2000 SeniorPrelim 2000

✁ ✂☎✄ ✂✝✆✟✞ ✠ ✡ ☛✌☞ ✍
✂☎✎ ✠ ✡ ☛✌☛✌✏ ✑ ✏ ✆
✒✔✓✖✕✘✗✚✙✜✛✣✢✤✗✚✥✧✦★✒✔✩✪✦✘✙✔✙✧✫✭✬✯✮✱✰✲✦✘✓✖✳✴✮✱✰✲✗✵✩✷✶✹✸✺✙✧✕✻✰✼✓✖✶✽✰
✾ ✛✲✓✖✫✵✗✚✳✿✗✚✕✘✮❀✛✼❁✴❂✣✙✧❃❄✕✘❅❆✬❇✮❀✛✪✩❈✦❊❉✔❋❍●❏■✜■✜■
❑▼▲

◆P❖✷◗❙❘▼❖❀❚❯❖❱❘❳❲❙❨❩◗❬❲❭❘❫❪❱◗✝❘❫❖❵❴✤❛❀❚❝❜❫❨❡❞❙❚❯❢❱❨❡❘❫❣✐❤▼❥❫❜❧❦✤▲♠◆♥❣♦◗❬❨♣❞✺q❀❨✹q❀❴❫❲✝r✽❘✲s❫❨♣❞t❨♣❢✉q❏❴❫✈✇❣①◗❬q❱❨✹❢❀❚❝❲t◗②❴❈❖❀r♣❨❡q❀❨
③ ❀❖ ❢❱❲✝◗❬q❏❴✪◗④q❀❨✣q❏❴❈❲④❴⑤s▼❨♣❞❙❴❫⑥▼❨✽❢❆❑✲⑦❈❜❧❦✣⑧✪q❀❞♣▲⑩⑨♥❨✣❢❀❨✽r♣❚❯❢❱❨♣❲✝◗❙❘⑩❲❙❶✧❨♣❨♣❢❵❪❱❶✔▲⑩❷❸q❀❨♠❞❬❴✪◗❬❨✣❴✪◗✝❹✐q❀❚❝r②q❵q❀❨
❦❭❪❀❲❺◗✐◗❬❞❬❴⑤s❫❨♣✈✔◗❬q❱❨❻❞t❨♣❲❺◗❼❘❈❣❽◗❬q❱❨❾◗❙❞❙❚❝❶♠❚❯❖❿❘▼❞❙❢❱❨♣❞❸◗❬❘➀❴⑤s▼❨✽❞❬❴❫⑥▼❨✝➁❫❥❫❜❧❦✹⑧❈q❀❞①❣➂❘❫❞➃◗❬q❀❨☎❹✐q❀❘▼✈❝❨①➄t❘▼❪❀❞❙❖❱❨✽➅♠❚❝❲♣➆
➇ ❴▼➈❸➁▼⑦❈❜❧❦✣⑧✪q❀❞
➇ ❛❏➈✐➉❫❥❫❜❧❦✣⑧❈q❱❞
➇ r⑤➈✐➉▼⑦❈❜❧❦✣⑧❈q❱❞
➇ ❢✜➈❸➉▼➊❈❜✖❦✹⑧❈q❀❞
➇ ❨✼➈➃❤✷❥❈❜✖❦✹⑧❈q❀❞
✱➁ ▲ ◆❊r♣❚❝❞❙r♣✈❝❨❸❹✐❚❝◗❬q➀r♣❨✽❖✷◗❬❞❙❨❼❴❈◗ ➇ ➉✱➋➌➁▼➈➍❚❯❖✷◗❬❨✽❞❙❲t❨♣r✽◗❙❲✭◗❙q❀❨❸➎❀➏➐❴✪➑✱❚❯❲➒❴❈◗➓◗❙q❀❨
❘▼❞t❚❯⑥▼❚❝❖✔➔✪→❡➔❈❴❫❖❀❢❭❴✪◗✘◗❙q❀❨①❶✧❘▼❚❝❖❧◗❄➣✹▲❄❷❸q❀❨✭◗❬❴❫❖❀⑥▼❨✽❖✷◗❬❲❄◗❙❘♥◗❙q❀❨①r✽❚❯❞tr♣✈❯❨
❴❈◗♥→↔❴❈❖❀❢↕➣➙❚❝❖❧◗❙❨♣❞t❲❙❨♣r❩◗❼❴❈◗➃◗❬q❱❨❻❶✧❘▼❚❝❖❧◗❸➛➀▲❍❷❸q❀❨❾➜✷➏➝r✽❘✱❘▼❞t❢❀❚❯❖❀❴❈◗❬❨
❘❫❣❽➛➞❚❯❲✽➆
➇ ❴▼➈P➟P➉✘➡➠ ➇ ❛❏➈☎➟♥❤ ➇ r⑤➈☎➟♥❤❄➡➠ ➇ ❢✜➈➢➟P⑦ ➇ ❨✼➈➃❖❀❘❫❖❀❨❾❘❫❣❄◗❙q❀❨♣❲t❨
(3,2)
O

