Cambridge University Press Paul Fannon , Vesna Kadelburg , Ben...
Transcript of Cambridge University Press Paul Fannon , Vesna Kadelburg , Ben...
Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information
www.cambridge.org© in this web service Cambridge University Press
✶� ✁✂✄☎✆✄✝✞✟ ✠✂✡✟✝✞☛✡☞
❊✌✍✎❝✏✑✍ ✒✓
✹ ✥
✤ ✔
✤ ✔
✢ ✕ ✛
✢ ✕ ✕ ✛
✢ ✕ ✛
② ✖ ✖
✖
✖
✻ ✗✗
✸ ✘ ✗✗
✸ ✙
✷
✷
✷
❜ ▼✐✚✐✜✉✜ ✣✦❧✉❡ ✧❢ ★ ✐s ✩✪
✺ ✥ ▼✐✚✐✜✉✜ ✦t ✫✬✭ ✮✯✰ ✱ ✲ ✳✴ ✵ ①✼ ✽✾ ✿❀
❙✧ ❛ ❁ ❂✬✭ ❃ ❁ ✮
❜ ❈✉❄✣❡ ❅✦ss❡s t❤❄✧✉❆❤ ✫❇✭ ❇❉✯✭ s✧s✉❋st✐t✉t✐✚❆ ● ❁ ❇ ✦✚❞ ★ ❁ ❇❉ ✐✚t✧
❍ ■❏ ❑ ▲◆ ❖ P ◗ ❘❚
❯
❱ ❲❳ ❨ ❩
❳
❳
❬
❬
❬
❭❪ ❭ ❫ ❴
❵ ❪
❣
❥
❦ ✥
♠ ♥
♠ ♥
♠ ♥
♦ ♣ q ♦r✈ ✇③ ♣
q ♦ ♣r✈
✇③ ♣
q ♦ ♣ ♣
q ♦ ♣
④ ④ ④ ④
④
④
④
⑤ ⑥ ⑦ ⑤ ⑤ ⑦
⑤ ⑦ ⑦ ⑦
⑤ ⑦ ⑤ ⑦
⑤ ⑦ ⑧
⑨ ⑨
⑨
⑨
⑨
❜ ⑩✐✚❡ ✧❢ s❶✜✜❡t❄❶ ✐s ● ❁ ❂❇
❷
❸ ❹
❸ ❹
❸ ❹
❺ ❻ ❼
❺ ❻ ❼
❺ ❼
❺ ❼
❺ ❼ ❽
❼ ❻ ❽
❾ ❾
❾
❾
❾
❾
❾
❿ ➀ ➁ ➂
❿ ➁ ➃ ➂
❿ ➁ ➃
➁➃
❿
➁➃
❿
➁➃
❿
➄
➄
➄
➄
❊✌✍✎❝✏✑✍ ✒➅
✹ ✥ ➆ ➇➆ ➇➈ ➉ ➊ ➉ ➈➋ ➋ ➋ ➋➌ ➍ ➎➌ ➌ ➏ ➐➑
❜ ➒❡ ❆❄✦❅❤ ➓❄✧ss❡s t❤❡ ●➔✦→✐s ➣❤❡❄❡★ ❁ ↔✭ ✐✪❡✪ ➣❤❡❄❡ ↕ ➙ ➛➜ ➜➝ ➞ ➟➝ ➠➡ ❯
➢ ➤➢ ➤
➥ ➦ ➧
➦ ➥ ➧
➦ ➧ ➧ ➧
➧ ➧ ➦
➨ ➨
➨ ➨
➨ ➨
➨ ➨
➩ ➫ ➭➩ ➯
➩ ➲ ➳ ➯
➩ ➲ ➯ ➵➸ ➳ ➯
➲
➩➵➸ ➳
➺
❙✧ t❤❡ ✐✚t❡❄s❡➓t✐✧✚s ➣✐t❤ t❤❡ ●➔✦→✐s ✦❄❡
✦t ➻➼➽
➾➚➪
➶
➹➘ ➴ ✦✚❞ ✫❂❉✭ ↔✯✪
✺
➷ ➬➷ ➬
➮
➱ ✃ ➮ ❐
✃ ❐ ➮
❒ ❮ ❰ ❰
❮❰ ❮❰ ❮
ÏÐÐÑÒ ÓÑ Ô ÓÕÖ ×
× Ô
Ø ÙÚÛ
❙✧ Ü ❁ ❂❇↔❛ ✦✚❞ ❃ ❁ ✬❛✪
★➔✐✚t❡❄➓❡❅t ✦t ✬ ✰Ü ❁ ✬
Ý
Ý
Þ ßà
Þ
ßà
á â ã
â ã
✦✚❞ ä åæçè
éêëä åì í
í
îï
ð
îï
❊✌✍✎❝✏✑✍ ✒ñ
✺ ✬●ò ❁ ❉● ó ❇ô✬●ò ❂ ❉● ❂ ❇ ❁ ↔õs✐✚❆ t❤❡ ö✉✦❞❄✦t✐➓ ❢✧❄✜✉❧✦ ➣✐t❤ ❛ ❁ ✬✭❃ ❁ ❂❉ ✦✚❞ Ü ❁ ❂❇❯
Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information
www.cambridge.org© in this web service Cambridge University Press
