1. džĂŵĞŶ ĚĞ ƌĞĐƵƉĞƌĂĐŝſŶ ĚĞů ϮǑ ƚƌŝŵĞƐƚƌĞ ͘ ͘d͘ ŝǀĞƌƐŝĨŝĐĂĐŝſŶ / /͘ ͘^͘ ,ƵĞƌƚĂ ZŽƐĂƌŝŽ
EŽŵďƌĞ LJ ĂƉĞůůŝĚŽƐ͗ͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺ ƵƌƐŽ͗ͺͺͺͺͺͺͺͺ &ĞĐŚĂ͗ͺͺͺͺͺͺͺͺͺͺ
0DWHPiWLFDV
'L TXp H[SUHVLRQHV VRQ PRQRPLRV FXiOHV SROLQRPLRV
D ͵‫ ݔ‬ଶ E ͷ‫ ݔ‬ଶ ൅ ʹ F ‫ ݔ‬ȉ ሺെ͵‫ ݔ‬ଶ ሻ G ‫ ݕݔ‬ଶ ȉ ሺെ‫ݑ‬ሻ ȉ ‫ ݒ‬ହ H ‫ݔ‬൅‫ݕ‬
(VFULEH OD SDUWH OLWHUDO GH ORV VLJXLHQWHV PRQRPLRV
D ‫ݔ‬ଷ E െͺ‫ ݕݔ‬ଶ ‫ݑ‬ଷ ‫଼ ݖ‬ F Ȃ ‫ݔ‬ଶ G ͵‫ ݕݔ‬ଶ
¢&XiO HV HO FRHILFLHQWH GH FDGD XQR GH ORV PRQRPLRV DQWHULRUHV"
¢&XiO HV HO JUDGR GH FDGD XQR GH ORV PRQRPLRV GHO HMHUFLFLR "
&DOFXOD HO YDORU QXPpULFR GH ORV VLJXLHQWHV PRQRPLRV
ଶ ‫ ݖݕݔ‬ଷ ʹ‫ݕݔ‬ ‫ݔ‬ଶ‫ݕ‬ଷ
D ൜ ‫ݔ‬ E ൜ F ൜ G ൜
‫ ݔ‬ൌ െͳ ‫ ݔ‬ൌ Ͳ ǡ‫ ݕ‬ൌ ͳ ǡ‫ ݖ‬ൌ ʹ ‫ ݔ‬ൌ ʹ ǡ‫ ݕ‬ൌ ͵ ‫ ݔ‬ൌ െʹ ǡ ‫ ݕ‬ൌ െͳ
&DOFXOD ODV VLJXLHQWHV VXPDV UHVWDV GH PRQRPLRV
D ʹ‫ ݔ‬൅ ͵‫ݔ‬ E ͵‫ ݔ‬ଶ ൅ ͷ‫ ݔ‬ଶ െ ͺ‫ ݔ‬ଶ F ‫ ݖݕݔ‬െ ʹ‫ݖݕݔ‬ G ʹ‫ ݔ‬൅ ͵‫ ݔ‬ଶ
&DOFXOD ORV VLJXLHQWHV SURGXFWRV GH PRQRPLRV
D ‫ݔ‬ଶ ȉ ‫ݔ‬ଷ E ʹ‫ ݕݔ‬ଶ ȉ ͷ‫ି ݔ‬ଵ ‫ݑݕ‬ F ‫ ݔ‬ଶ ȉ ‫ି ݔ‬ଶ G ͵‫ ݖݕݔ‬ଶ ȉ ʹ
&DOFXOD ODV VLJXLHQWHV GLYLVLRQHV GH PRQRPLRV
D ‫ݔ‬ଷǣ ‫ݔ‬ଶ E ‫଼ݔ‬ǣ ‫଼ݔ‬ F ͸‫ ݕݔ‬ଶ ‫ ݖ‬ହ ǣ ͵‫ ݔ‬ଶ ‫ ݖݕ‬ଷ G Ͷ‫ ݔ‬ଶ ǣ ʹ‫ ݕ‬ଶ
'L FXiOHV GH HVWDV H[SUHVLRQHV VRQ PRQRPLRV FXiOHV SROLQRPLRV
D ʹ‫ ݔ‬ଷ E Ͷ‫ ݔ‬ଶ ൅ ͵ F ͵‫ ݔ‬ଶ െ ʹ‫ ݔ‬ଷ G ͵‫ ݔ‬ଶ ȉ ሺെʹ‫ ݔ‬ଷ ሻ
'DOH XQ QRPEUH D ORV VLJXLHQWHV SROLQRPLRV FRPR HQ HO HMHPSOR
ʹ‫ ݔ‬െ ͷ‫ ଻ ݔ‬൅ Ͷ‫ ݔ‬െ ʹ OR OODPDUp ܲሺ‫ݔ‬ሻ
ସ