B

➤P
➉❱▲
❤❀▲

❏➥ ❞❙❘▼❦ ③ s▼❨✹❲❺◗❬❪❀❢❱❨♣❖✷◗❬❲✝❹✐q❱❘▼❲❙❨♠❴❈⑥▼❨♣❲✺❴❫❞❙❨❡➊❱➔➍➦✱➔➍➧❱➔❄➨❱➔❽❴❫❖❀❢➩❑⑤❥❱➔❄◗➝❹✭❘⑩❴❫❞t❨❡❞❙❴❫❖❀❢❀❘▼❦➀✈❝➅➫r②q❀❘▼❲❙❨✽❖✔▲↕❷❸q❀❨
❶❀❞t❘▼❛❏❴❫❛❀❚❝✈❯❚✇◗➝➅➀◗❙q❏❴❈◗✐◗❬q❱❨❻❢❱❚❝➭✻❨♣❞❙❨✽❖❀r♣❨❾❚❝❖❿◗❙q❀❨♣❚❝❞✐❴❫⑥▼❨✽❲✐❹✐❚❝✈❯✈✻❛✻❨❻❴❈◗✐✈❝❨⑤❴❫❲❺◗❼➁④➅❫❨⑤❴❫❞t❲♥❚❝❲♣➆
➇ ❴▼➈➀➡➠
➇ ❛✜➈ ➯➡
➇ r✼➈❭➲➯
➇ ❢❏➈➵➳
➇ ❨✼➈❭➺➲
➠✚➸
❷❸q❀❨♥r♣❨✽❖❧◗❙❞❙❨✽❲➃❘❫❣➻◗❙q❀❞❙❨✽❨❼r✽❚❯❞tr♣✈❯❨✽❲➓❘❫❣✔❞❙❴❫❢❀❚❯❪❱❲①➁☎❪❀❖❀❚✇◗❬❲➒❴❫❞t❨❼✈❝❘✱r♣❴❈◗❬❨✽❢
❴❈◗❿◗❬q❱❨➼❶✧❘▼❚❯❖✷◗❙❲ ➇ ❥❱➋②❥✷➈➌➔ ➇ ❑✼➁✱➋②❥✷➈♠❴❫❖❀❢ ➇ ❥❱➋②⑦▼➈❩▲➾➽➚❣✝◗❬q❱❨➼r✽❚❯❞❙r✽✈❯❨✽❲
(0,5)
❞❙❨✽❶❀❞❙❨✽❲❙❨✽❖❧◗❻❶❀❪❱✈❯✈❯❨❩➅✖❲♣➔➻❹✐q❏❴✪◗☎❚❯❲P◗❙q❀❨❭✈❝❨♣❖❀⑥❫◗❙q⑩❘❫❣❍◗❬q❱❨④❛✻❨✽✈❝◗P❹✐q❱❚❯r②q
⑥▼❘✖❨♣❲✐❴❫❞t❘▼❪❀❖❀❢✤❴❫✈❝✈➪➉④❶❀❪❀✈❯✈❝❨✽➅✖❲✐❴❫❲✐❲❙q❱❘✲❹✐❖✤❚❯❖♠◗❬q❱❨❻❢❱❚➶❴❫⑥▼❞❙❴❫❦✹➹

(0,0)

(12,0)