❚♦�✁✂ ✄☎ ❚✆✝ ✞✟✠✡☛✠☞✁✂ ✌♦☛♠✟✍✠ ✠✎✡ ☞✆✝ ✡✁✏✂☛✁♠✁✎✠✎☞✷
✤✣ ✣ ✢ ✣ ✣ ✑ ✑ ✣
✑①
✭ ✒✮ ✭ ✒✮ ✒ ✹ ✭ ✓✮
✔ ✹
✕
✤✢
✤✢
✒ ✔✽
✻
✔ ✖
✹
✗ ✘❡ ✙✚s❝✛✚✐✚✜❛✜t ✥✚t❤ ✦ ✧ ★✩ ❜ ✧ ✪ ❛✜✙
✫✬✶
✶✯✚s
✰ ✱ ✲
✱ ✲ ✳ ✳
✱
✴ ✵✸✺
✼ ✺ ✺✼
✼✾
✿
❀
❀
❙❁ t❤❡✛❡ ✚s ❁✜❧② ❁✜❡ ✛❁❁t✩ ✚❂❡❂ t❤❡ ❃❡✛t❡❄
❧✚❡s ❁✜ t❤❡ ❅❆❛❄✚s❂
❇ ❊q✉❛❧ ✛❁❁ts ✥❤❡✜ ✙✚s❝✛✚✐✚✜❛✜t ✚s ❈❡✛❁❉
❋ ● ❍ ●
❍ ❍ ■ ■ ●
❍ ●
●
● ❏
❑ ▲▼
◆ ◆
◆
◆
◆
❖ P
◗ ❖❘ ❖ ❯ P
❱❲ ❳ P
❯
❯
❨
❨
❨
❨
❩ ❬❛✜❣❡✜t t❁ t❤❡ ❅❆❛❄✚s ✚✐♣❧✚❡s ❡q✉❛❧ ✛❁❁ts✩
s❁ ✙✚s❝✛✚✐✚✜❛✜t ✚s ❈❡✛❁❉
❭ ❪ ❭ ❪❫ ❴
❵ ❞ ❢ ❞
❥ ❢ ❦ ❢ ❦ ❢ ❞
❥ ❥ ❢ ❞
❢ ❥ ❞
❞♥ ❢ ❦ ❦
❦
❞♥
❞ ♥
r ✈✇
③ ③
③ ③ ③
③ ③
③
④ ⑤
⑥ ⑦ ④ ⑧ ④ ⑤
④ ④ ⑦ ④⑨ ⑤
④ ④④ ⑦ ⑤
④④ ④④ ④ ④ ⑦
⑥ ④
④④ ⑦⑩⑥⑤
⑨
⑦⑦
⑥⑧⑤
❶
❶
❶
❶
❶
❷ ❸❁ ✛❡❛❧ s❁❧✉t✚❁✜s ✥❤❡✜ ✙✚s❝✛✚✐✚✜❛✜t ❹ ❺ ❻❉
❼ ❽
❾ ❿
❾ ❾ ➀ ➀ ❿
❾ ❿
➁
➂ ➃➄
➅
➅
➅
➆ ➇
➈ ➆ ➉ ➊ ➇
➋➈ ➌ ➇
➍
➊
➎
➎
➏➐ ➑❁✛ ❛ q✉❛✙✛❛t✚❝ t❁ ➒❡ ✜❁✜❆✜❡❣❛t✚❃❡ ➓➔❻→
➣❁✛ ❛❧❧ ❅✩ ✚t ✐✉st ❤❛❃❡ ❛t ✐❁st ❁✜❡ ✛❁❁t✩ s❁
❹ ↔ ❻ ❛✜✙ ✦ ↕ ❻❂
➙ ➛ ➙ ➛
➜ ➝
➜ ➜ ➞ ➞ ➜ ➝
➜ ➟ ➝
➠
➡ ➢➤
➤
➤
➤
➥ ➦
➧ ➥ ➨ ➨ ➩ ➦
➫ ➩➭ ➯ ➦
➩➲
➩➭
➳
➳
➵➸➺➺➻➼➽
➾➚➪➶ ➪➹➘➪ ❹ ↔ ➴ ➷➬ ➮➚➪ ➬➱✃❐❒➷➶➮➪ ➷➮ ❮➶➮➶❰➘Ï
✃➚❰ ➘ Ð➱➘Ñ❰➘➪➷❒ ➪➚ Ò➶ ➮➚➮Ó➮➶❮➘➪➷Ô➶Õ Ö➹➶
❒➚➮Ñ➷➪➷➚➮ × Ø ➴ ➷➬ ➘Ï➬➚ ➮➶❒➶➬➬➘❰Ù ➪➚
➶➮➬➱❰➶ ➪➹➘➪ ➪➹➶ Ð➱➘Ñ❰➘➪➷❒ ➹➘➬ ➘ Ú➚➬➷➪➷Ô➶
➬➹➘Ú➶ Û➚Ú➶➮➷➮❮ ➱ÚÜ➘❰ÑÝ ❰➘➪➹➶❰ ➪➹➘➮ ➘
➮➶❮➘➪➷Ô➶ ➬➹➘Ú➶ Û➚Ú➶➮➷➮❮ Ñ➚Ü➮Ü➘❰ÑÝÞ ➬➚
➪➹➘➪ ➪➹➶ ❒➱❰Ô➶ ❰➶ß➘➷➮➬ ➘Ò➚Ô➶ ➪➹➶ àÓ➘á➷➬
➘➮Ñ ➮➶Ô➶❰ ❮➚➶➬ Ò➶Ï➚Ü ➷➪Þ ➘➬ Ü➚➱ÏÑ Ò➶ ➪➹➶
❒➘➬➶ ➷✃ × â ➴Õ ã➮ ➪➹➷➬ Ð➱➶➬➪➷➚➮ × Ü➘➬ ❮➷Ô➶➮
➘➬ Ú➚➬➷➪➷Ô➶ ÛäÝÞ ➬➚ Ü➶ Ñ➷Ñ ➮➚➪ ➮➶➶Ñ ➪➚ ➱➬➶
➪➹➷➬ ❒➚➮Ñ➷➪➷➚➮ ➘➪ ➘ÏÏÕ
➏➏ ➑❁✛ ❛ q✉❛✙✛❛t✚❝ t❁ ➒❡ ✜❡❣❛t✚❃❡ ➣❁✛ ❛❧❧ ❅✩
✚t ✐✉st ❤❛❃❡ ✜❁ ✛❡❛❧ ✛❁❁ts✩ s❁ ❹ ❺ ❻ ❛✜✙
✦ ❺ ❻❂
å æ
å ç ç å æ
è æ
æ å
é êë
ì
ì
ì
í î
ï í ð íñ î
ò óô î
ò
óô