D Ȃ ‫ ݔ‬൅ Ͷ‫ ݔ‬െ ͺ‫ ݔ‬ଶ ൅ ͷ‫ ݔ‬ସ E ͷ‫ ݕݔ‬ଶ െ ͻ‫ ݔ‬ଶ ‫ݕ‬ F Ȃ ‫ ݔ‬ଶ ‫ ݒݑݖݕ‬൅ ͵‫ݖݔ‬ G ‫ݔ‬൅‫ݕ‬
'L FXiO HV HO JUDGR GH ORV VLJXLHQWHV SROLQRPLRV
D ‫ ݔ‬െ Ͷ‫ ݔ‬ସ ൅ ‫ ݔ‬ଷ െ ͹‫ ݔ‬ଶ ൅ ‫ ݔ‬െ ͳ E ‫ ݔ‬ଶ ‫ ݕ‬ଷ ൅ ‫ ݕݔ‬െ ‫ ݕݔ‬ହ
ହ
F ‫ ݔ‬ହ ൅ ʹ‫ ݔ‬ଶ െ ‫ ݔ‬ହ G ‫ ݔ‬ଶ ‫ ݖݕ‬ଷ ൅ ʹ
5HGXFH ORV VLJXLHQWHV SROLQRPLRV
D ͳ ൅ Ͷ‫ ݔ‬ସ െ ‫ ݔ‬൅ ͵‫ ݔ‬ଷ െ ʹ‫ ݔ‬൅ ͷ‫ ݔ‬ଶ െ ͺ‫ ݔ‬ସ ൅ ͵‫ ݔ‬ଷ െ ͷ E ʹ‫ ݔ‬ଶ െ ͳ െ ‫ ݔ‬ଶ ൅ ͺ
'L FXiO HV HO WpUPLQR LQGHSHQGLHQWH GH ORV SROLQRPLRV GHO HMHUFLFLR
'DGR HO SROLQRPLR ܲሺ‫ݔ‬ǡ ‫ݕ‬ሻ ൌ ‫ ݔ‬ଶ ൅ ‫ ݕݔ‬FDOFXOD
D ܲሺͳǡͲሻ E ܲሺͲǡͳሻ F ܲሺͳǡͳሻ G ܲሺെͳǡ െͳሻ
'DGRV ORV VLJXLHQWHV SROLQRPLRV ܲሺ‫ݔ‬ሻ ൌ ͵‫ ݔ‬ସ െ ‫ ݔ‬ଷ ൅ ʹ‫ ݔ‬൅ Ͷ ܳሺ‫ݔ‬ሻ ൌ Ͷ‫ ݔ‬ସ ൅ ͸‫ ݔ‬ଷ െ ‫ ݔ‬ଶ ൅ ʹ ܴሺ‫ݔ‬ሻ ൌ ‫ ݔ‬ଶ ൅ ͳ
&DOFXOD ܲሺ‫ݔ‬ሻ ൅ ܳሺ‫ݔ‬ሻ ܲሺ‫ݔ‬ሻ െ ܳሺ‫ݔ‬ሻ ܳሺ‫ݔ‬ሻ െ ܲሺ‫ݔ‬ሻ ܲሺ‫ݔ‬ሻ ȉ ܴሺ‫ݔ‬ሻ
'D HO GHVDUUROOR GH ODV VLJXLHQWHV H[SUHVLRQHV
D ሺ‫ ݔ‬൅ ͸ሻଶ E ሺʹ‫ ݔ‬െ ͵ሻଶ F ሺ͵‫ ݔ‬ଶ ൅ Ͷሻ ȉ ሺ͵‫ ݔ‬ଶ െ Ͷሻ
(VFULEH ORV VLJXLHQWHV SROLQRPLRV FRPR HO FXDGUDGR GH XQD VXPD HO FXDGUDGR GH XQD UHVWD R XQD
VXPD SRU XQD GLIHUHQFLD VHJ~Q FRUUHVSRQGD HQ FDGD FDVR
D ‫ ݔ‬ଶ ൅ ͳ͸‫ ݔ‬൅ ͸Ͷ E ‫ ݔ‬ଶ െ ͳͶ‫ ݔ‬൅ Ͷͻ F ‫ ݔ‬ଶ െ ͺͳ

2. &RPSUXHED VL ‫ ݔ‬ൌ ͵ HV VROXFLyQ GH ODV HFXDFLRQHV
௫ ଽ௫
D Ͷ‫ ݔ‬൅ ʹ ൌ ͵Ͷ െ ͵‫ݔ‬ E ൅Ͷ ൌ
ଶ ଶ
5HVXHOYH ODV VLJXLHQWHV HFXDFLRQHV
Ͷ‫ ݔ‬െ ͵ ൌ ͷ ͵‫ ݔ‬൅ ͷ ൌ ‫ ݔ‬൅ ͳ ʹ െ ‫ ݔ‬ൌ െ͵ሺ‫ ݔ‬൅ ͷሻ Ͷሺʹ‫ ݔ‬൅ ͳሻ ൌ ‫ ݔ‬൅ Ͷ
௫ିସ ௫ ଷ௫ ଵ ହ
ൌ͵ ͵െ ൌ‫ݔ‬െͳ ൅ ൌ ͷ‫ ݔ‬൅
ଶ ହ ସ ଷ ଶ
%LRORJtD
(OLJH OD ~QLFD UHVSXHVWD FRUUHFWD
D 7RGRV ORV VHUHV YLYRV WLHQHQ HQ VX FRPSRVLFLyQ XQ GH DJXD