➇ ❴▼➈➃➉▼❥♥➘✉➴
➇ ❛✜➈➃➉▼❥♥➘➷❤❫➴
➇ r✼➈➃➉❫➊❼➘❵➴
➇ ❢❏➈➃➊▼❥☎➟❵❤❫➴
➇ ❨✼➈➃❖❀❘▼❖❀❨❾❘❫❣✘◗❬q❱❨♣❲❙❨
⑦✱▲ ➽➚❣➒➬❳❴❈❞❙❜❿⑥▼❨✽◗❙❲☎➦✱❑✺❘▼❖❳q❱❚❯❲♥❖❀❨❩➑✖◗➢➮❧❪❀❚❝➱❫➔✧q❀❚❯❲❼❴⑤s▼❨✽❞❬❴❫⑥▼❨❻❹✐❚❯✈❝✈➪❛✻❨✝➧▼➉❱▲❸➽➚❣❍q❀❨✺⑥▼❨✽◗❙❲➢➨▼➨✱➔✧q❱❚❯❲❼❴✼s❫❨♣❞❙❴❫⑥▼❨✺❹✐❚❝✈❯✈
❛✧❨✺➧▼➦✱▲➓⑨❼❘✼❹✃❦❡❴❫❖✷➅✣➮❧❪❀❚❝➱♣➱✽❨♣❲♥q❏❴❫❲❼➬❳❴❫❞t❜♠❴❫✈❯❞t❨⑤❴❫❢✱➅✹◗②❴❈❜❫❨♣❖❏➹
➇ ❴▼➈①❤
➇ ❛❏➈♥⑦
➇ r⑤➈✐➊
➇ ❢✜➈✐➦
➇ ❨✼➈❸➧
➊❱▲ ❐❊q❀❚❝✈❯❨✴❑⑤❥✴❶❀❚❯❖➩❛✻❘✼❹✐✈❯❚❝❖❀⑥ ➇ ❲❙❨♣❨❳❢❀❚➶❴❫⑥❫❞❬❴❫❦✹➈❡❒✱❴❫❦ ✈❝❨✽❣♦◗✣➉✴❶❀❚❯❖❱❲✣❲t◗❬❴❫❖❀❢❀❚❝❖❀⑥
❹✐q❀❚❝r②q❳❣➂❘▼❞❙❦➀❨♣❢↕◗❬q❀❨✺s▼❨♣❞❺◗❬❚❝r♣❨♣❲P❘❫❣➓❴❫❖➫❨✽➮❧❪❀❚❯✈❯❴❈◗❬❨✽❞❬❴❫✈➪◗❬❞t❚➶❴❫❖❱⑥▼✈❯❨❈▲✐⑨❼❘✼❹❮❦✹❴❫❖✷➅
❲❙❪❱r②q❳❨♣➮❧❪❀❚❝✈➶❴❈◗❙❨♣❞❙❴❫✈➻◗❬❞t❚➶❴❫❖❱⑥▼✈❯❨✽❲❸❴❫❞❙❨☎❶✧❘▼❲t❲❙❚❯❛❱✈❯❨✼➹
➇ ❴▼➈P❑✲⑦

➇ ❛❏➈P❑⑤❤
➇ r⑤➈P❑✲➁
➇ ❢✜➈➢❑✼❥
➇ ❨✼➈➃❖❀❘▼❖❀❨❾❘❫❣✘◗❬q❱❨♣❲❙❨
➦✱▲

➽➚❣❄➽①❶❀✈❯❴❫r♣❨❾❴❰➊④r♣❦ÐÏ➩➊❰r✽❦Ñ❲❙➮❧❪❏❴❈❞❙❨❻❘▼❖↕❴④◗❙❞❙❚❯❴❫❖❀⑥▼✈❝❨❫➔✖➽①r⑤❴❈❖↕r✽❘✼s▼❨♣❞♥❪❀❶❿◗❬❘➀➊▼❥✷ÒÓ❘❫❣✘◗❬q❀❨➢◗❙❞❙❚➶❴❈❖❀⑥▼✈❯❨❈▲➍➽➚❣
➽①❶❱✈➶❴❫r✽❨➢◗❬q❀❨☎◗❬❞t❚➶❴❫❖❱⑥▼✈❯❨❼❘▼❖↕◗❙q❀❨❾❲❙➮❧❪❏❴❫❞t❨❫➔✜➽➒r⑤❴❫❖↕r♣❘✼s▼❨✽❞❼❪❱❶↕◗❙❘ ➡➲ ❘❫❣✘◗❬q❀❨❾❲❙➮❧❪❏❴❈❞❙❨❫▲❍❐❊q❏❴✪◗❼❚❝❲➃◗❬q❀❨❻❴❫❞t❨⑤❴❱➔
❚❯❖❿r✽❦ ➡ ➔❱❘❫❣❄◗❙q❀❨☎◗❬❞t❚➶❴❫❖❀⑥❫✈❯❨✼➹
➇ ❴▼➈❸➁▼➁ ➺➯
➇ ❛❏➈❸➁❈❤
➇ r✼➈❸➉▼➊
➇ ❢✜➈①❤✷❥
➇ ❨✼➈❸➊▼❥