õ
õ
Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information
www.cambridge.org© in this web service Cambridge University Press
✸✶ �✁✂✄☎✂✆✝✞ ✟✁✠✞✆✝✡✠☛
☞✌✍✍✎✏✑
❚✒✓ ✔✕✖✗✘✙✘✕✖ ❛ ✤ ✚ ✓✖✛✜✢✓✛ ✙✒✣✙ ✙✒✓❢✜✖✔✙✘✕✖ ✘✛ ✖✓✥✣✙✘✦✓ ✛✒✣✧✓✗ ✣✖✗ ✙✒✓✢✓❢✕✢✓✢✓r✣✘✖✛ ★✓✩✕✪ ✙✒✓ ①✲✣✫✘✛✬ ✭✖ ✙✒✘✛ ✔✣✛✓❛ ✮ ♠✱ ✣✖✗ ✘✙ ❢✕✩✩✕✪✓✗ ❢✢✕r ✙✒✓ ✔✕✖✗✘✙✘✕✖✕✖ ✯ ✙✒✣✙ ❛ ✤ ✚✱ ✣✛ ✛✓✓✖ ✘✖ ✙✒✓ ✣✖✛✪✓✢✬
✰✳ ✴❡ ✵✇♦ ✷❡✹♦s ♦✺ ✻ ✻✼✽ ❜✽ ❝✾ ✿✹❡
❀ ❁ ❀❂ ❂ ❃❄
❃
❅
❆
❇✿❈❞
❉ ❉ ❉❊ ❊ ❋●
❋
❍
■
❏❑
✴❡ ▲♦s✐✵✐✈❡ ❞✐▼❡✹❡❈◆❡ ❖❡✵✇❡❡❈ ✵❤❡s❡✷❡✹♦s ✐s
P ◗ PPP P P
❘P
❘P
❙ ❙ ❯❱
❯
❙ ❙ ❯❱
❯
❙ ❯❱
❯
❙ ❯❱
❯
❲
❳
❲
❳
❳ ❲
❳
❲
❨ ❨ ❨
❨
❩♦❬ ✐❈ ✵❤✐s ◆✿s❡❬
❭❪
❭ ❪
❪
❪ ❫
❦
❦
❦
❦
❴❵
❴❣❥
❴❵ ❣❥
❧❴
❥
♥
♥
♥
☞✌✍✍✎✏✑
♣✕✙✓ ✙✒✣✙ r✕✗✜✩✜✛ ✛✘✥✖✛ ✪✓✢✓ ✜✛✓✗ ✘✖✙✒✓ ✥✓✖✓✢✣✩ ✓✫✧✢✓✛✛✘✕✖ ❢✕✢ ✙✒✓ ✧✕✛✘✙✘✦✓✗✘✛✙✣✖✔✓✱ ✣✛ ❛ ✔✕✜✩✗ ★✓ ✖✓✥✣✙✘✦✓✬ q✓✢✓❛ ✮ t ✣✖✗ ✛✕ ✙✒✓ r✕✗✜✩✜✛ ✪✣✛ ✖✕✙ ✢✓✉✜✘✢✓✗✘✖ ✙✒✓ ✛✧✓✔✘②✔ ✔✣✛✓ ✘✖ ✙✒✘✛ ✉✜✓✛✙✘✕✖✬
③④⑤⑥⑦⑧⑨⑤ ⑩③
❶ ❷ ❸
❷ ❸
❹ ❺
❹ ❺
❻ ❼❽❾
❿ ❼➀❾
➁ ➂
➂
❩➃❖s✵✐✵➃✵✐❈➄ ➅➆➇ ✐❈✵♦ ➅➈➇➉
➊ ➋ ➊➌ ➌➍ ➎➏
➐ ➑➐ ➑
➒ ➊ ➋
➊ ➒ ➋
➋ ➋ ➊
➌ ➌
➌ ➌
➌ ➌
➓➔ →
➣ ➍ →
➣ ↔↕ ➍
➏
❩➃❖s✵✐✵➃✵✐❈➄ ✐❈✵♦ ➅➈➇➉
➙ ➛
➜ ➜ ➝ ➜
➜ ➝ ➜ ➝ ➝ ➜
➞ ➟
➞ ➟
➠ ➡ ➢ ➠ ➤
➥ ➡ ➢ ➥ ➦➧
❩♦ ✵❤❡ ▲♦✐❈✵s ♦✺ ✐❈✵❡✹s❡◆✵✐♦❈ ✿✹❡ ➅➨❬ ➩➇ ✿❈❞➅➫➭❬ ➆➈➇❑
➯ ➲
➲
➳ ➵ ➵
➵ ➳
➸ ➺ ➸ ➻➼➽
➺ ➸ ➾ ➻➸➽
➚➪ ➶ ➹
➹ ➪
❩➃❖s✵✐✵➃✵✐❈➄ ➅➆➇ ✐❈✵♦ ➅➈➇➉
➘ ➴
➷ ➬➷ ➬
➮ ➱ ➮ ✃
➱ ➱ ✃
➮ ➱ ✃
✃ ➱ ✃
❐ ❐ ❐
❐ ❐
❐ ❐
❐ ❐
❒ ❮ ❮ ❒ ❮ ❰
Ï ❒ Ð Ñ
Ï Ð Ð Ñ
Ð
ÏÒÓ Ð
Ô
Ô
❩➃❖s✵✐✵➃✵✐❈➄ ✐❈✵♦ ➅➆➇➉
Õ Ö Õ Ö×ØÙ
ÚÛÜÖ Ö×
ØÙÚÛÜÝ Õ
Õ Õ Þ Ö Þ Ý Õ
ß à
ß à
á
âã ä
á
âå
á
âä
äå
æ
áã ä á å á ä á
ç
ç
❩♦ ✵❤❡ s♦è➃✵✐♦❈s ✿✹❡ éêëì
íîï
ð
ñòóô
õ✿❈❞ ➅➆❬ ➆➇❑
ö ÷ ø
ø
ù ù ú ú
ú ù
û ü ý þ ÿ✭✮
ý ÿü✮
✷ ✷✤ � ✤ ✤ ✢
✢ ✤
❩➃❖s✵✐✵➃✵✐❈➄ ➅➈➇ ✐❈✵♦ ➅➆➇➉