E 7RGRV ORV VHUHV YLYRV WLHQHQ HQ VX FRPSRVLFLyQ XQ GH DJXD
F 7RGRV ORV VHUHV YLYRV WLHQHQ HQ VX FRPSRVLFLyQ XQ GH DJXD
G 1R WRGRV ORV VHUHV YLYRV WLHQHQ DJXD HQ VX FRPSRVLFLyQ DOJXQRV FRPR ODV SODQWDV VyOR WLHQHQ
KLGUyJHQR
D /D YLGD HQ OD 7LHUUD H[LVWH JUDFLDV D OD SUHVHQFLD GH FDUERQR R[tJHQR
E /D YLGD HQ OD 7LHUUD H[LVWH JUDFLDV D OD SUHVHQFLD GH KLGUyJHQR
F /D YLGD HQ OD 7LHUUD H[LVWH JUDFLDV D OD SUHVHQFLD GH + 2
G /D YLGD GH OD 7LHUUD H[LVWH JUDFLDV D OD H[LVWHQFLD GH YLWDPLQDV TXH OHV FRQILHUHQ HQHUJtD
D /RV KLGUDWRV GH FDUERQR GHEHQ VHU ORV QXWULHQWHV PDRULWDULRV HQ QXHVWUD GLHWD
E /RV KLGUDWRV GH FDUERQR D SHVDU GH VHU PX LPSRUWDQWHV QR GHEHQ VHU ORV QXWULHQWHV
PDRULWDULRV HQ QXHVWUD GLHWD
F /RV KLGUDWRV GH FDUERQR MXQWR FRQ ODV SURWHtQDV ODV JUDVDV ODV YLWDPLQDV GHEHQ VHU ORV
QXWULHQWHV PDRULWDULRV HQ QXHVWUD GLHWD
G 7RGDV ODV DQWHULRUHV VRQ YHUGDGHUDV
D /RV DOLPHQWRV DQLPDOHV VRQ XQD IXHQWH GH ILEUD DOLPHQWDULD
E /RV DOLPHQWRV YHJHWDOHV VRQ XQD IXHQWH GH ILEUD DOLPHQWDULD
F /DV JUDVDV FRQVWLWXHQ XQD IXHQWH GH ILEUD DOLPHQWDULD
G /DV YLWDPLQDV FRQVWLWXHQ XQD IXHQWH GH ILEUD DOLPHQWDULD
D /DV YLWDPLQDV VRQ LQGLVSHQVDEOHV SDUD OD YLGD DXQTXH QR QRV DSRUWHQ HQHUJtD
E /DV YLWDPLQDV VRQ LQGLVSHQVDEOHV SDUD OD YLGD QRV DSRUWDQ HQHUJtD
F /DV YLWDPLQDV QR VRQ LQGLVSHQVDEOHV SDUD OD YLGD DXQTXH QRV DSRUWDQ JUDQ FDQWLGDG GH HQHUJtD