✒✔✓✖✕✘✗✚✙✜✛✣✢✤✗✚✥✧✦❆✒➪✩✪✦✘✙➻✙✻✫①✬✯✮✱✰✲✦✘✓✖✳✴✮✱✰✲✗✵✩✷✶✹✸✺✙✧✕✻✰✼✓✖✶✽✰✽Ô ✾ ✛✲✓✱✫✚✗✚✳✿✗✵✕Õ✮❀✛✼❁✿❂✹✙✻❃✘✕✘❅❆✬✯✮❱✛❈✩✪✦❊❉✔❋❍●❏■✜■✜■
➧❱▲

❷➃❹✭❘④r♣❚❯❞tr♣✈❝❨♣❲♣➔✱❨⑤❴❫r②q✣❹✐❚✇◗❬q✣❞❙❴❫❢❀❚❝❪❀❲P❑✼❥❻r♣❦↕➔❀❴❫❞t❨P❶❀✈❯❴❫r♣❨✽❢✣❲❙❘❭◗❙q❀❨✽➅
❴❫❞t❨♥◗❬❴❫❖❀⑥▼❨✽❖❧◗➒◗❬❘❻❨⑤❴❈r②q✣❘❫◗❬q❱❨♣❞✭❴❫❖❀❢✣❴❻❲t◗❙❞❬❴❫❚❝⑥▼q✷◗✭✈❝❚❯❖❀❨❈▲❽◆★❲❙❦❡❴❫✈❯✈❝❨♣❞

r♣❚❝❞❙r✽✈❯❨❰❚❯❲❾❖❀❨✽❲t◗❬✈❝❨♣❢➼❛✻❨❩◗➝❹①❨✽❨♣❖✿◗❬q❱❨♣❦Ö❲❙❘↕◗❬q❏❴❈◗❻❚✇◗✺❚❝❲☎◗②❴❫❖❀⑥❫❨♣❖✷◗✺◗❙❘
◗❬q❱❨❡✈❯❴❫❞❙⑥▼❨✽❞✺r✽❚❯❞tr♣✈❯❨✽❲❻❴❫❖❀❢✴◗❙q❀❨❡✈❝❚❯❖❀❨❈▲✹❐❊q❏❴❈◗✝❚❯❲☎◗❬q❱❨✹❞❬❴❈❢❀❚❯❪❀❲✽➔❽❚❝❖
r♣❨✽❖✷◗❬❚❯❦➀❨✽◗❙❞❙❨✽❲♣➔❏❘❫❣✘◗❬q❀❨❾❲t❦✹❴❫✈❝✈❯❨✽❞➃r♣❚❝❞❙r♣✈❝❨✼➹
➇ ❴▼➈♥× ❑✼❥ ➇ ❛❏➈♥➁✖ØÙ⑦ ➇ r⑤➈♥× ➁ ➇ ❢✜➈➢❑ ➇ ❨⑤➈❸❖❱❘▼❖❀❨❾❘❫❣✘◗❬q❀❨✽❲❙❨
➨❱▲ ◆P❞t❞❬❴❫❖❱⑥▼❨➢◗❬q❀❨☎❣➂❘▼✈❝✈❯❘✼❹✐❚❯❖❱⑥❭❚❯❖↕❴❫❲tr♣❨♣❖❱❢❀❚❯❖❀⑥➀❘▼❞t❢❀❨♣❞✽➆
➯➝➯➝➯➝➯
➁
➉ ➲➝➲➝➲➝➲ ➊ ➡➝➡➝➡➝➡
➯➝➯➝➯➝➯
➝
➯
➝
➯
➝
➯
➯
➯➝➯➝➯➝➯
➇ ❴▼➈❸➁
➇ ❛✜➈✐➁
➇ r✼➈❸➊ ➡➝➡➝➡➝➡ ➉ ➲➝➲➝➲➝➲ ➁