✁ ✂ ✁ ✂✄ ☎ ✄ ✄ ✄ ✄ ✛
✄ ☎ ✛
✄ ☎ ✛
① ① ① ①
① ①
① ①
✻ ✆ ✝ ✆ ✆ ✽
✝ ✝✹ ✞✝ ✽
✶✝ ✸✻ ✽
✟ ✟
✟
✟
✿s ✹❡q➃✐✹❡❞❑
❜
✠ ✡
☛ ☞ ✌
☛ ✌
✌
✍ ✍
✍
✍
✎✏ ✑✒ ✵
✒ ✵
✒
✓
✓
Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information
www.cambridge.org© in this web service Cambridge University Press
✹ ❚♦�✁✂ ✄☎ ✆✝✁✞✟ ✠✡☛☞✌☛✍✁✂ ✎✡✞✂✍✁♦✞✝ ✍♦ ✝♦✏✑✒ �✌♦✓✏✒✔✝
✣❡r❡ ✕s ✖♥❧② ✖♥❡ ✗✖✕♥t ✖❢ ✕♥t❡rs❡❝t✕✖♥✘✇❤✕❝❤ ✙❡❛♥s t❤❛t t❤❡ ❧✕♥❡ ✕s t❛♥❣❡♥t t✖t❤❡ ❝✕r❝❧❡✳
✻ ✤
✤
✚ ✛①
✚ ① ①
✸ ✜✶✢
✸ ✥ ✜✭✢✷✦ ✧
✦ ★ ✧
❙✉❜st✕t✉t✕♥❣ ✩✪✫ ✕♥t✖ ✩✬✫✮
✯ ✰
✱ ✲ ✴ ✱
✴ ✴ ✱ ✲
✴ ✱ ✱ ✲
♠✵ ✵ ✵
✵ ✵ ♠✵
✵ ♠ ✵
✺ ✺ ✼
✺ ✽ ✾
✺ ✿ ✽ ✾
❀
❀
❀
❖♥❧② ✖♥❡ ✕♥t❡rs❡❝t✕✖♥ ✙❡❛♥s t❤❛t t❤✕sq✉❛❞r❛t✕❝ ❤❛s ❛ s✕♥❣❧❡ r✖✖t✘ s✖ ❁ ❂ ❃✮
❄ ❅
❆ ❇
❆ ❈ ❆ ❉ ❉ ❇
❈ ❇
❈ ❇ ❊
❇ ❆ ❊ ❇ ❆ ❊
❋ ●❍
■
■
■
■
❏ ❑
❬ ▲ ▼◆❪ ❏ P ◗ ❑
▼ ◗❏
▼ ◗❏
▼ ◗❏ ▼ ◗ ❘
❯
❯
❯
❱❲❳❨❩❭❫❳ ❴❵
✐ ❥❡t ✖♥❡ ♥✉✙❜❡r ❜❡ ❦ ❛♥❞ t❤❡ ✖t❤❡r ❜❡ ♣✳
❙✉✙ ✖❢ ❦ ❛♥❞ ♣ ✕s ✈✮ ③④ ⑤ ⑥ ⑦⑧⑨⑩ ❶
❷r✖❞✉❝t ✕s ❸✳❹❺✮ ❻❼❽ ❾❿➀➁ ➂➃➄➅
➆r✖✙ ✩✪✫✮ ➇➈ ➉➊ ➋➌➍➎ ➏
❙✉❜st✕t✉t✕♥❣ ✩➐✫ ✕♥t✖ ✩✬✫✮
➑ ➒
➑ ➒➑ ➒
➓ ➔
➓ → ➔
➓ → ➔
➓ ➓ ➔
➔ ➔
➣ ➣
➣ ➣
➣ ➣
➣ ➣
➣ ➣
↔ ↕➙➛➜
↔➝↕
➞➟
➞ ➝➠ ➝↕ ➟
➠ ➝ ➠ ➡➝ ➟
➝
➠➢➤
➡➝
➠
➥
➥
✣❡ t✇✖ ♥✉✙❜❡rs ❛r❡ ✪✳❺ ❛♥❞ ➦✳❺✳
➧➨➩➩➫➭➯
➲➳ ➵➸ ➺➻➳➼➽ ➾➵➸➼ ➳➺ ➚➺➽➪➼➶➳ ➹➼➚➵➘➴➷➸➬➸➮➚➱ ➴➸ ✃❐❒❮❰ ➵➽➳➺ ➻➶➴➚➳➵➺➽➸ ➳➺ ➘➴Ï➼➸➮Ð➸➼Ñ➮➼➽➳ ➘➴➽➵Ò➮➷➴➳➵➺➽ ➼➴➸➵➼➶❐ Ó➱➼Ñ➮➴➹➶➴➳➵➚ ➚➺➮➷➹ ➴➷➸➺ ➱➴➪➼ Ð➼➼➽ ➸➺➷➪➼➹➾➵➳➱ ➴ ÔÕÖ× ➺➻ ➚➺➮➶➸➼❐
Ø ✣❡ ❧❡♥❣t❤ ✕s ❦Ù ❧❡t t❤❡ ✇✕❞t❤ ❜❡ ♣✳❷❡r✕✙❡t❡r ✖❢ ✪✬✮
Ú ÛÜ Ý
Ü Ý
Ý Þ
ß à
ß à
à ß
á âá
ã
ã
ä å
æ
æ ç
æ ç
è éê
é é
é é
ëìíî
ï
ï ð
ñ✖✙✗❧❡t✕♥❣ t❤❡ sq✉❛r❡✮
ò ó
ô õ õ
ô õ õ ö
÷ ø ø
ø
ù ú û
ü ý
þ
þ
❙✖ t❤❡ ✙❛ÿ✕✙✉✙ ❛r❡❛ ✕s ❸ ❝✙✷ ✩❛♥❞ ✖❝❝✉rs✇❤❡♥ ❦ ❂ ♣ ❂ ➐✘ ✕✳❡✳ ✇❤❡♥ t❤❡ r❡❝t❛♥❣❧❡ ✕s ❛sq✉❛r❡ ✇✕t❤ s✕❞❡ ➐❝✙✫✳