G /DV YLWDPLQDV QR QHFHVLWDQ VHU LQJHULGDV D TXH ODV VLQWHWL]DPRV HQ QXHVWUR FXHUSR
D /DV JUDVDV QRV DXGDQ D IRUPDU QXHYDV HVWUXFWXUDV
E /DV JUDVDV WLHQHQ XQD IXQFLyQ UHJXODGRUD HQ QXHVWUR RUJDQLVPR
F /DV JUDVDV QR WLHQHQ QLQJXQD XWLOLGDG HQ QXHVWUR RUJDQLVPR FRQ HOOD VyOR DXPHQWDPRV GH SHVR
G /DV JUDVDV WLHQHQ XQD IXQFLyQ HQHUJpWLFD HQ QXHVWUR RUJDQLVPR
&RQ OD UXHGD GH ORV DOLPHQWRV TXH KDEUiV HODERUDGR FRQWHVWD D ODV VLJXLHQWHV FXHVWLRQHV
D ¢3RGUtDV GHFLU TXp IXQFLyQ WLHQH FDGD JUXSR IXQFLyQ TXH GHVHPSHxD HQ HO RUJDQLVPR "
E &ODVLILFD ORV VLJXLHQWHV DOLPHQWRV VHJ~Q OD IXQFLyQ R IXQFLRQHV TXH GHVHPSHxDQ
)LOHWH GH WHUQHUD 7RUWLOOD D OD IUDQFHVD %DWLGR GH QDWD <RJXU 3DWp GH KtJDGR GH FHUGR
3ROOR HQ SHSLWRULD &HUHDOHV FRQ OHFKH 3DQ FRQ DFHLWH GH ROLYD 3ODWR GH OHQWHMDV 1DUDQMD

3. ¢3RU TXp HQ ODV GLHWDV YHJHWDULDQDV HVWULFWDV VH SXHGHQ SURGXFLU HVWDGRV FDUHQFLDOHV GH DOJXQRV
DPLQRiFLGRV HVHQFLDOHV"
¢$ TXp VH UHILHUH HO WpUPLQR ´FDORUtDV YDFtDVµ" ¢4Xp DOLPHQWRV QRV SURSRUFLRQDQ HVWDV FDORUtDV
YDFtDV"
&LWD ODV IXQFLRQHV TXH FXPSOH OD ILEUD GLHWpWLFD HQ QXHVWUR RUJDQLVPR ¢4Xp HV HO SHULVWDOWLVPR
LQWHVWLQDO"
5HOOHQD ORV KXHFRV GHO HVTXHPD SXHGHV KDFHUOR D OiSL]
3UHJXQWDV D UHDOL]DU
0DWHPiWLFDV
0RQRPLRV
3ROLQRPLRV
(FXDFLRQHV
0RQRPLRV SROLQRPLRV
0RQRPLRV HFXDFLRQHV
3ROLQRPLRV HFXDFLRQHV
7RGR
%LRORJtD
%LRORJtD
(VTXHPD