn ‚x― efnutls y gbab efnutl gumstb $2??. Bameâs, afgcb `bgturb yb tfmnm un gbrdl `fkl am $9???. $9 ???. Mntlngms; (() 5 2? 2?? ? ∔ x + 9? 9??? ?? :5 y 5 ex + i Mntlngms ms unb `ungf÷n b`ån i) ]n ms`mrl gumstb $4=? mn un mstbijmgfefmntl. Bj vmnamrjl b mstm prmgfl amkb unb dbnbngfb amj 2?%. Wbimels qum un ms`mrl gumstb $4=? mn un mstbijmgfefmntl, qum bj vmnamrjl mstm efsel amkb unb dbnbngfb amj 2?% 5 ?.2? ?.2? (() 5 4=? ∔ ?.2? :5 y 5 ex Mntlngms ms unb `ungf÷n Jfnmbj.
9. ]n butle÷vfj, mn prlemafl, glnsuem un dbj÷n am dbsljfnb plr gbab 1= he mn jb gfuaba. Amtmrefnbr jb mxprmsf÷n qum rmjbgflnb jb gbntfaba am dbsljfnb gln gl n jb afstbngfb rmglrrfab. Jumdl, glnstrufr jb drâ`fgb am jb `ungf÷n. 5 1=
x(Dbj÷n) y(He)
2 1=
9 6?
7 27=
1 23?
y
- x
x
- y
7. Qrms hfjls am pmrbs nls cbn glstbal 1,= ₪8 y, plr sfmtm hfjls, cbiråbels pbdbal 2?,= ₪.
Amtmrefnbr jb pmnafmntm y rmbjfzbr jb rmgtb am jls puntls litmnfals. x(Hfjls) y(Glstl)
7 1.= _untls; B 5 (7,1.=) y I 5 (4,2?.=)
4 2?.=
y
_mnafmntm;
5 ∙ ∙
5
.∙.
0
∙7
5
x
-x -y 1. ]nb bdmngfb am bjqufjmr am vmcågujls l`rmgm butle÷vfjms plr 29?.??? pmsls aurbntm = aåbs eâs 2?.??? pmsls plr clrb bafgflnbj. ¼Guâj ms jb mgubgf÷n qum rmprmsmntb jls fndrmsls am jb bdmngfb plr bjqufjbr un butle÷vfj< butle ÷vfj< Wbimels qum plr 29?.?? pmsls, jb bdmngfb bjqufjb mj vmcågujl plr = aåbs, eâs 2?.??? pmsls plr clrb(x) bafgflnbj. Mntlngms;
(() 5 2?.??? ∔ ( ∔ ( ) + (29?.??) Alnam S, rmprmsmntb jb gbntfaba am clrbs bafgflnbjms y `(x) jbs Dbnbngfbs mn pmsls.
=. Mj prmgfl am 7 ji am nbrbnkb ms am 2.3?? pmsls y mj prmgfl am = jfirbs ms 9.=??. så V ms mj prmgfl am jb nbrbnkb y S ms m s mj pmsl, amtmrefnbr jb mgubgf÷n qum rmprmsmntb mj prmgfl am jb nbrbnkb smdûn su pmsl. Wbimels qum mj prmgfl plr 7 ji am nbrbnkb sln 2.3?? pmsls y mj prmgfl plr = jfirbs jf irbs sln 9.=??, tmnfmnal qum mj prmgfl am jb nbrbnkb ms (y) y mj pmsl ms (x). Mntlngms;
x(jfirbs) y(prmgfl)
7 2.3??
= 9.=??
(() 5 Alnam S, rmprmsmntb mj pmsl y `(x) mj prmgfl am jb nbrbnkb pmsl y h smrâ jb glnstbntm amj pmsl.
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