➧➨➩➩➫➭➯
◆➺➳➼ ➳➱➴➳ ➳➱➼ ➽➼�➴➳➵➪➼ ➸➵�➽ ➘➴Ï➼➸ ➳➱➼Ñ➮➴➹➶➴➳➵➚ ➽➼�➴➳➵➪➼ ➸➱➴Ò➼➹× ➾➱➵➚➱ ➶➼➸➮➷➳➸➵➽ ➴ ➘➴✐➵➘➮➘ ➶➴➳➱➼➶ ➳➱➴➽ ➘➵➽➵➘➮➘➳➮➶➽➵➽� Ò➺➵➽➳❐
✸ ❛ ✁❡✇ ❢❡♥❝✕♥❣ r❡q✉✕r❡❞ ✕s ✬❃❃✙✘ s✖
✤ ✂ ✢
✜ ✢ ✤
① ✄
✄ ①
☎ ✆✵ ☎✵✵
☎✆✵ ☎
✝ ✞
✟
✟ ✠
✟ ✠
❆ ✡②
✡ ✡
✡ ✡
☛☞❡✌
✍✎✏ ✍
✍✎✏ ✍✑
Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information
www.cambridge.org© in this web service Cambridge University Press
✺✶ �✁✂✄☎✂✆✝✞ ✟✁✠✞✆✝✡✠☛
❜ ❈♦♠♣❧❡☞✐✌❣ ☞❤❡ ✍q✉❛r❡✎
✤ ✏ ✏✢✜ ✛✚
✤ ✏ ✏✙✘✗
✖✕✔
✏✙✘✗
✖✕✔
✢
✜✓
✛
✚✒
✤ ✏✙✘✗
✖✕✔
✏
❆ ✑ ✑
✑
✑
✷ ✣✥✦
✷✣✥✦
✷
✣✥✦
✷
✷✣✥✦
✷
✣✥✦
✷
✧
✧ ✧
✧ ✧
★♠❛✩✐♠✉♠ ❛r❡❛ ✪❤❡✌
✫ ✫①✬✭✮
✯✮✯✰✮✱✲ ✳♦r ✪❤✐❝❤
✴ ✵ ✸ ✴② ✹✻✼ ✹✻✼✽
✹✻✼✽✾
✿ ❀ ❇❛❧❧ ✐✍ ❛☞ ❣r♦✉✌❞ ❧❡✈❡❧ ✪❤❡✌ ❁ ❂ ❃❄
❅ ❉
❊ ❋
❊ ❋
❋ ❋ ❋
t t
t t
t t
● ❍■❏ ❑
● ❍■❏ ❑
❑ ▲▼●
❍■❏◆■❖P
◗
❘❙❚❯❱
❚♦ ☞❤❡ ❲❛❧❧ r❡☞✉r✌✍ ☞♦ ☞❤❡ ❣r♦✉✌❞
❛❳❡r ❨❄❩❙ ✍❄
❜ ❇❬ ✍❬♠♠❡☞r❬ ♦✳ ❛ q✉❛❞r❛☞✐❝✲ ♠❛✩✐♠✉♠
❤❡✐❣❤☞ ❘✈❡r☞❡✩❱ ✐✍ ❤❛❧✳✪❛❬ ❲❡☞✪❡❡✌ ☞❤❡
r♦♦☞✍✲ ❭ ❂ ❃ ❛✌❞ ❪❫❴
❵❢❥❄
❦♥
❦
s ❦✇③④
⑤⑥⑦⑧
✇③④
⑤⑥⑦
❦⑧
❦ ❦
⑨
⑩
❶❷
❸❹❺
❻
❸
❸❹❺
❷❸
❸❹❺❸❹❺
❸
❸❹❺
❼❻ ❽❾
❸❹❺
❽❾
❸❹❺❼❹❻❿➀
➁➂➃
➁➂➃
➄
❘❙❚❯❱
➅➆➇➇➈➉➊
➋➌➍➎ ➏➐➑➒➓ ➔➒➎➐ ➌➔→➣ ↔➣➣↕ ➎➐➒→➣➓ ➑➎➍↕➙ ➔➛➜➝ ➐➞ ↔➟ ➏➐➠➡➒➣➢➍↕➙ ➢➌➣ ➎➤➑➔➞➣➥
➦ ❀ ➧❡r✐♠❡☞❡r ♦✳ ❩❃✎
➨ ➩
➫ ➩ ➭
➫ ➩ ➭
➯ ➲
➯➲
➯➲
➳➵
➳➸ ➺➻
➳ ➺➻➸
➳
➼➻➸
➽
➾ ➚➪➶➹
➘➴➷
➾ ➬➪➶➹
➘➴➷
➚
➾ ➬ ➚
➾ ➬
➮ ➱✃✃
✃✃
✃
✃✃ ✃
✃ ✃
❐
❒❮
❒
❰Ï❮
Ð
❮
Ñ
❰Ï❮
Ð
❮
Ñ
❰Ï❐
Ñ❮
Ò
Ò
Ò Ò
Ò
❜ ❯✐✌❞✐✌❣ ☞❤❡ r♦♦☞✍ ♦✳ ☞❤❡ ❛r❡❛
❡✩♣r❡✍✍✐♦✌✎
ÓÔÕÖ
×ØÙÚ
ÓÔÕÖ
×ØÙÚ
Ú Ú
Û Û
Û Û
Û Û
ÜÝÞ
ßà Ý
ÜÝÞ
ßà Ý
Ý áâãäÝ
à
å
❇❬ ☞❤❡ ✍❬♠♠❡☞r❬ ♦✳ ❛ q✉❛❞r❛☞✐❝✲ ☞❤❡
♠❛✩✐♠✉♠ ❛r❡❛ ❘✈❡r☞❡✩❱ ✐✍ ❤❛❧✳✪❛❬
❲❡☞✪❡❡✌ ☞❤❡ r♦♦☞✍✎
æç
è æéê
ëìê
ë
íëê
î
ï❤❡✌ ðñòóô
õ✲
ö ÷
ö ÷øùú
ûüý
ö ÷
ö
þÿ
✤✵✣
✹
✤✵✣
✹
✶�✵
✣
✤✵ ✤✵
✵
Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information
www.cambridge.org© in this web service Cambridge University Press
✻ ▼�✁✂✄ ✂✁☎✆�✝☎✞�✟✝ ✠✡☎☛✞�☛✂ ☞
✌✍✎✎✏✑✒
❚✓✔✕ ✖✗✘✙✚ ✛✙✕✗ ✓✛✜✢ ✣✢✢✤ ✕✗✙✜✢✚ ✘✕✔✤✥ ✛●✦✧ ✗★ ✣✩ ✖✗✪✫✙✢✬✔✤✥ ✬✓✢ ✕✭✘✛★✢✮
❝ ■✯ ❆ ✰ ✱✲✲✳
✴ ✵
✴ ✶ ✵
② ②
②②
✸✷✹
✽✺ ✼✷✷
✺
✽✸✷ ✼✷✷ ✷
✾
✾
❯s✐✿❣ ❀❤❡ ❁✉❛❞❂❛❀✐❃ ✯♦❂♠✉❧❛ ❄✐❀❤
❅❇❈
❉✳ ❜ ✰ ❊❋✲ ❛✿❞ ❍ ✰ ✱✲✲❏
❑▲ ◆ ❖
P❖
P
❑
◗❘❙ ❘❙ ❱
❲❳❙❙
❱❨❩❘❲ ❬❭ ❪❫❩❙❴❘❵❢❥
❦
♥❤❡✿ ♣ ♣ qr
♣t ✈✇①③④⑤ ③⑥⑦ ✇①③④
⑧⑨⑧①⑨
♥❤❡✿ ⑩ ⑩ ❶❷
❸ ❹❺❻❼❽❾ ❿❽➀ ❺❻❼❽
➁➂ ❊✱➃➄✱
➅❀❤❡❂❡✯♦❂❡ ❂❡➆❡❃❀ ❛s ➇ ➈ ✲➉➊♦ ➇ ✰ ✱➃➄✱♠ ❛✿❞ ➋ ✰ ➌➄❋➍♠➄
➎ ➏♦❀❛❧ ➐❂♦➑❀ ✰ ➒ ➓ ➒ ➓➔ → ➔➣ ➣ ➣ ➣↔↕↕ ➙ ➙ ➛↕
➜✐✿❞✐✿❣ ❀❤❡ ❂♦♦❀s ♦✯ ❀❤❡ ❀♦❀❛❧ ➐❂♦➑❀✯✉✿❃❀✐♦✿❏
➝ ➞➟ ➠
➠ ➠
➡ ➡
➡ ➡
➢ ➤➥ ➥
➥ ➦➧ ➤➥
➨➩ ❀❤❡ s➩♠♠❡❀❂➩ ♦✯ ❛ ❁✉❛❞❂❛❀✐❃✳ ❀❤❡♠❛➫✐♠✉♠ ❧✐❡s ❤❛❧✯❄❛➩ ➭❡❀❄❡❡✿ ❀❤❡ ❂♦♦❀s✳✐➄❡➄ ❛❀ ➯ ✰ ✱➲➄
✌✍✎✎✏✑✒
❚✓✔✕ ✖✗✘✙✚ ✛✙✕✗ ✓✛✜✢ ✣✢✢✤ ✕✗✙✜✢✚ ✣✩✖✗✪✫✙✢✬✔✤✥ ✬✓✢ ✕✭✘✛★✢✮
➳➵➸➺➻ ➺➸➼➽➵➾➼➚➵➪➾ ➶➹➼➘➚➵➘➺ ➴
➷➬➮➱✃ ❐❒❮❰✃Ï➮Ð❰
Ñ Ò Ó Ô Õ Ó ÔÖ Ö Ö Ö× ØÙ Ú ÛÜÚ ÝÜÞ
ß
à áà á
â ã ä
â ã ä
ä ã ä
å å
å å
å å
æ çè é
ê ë é
ê ìí ë
î
ï Ò ð♦s✐❀✐ñ❡ ❁✉❛❞❂❛❀✐❃✳ s♦ ❀❤❡ ñ❡❂❀❡➫ ✐s ❛♠✐✿✐♠✉♠ ➐♦✐✿❀➄
ß ò✐✿✐♠✉♠ ❛❀ ➅❋✳ ➌➉ ó ô õö ÷ øù ú û üý
➊♦ þ ✰ ❋✳ ❜ ✰ ➌
ÿ ò❛➫✐♠✉♠ ➋✲ñ❛❧✉❡ ✐s ➃➍ó❍ ✰ ➃➍➄ð❛ss❡s ❀❤❂♦✉❣❤ ➅❊✱✳ ✲➉ ❛✿❞ ➅❞✳ ✲➉ ♠❡❛✿s❀❤❛❀ ✐❀s ❂♦♦❀s ❛❂❡ ➇ ✰ ❊✱ ❛✿❞ ➇ ✰ ❞➄✤❡ ❧✐✿❡♦✯ s➩♠♠❡❀❂➩ ✐s ♠✐❞❄❛➩ ➭❡❀❄❡❡✿ ❀❤❡ ❂♦♦❀s✳✐➄❡➄ ❛❀ ➇ ✰ ✱✳ s♦ ❜ ✰ ✱➄
➊✉➭s❀✐❀✉❀✐✿❣ ➇ ✰ ❊✱ ❛✿❞ ➋ ✰ ✲ ✐✿❀♦
� ✁✢ ✂ ✛② ✄ ① ✷ ☎✽✆
❏
✝ ✞✟ ✠ ✠ ✜
✟ ✜
✟ ✠
❛
❛
❛
✵ ✡ ✡ ☛☞
✵ ✌✻ ☛☞
✸
✍
➊♦ þ ✰ ❊❋✳ ❜ ✰ ✱ ❛✿❞ ❍ ✰ ➃➍➄
✹ ❘♦♦❀s ❛❀ ➇ ✰ ❦ ❛✿❞ ➇ ✰ ❦ ✎ ➃ ó❧✐✿❡ ♦✯s➩♠♠❡❀❂➩ ✐s ➇ ✰ ❦ ✎ ✱ ➅♠✐❞❄❛➩ ➭❡❀❄❡❡✿❀❤❡ ❂♦♦❀s➉➄➊♦ ❀❤❡ ➇✲❃♦♦❂❞✐✿❛❀❡ ♦✯ ❀❤❡ ❀✉❂✿✐✿❣ ➐♦✐✿❀✐s ❦ ✎ ✱➄