➉ ➲➝➲➝➲➝➲ ➊ ➡➝➯➝➡➝➯➝➡➝➯➝➡ ➯
➊ ➯➝➡➝➯➝➡➝➯➝➡➝➯ ➡ ➉ ➲➝➲➝➲➝➲
➇ ❢❏➈➃➉ ➲➝➲➝➲➝➲ ➊ ➡➝➡➝➡➝➡ ➁
➇ ❨✼➈❸➉ ➲➝➲➝➲➝➲ ➁
➊ ➡➝➡➝➡➝➡
❑✼❥❱▲✟Ú☎❚❝s▼❨✽❖➷◗❙q❏❴❈◗➀❥➩Û✌➎✯Û✌➜ÜÛÝ➁❫❥✱➋❽◗❬q❀❨↕❖❧❪❀❦❭❛✧❨♣❞❰❘❫❣P❚❯❖✷◗❬❨✽⑥▼❨♣❞④❲t❘▼✈❯❪❱◗❙❚❯❘▼❖❱❲ ➇ ➎Õ➋❬➜❱➈✺◗❬❘Þ◗❬q❀❨❿❨✽➮✖❪❀❴❈◗❬❚❝❘▼❖
➁✪➎❭➘➵➉❫➜④ß✟⑦❫❥④❚❯❲✽➆
➇ ❴▼➈❸➁▼⑦
➇ ❛❏➈P❑✼➊
➇ r⑤➈❸➧
➇ ❢❏➈♥⑦
➇ ❨✼➈❸➉
❑▼❑▼▲✟❒✱❪❀❶❱❶✻❘▼❲t❨❾à✝➋②➣✹➋✜❴❈❖❀❢❳á➞❴❫❞❙❨❾❶✧❘▼❲❙❚✇◗❬❚❝s❫❨☎❚❯❖✷◗❬❨✽⑥▼❨♣❞t❲✐❲❙❪❀r②q↕◗❬q❏❴❈◗
➁❈❤ ßÜà➷➘
❑
❑
⑦
➣★➘ á❆➘❊
❑

❷❸q❀❨☎s❈❴❫✈❯❪❱❨☎❘❫❣❽à➵➘➵➁❫➣★➘➵➉▼á➞❨✽➮❧❪❏❴❫✈❯❲✽➆
➇ ❴▼➈➃➨
➇ ❛✜➈➢❑✲➁
➇ r✼➈➢❑✲⑦
➇ ❢✜➈➢❑✼➊
➇ ❨✼➈❸➁❫❥
❑✲➁✱▲★◆â❛✧❘⑤➑ãr✽❘▼❖✷◗②❴❫❚❝❖❀❲✣ä ❹✐q❀❚✇◗❬❨➫❛❀❴❫✈❯✈❝❲✹❴❫❖❱❢ãå✃❛❀✈❯❴❫r②❜✉❛❏❴❫✈❯✈❝❲♣▲Ü❷➃❹①❘❵❛❏❴❈✈❯✈❯❲❡❴❫❞t❨➫❞❙❨✽❦❡❘✼s▼❨✽❢❆❞❬❴❫❖❱❢❀❘▼❦➀✈❝➅
❹✐❚❝◗❙q❀❘▼❪❱◗✐❞t❨♣❶❀✈❯❴❫r♣❨✽❦❡❨✽❖✷◗⑤▲➓❷❸q❀❨❾❶❀❞❙❘❫❛❏❴❫❛❀❚❝✈❯❚❝◗➝➅❡❘▼❖❀❨☎❛❀❴❫✈❯✈✔❘❈❣❽❨♣❴❫r②q❳r✽❘▼✈❯❘▼❪❱❞➃❚❯❲✐r②q❀❘▼❲t❨♣❖✤❚❯❲♣➆
➡
➡
➇ ❴▼➈ è æ✘è ç
➇
➇
➇
➇
æ è æ➒ë ➠ ê
æ❽é❱ç✼ê æ❽é❱ç❈ë ➠ ê ❛✜➈ è æ➍æ❄é❱ç ç⑤ê❝ì r✼➈ è æ➍é❱ç✪ë ➠ æ✘ê è æ➍ç é❱ç✪ë ➠ ê ❢✜➈ è æ❽é❱ç✼ê è æ❄æ❽ç é❱ç❈ë ➠ ê ❨⑤➈ è æ❽é❱ç✼ê è æ❽é❱ç❈ë ➠ ê
❑✼➉❱▲★➽➚❣❄❚❝◗❸◗②❴❈❜❫❨♣❲❸➎❳❛❀❪❀❚❯✈❝❢❀❨♣❞t❲❸➜✣❢❏❴⑤➅✖❲❸◗❬❘➀❛❀❪❀❚❯✈❝❢❿í➀q❱❘▼❪❀❲❙❨✽❲♣➔✜q❀❘✼❹✃❦❡❴❫❖✷➅✣❢❀❴✼➅✖❲✐❹①❘❫❪❀✈❯❢↕❚❝◗➃◗❬❴❫❜❫❨❾î❭❛❱❪❀❚❯✈❝❢❀❨♣❞t❲
◗❬❘❰❛❀❪❱❚❯✈❯❢♠ï④q❱❘▼❪❀❲❙❨✽❲②➹❳◆❼❲❙❲❙❪❱❦❡❨❾◗❬q❀❨✽❲❙❨❻❛❀❪❀❚❝✈❯❢❀❨✽❞❙❲➃❹✭❘▼❞❙❜♠❴✪◗❸◗❬q❀❨❾❲❬❴❈❦❡❨❾❞❬❴✪◗❬❨❾❴❫❲❸◗❬q❱❨❻❘❈◗❬q❀❨✽❞❙❲♣▲
➇ ❴▼➈✝ðòñ➚ó