✺ Ò ❘♦♦❀s ❛❀ ✏✶
✑❛✿❞ ✱✳ s♦
✒ ✓ ✒ ✓✔ ✕✖✚✙
✘✗✣
✥❢ ✦ ✦ ✦✧
★★
✐➄❡➄ ✩ ✪ ✩♣ ✫✬
✭✱ ✭
Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information
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✼✶ �✁✂✄☎✂✆✝✞ ✟✁✠✞✆✝✡✠☛
❜ ▲✐☞❡ ✌❢ ✍②♠♠❡✎r② ✐✍ ♠✐❞✇✏② ✑❡✎✇❡❡☞
✎❤❡ r✌✌✎✍t ✤
✣ ✒✜✛✚
✙✘✗✤①
✷✓
✷
✷
✸
✹
✔ ✕✲✖✌✌r❞✐☞✏✎❡ ✌❢ ✢ ✐✍✥
✦
✻ ✧ ◆❡❣✏✎✐✈❡ ★✉✏❞r✏✎✐✖ ✩❛ ✐✍ ☞❡❣✏✎✐✈❡
✧ ◆❡❣✏✎✐✈❡ ✪✲✐☞✎❡r✖❡✫✎ ✩❝ ✐✍ ☞❡❣✏✎✐✈❡
✧ ❙✐☞❣❧❡ ✬r❡✫❡✏✎❡❞✭ r✌✌✎ ✩ ✮ ✯✰ ✱✳✴ ✵✺
✧ ▲✐☞❡ ✌❢ ✍②♠♠❡✎r② ✽ ✾✿❀
❁❂✐✍ ✫✌✍✐✎✐✈❡
✩❃ ✐✍ ✫✌✍✐✎✐✈❡ ✬✏✍ ❛ ✐✍ ☞❡❣✏✎✐✈❡✭
❄❅❆❇❈ ❉❊❋●❍
■❏❑▼❖PP◗❘❚ ❯❘P◗❱◗❲❖ ❳❖❨❩❱◗❲❖ ❬❖▼❘
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❜ ❹r✌♠ ✬✏✭❺ ✎❤❡ ♠✐☞✐♠✉♠ ✈✏❧✉❡ ✌❢
❻ ❼❽ ❽❾❿ ➀➁➂ ✐✍ ➃➄➅
➆❡☞✖❡ ✎❤❡ ♠✏➇✐♠✉♠ ✈✏❧✉❡ ✌❢
➈ ➉➊ ➊
➋
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↔ ↕★✉✏❧ r✌✌✎✍ ✩➙ ➛ ➄
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➞ ➟
➠ ➞ ➡ ➡ ➟
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❐❒ ❮☞❧② ✌☞❡ ❰❡r✌ ✩➙ ➛ ➄
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✷ ✝✺ ✟
✺ ✠ ✟
✺ ✡r ✠
☛ ☛
☛
☛
☛
Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information
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✽ ▼�✁✂✄ ✂✁☎✆�✝☎✞�✟✝ ✠✡☎☛✞�☛✂ ☞
▲✌✍✎ ✏✑✒✓✔✕✌✍✓
✶ ❛ ✖ ❙q✉✗r❡ ✘❡r✐✙❡✚❡r ✛ ✥①
✖✖ ❈✐r❝❧❡ ✘❡r✐✙❡✚❡r ✛ ✜✢②
❜ ✤ ✣ ✦ ✣ ✧★ ✩ ★ ✩✹ ✪✫ ✬ ✪✫
✪
✭
✮ ✯
✰ ✱
✰ ✱
✰ ✲✳✴✵
✷✸✺
✱
✰ ✲ ✱ ✱
✰ ✱ ✲ ✱
❆
✻ ✼
✼✼
✼✼
✼
✼ ✼
✾✿❀✾ ♦❁ s❂❃✾✿❀ ✾✿❀✾ ♦❁ ❄❅✿❄❇❀
❉
❊❉
❊❉
❋ ❊❉❉
❋❉
❉
❋❉ ❋ ❊❉ ❋
● ●
●●
● ●●
●
❞ ❈❍✙✘❧❡✚✐■❣ ✚❤❡ ❏q✉✗r❡❑
◆ ❖◆ ❖
◆ ❖◆ ❖
P ◗ ❘◗
◗◗
❚
❯❱
❲
❳❨
P ◗ ❘◗
❩❬❭
❪❫❴
❘◗
❩❬❭
❪❫❴
◗◗
❚
❯❱
❲
❳❨
❵ ❢ ❢
❢
❥
❦❥ ❦
♠
❥ ❦
♥♣
❥ ❥ ❦
❥
❦❥ ❦