➇ ❛✜➈✺ñ➚ó õ
➇ r⑤➈❊ð õ
➇ ❢✜➈ ô ó❺ñ
➇ ❨⑤➈ ñ õ
ô➌õ
ðô
ñôó
ðõ
ðôó
❑⑤❤❀▲★➽➚❣Õ➎ ➡ ➘✴➎✜➜P➘✴➎♠ßö❑⑤❤❰❴❫❖❀❢♠➜ ➡ ➘✴➎✜➜❼➘✿➜❰ß✟➁❫➧✱➔✱◗❬q❱❨♣❖✤❴❭❶✻❘▼❲t❲❙❚❝❛❀✈❯❨Ps❈❴❫✈❝❪❀❨❼❣➂❘❫❞①◗❬q❀❨☎❲t❪❀❦Ñ❘❫❣Õ➎✺➘✿➜➀❚❯❲♣➆
➇ ❴▼➈➒➏❺➦
➇ ❛❏➈➒➏➐➊
➇ r⑤➈❸❥
➇ ❢✜➈➢❑
➇ ❨⑤➈❸➉
❑✲⑦✱▲★❷➃❹✭❘❼r✽❘▼❖❀⑥▼❞t❪❀❨♣❖✷◗✘❞❙❨✽r✽◗②❴❈❖❀⑥▼✈❯❨✽❲➪❨⑤❴❫r②q❻❦➀❨⑤❴❫❲t❪❀❞❙❚❝❖❀⑥♥➉❫r♣❦➼Ï➃➦❈r✽❦❇❴❫❞t❨
❶❀✈❯❴❫r♣❨✽❢✿❴❫❲❻❚❯❖Þ◗❬q❀❨ ③ ⑥▼❪❱❞❙❨❫▲✹❷❸q❀❨✣❴❫❞t❨⑤❴↕❘❫❣➃❘✼s▼❨✽❞❙✈❯❴❫❶ ➇ ❲❙q❏❴❫❢❱❨♣❢✜➈➌➔
❚❯❖❿r✽❦ ➡ ➔❱❚❯❲♣➆
➇ ❴▼➈✝÷➐➳ ➇ ❛❏➈ ➡➝ø ➇ r⑤➈ ➡ ➸ ➇ ❢✜➈ ➡ ➡ ➠ ➇ ❨✼➈①❖❱❘▼❖❀❨❾❘❫❣✘◗❬q❀❨✽❲❙❨
➳

➳
➳