❦
❥ ❦
❦
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♥♣
❥ ❥ ❦
t
t t
❙❍ ✚❤❡ ✙✐■✐✙✉✙ ✗r❡✗ ❍❝❝✉r❏ ✈❤❡■ ✇③
④⑤
⑥ ⑤
⑦ ⑧
⑦ ⑧
⑦⑨
⑩❶❷
❸❹❺⑧
⑦
❻
❼❽❾❿❽➀➁➂➃❽ ➄➅ ➆➇❾❽ ➇➀ ❿➇❾❿➈❽
➈❽➀➃➁➉ ➄➅ ➆➇❾❽ ➇➀ ❿➇❾❿➈❽
➁➄➁➂➈ ➈❽➀➃➁➉ ➄➅ ➆➇❾❽➊➋➋➌
➍➎
➏➊➋➋➌
➍➎➐
➎ ➐
➏➊➋➋➌
➐➐➑➋➌➒➓➔→➣
↔↕➙➙➛➜➝
➞➟➠➡ ➠➢➤➠ ➥➠ ➥➦➧➨➠ ➧➡➩➡➦➦➤➫➭ ➠➟ ➦➥➯➲➳➥➵➭ ➠➢➡ ➩➟➧➦➠➤➧➠ ➥➧ ➠➢➡ ➡➸➲➫➡➦➦➥➟➧ ➵➟➫ ➺➤➵➠➡➫ ➩➟➯➲➳➡➠➥➧➻ ➠➢➡ ➦➼➽➤➫➡➾ ➤➦ ➠➢➡ ➼➽➡➦➠➥➟➧ ➤➦➚➦ ➟➧➳➭ ➵➟➫ ➠➢➡ ➪➤➳➽➡ ➟➵ ➶➹➢➡➫➡ ➠➢➡ ➤➫➡➤ ➥➦ ➯➥➧➥➯➥➦➡➘ ➤➧➘ ➧➟➠ ➵➟➫ ➠➢➡ ➤➩➠➽➤➳ ➪➤➳➽➡ ➟➵ ➠➢➤➠ ➯➥➧➥➯➽➯➴
Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information
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✾✶ �✁✂✄☎✂✆✝✞ ✟✁✠✞✆✝✡✠☛
✷ ❛ ❈☞r ✌ ✍☞s ✎♦s✐t✐♦♥ ✏✑✒✓ ✔ ✤✒✕ ✒✖ ☞♥❞❈☞r ✗ ✍☞s ✎♦s✐t✐♦♥ ✏✒✕ ✘✤✓ ✔ ✙✒✖✚
✛ ✜ ✛ ✜
✢ ✣✥ ✦
✧ ★ ✧ ★
✧ ★ ✧ ★
✩ ✪ ✫ ✪
✩ ✪ ✪ ✫ ✪ ✪
✩ ✪ ✫ ✪
✩ ✪ ✫ ✫ ✪ ✫
✩ ✪ ✫
✬ ✭ ✭ ① ①
✮ ✮
✮ ✮
✮ ✮ ✮ ✮
✮ ✮
✵ ✯✵ ✰✵ ✱✰ ✺✵ ✵
✯✵ ✰✵ ✱✰ ✺✵
✹✵✵ ✯✵✵✵ ✯✰✵✵ ✯✯✰ ✲✵✵ ✲✵✵
✻✯✰ ✯✲✵✵ ✺✹✵✵
✳✳ ✴
✳✳ ✴
✳
✳ ✳
✳ ✳
✳ ✳
✳
❜ ❈♦♠✎❧❡t✐♥❣ t✍❡ sq✉☞r❡✸
✼ ✽✿❀❁
❂❃❄❅
✼ ✽❆❇❉
❊❋●
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✿
❀❁
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❅
❍ ■ ■
■
■
■
❏❑▲▼▼❏
❑▲◆❖PP
❏❑▲▲◗
❑▲
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❑▲◆❖PP
❏❑▲▲◗
❑▲▲◗ ◆❖PP
❏❑▲▲◗
❑▲◆❏
❘ ❘
❘ ❘
❘❘
❘
❙♦ ❚❯ ❱❲❳ ☞♥❞✕ s✐♥❝❡ ❨ ❩ ✒✕ ✐t ❬♦❧❧♦✇st✍☞t t✍❡ ♠✐♥✐♠✉♠ ❭☞❧✉❡ ♦❬ ❨ ✐s ❪❦♠✚
❫ ❛ ❴❡rt❡❵ ♦♥ t✍❡ ❢❤☞❵✐s❥✍☞s ♦♥❧② ♦♥❡ r♦♦t✕ s♦ ♣ ✈ ✒✚
③ ④
③ ④
④
⑤ ⑥⑦
⑧
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❶❷ ⑨ ⑩
❸
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❜ ❺q✉☞t✐♦♥ ♦❬ ❻rst ❣r☞✎✍ ✐s
❼ ❽❾ ❿ ➀ ❾ ❿➁ ➂ ➂ ➂➃ ➄ ➅➆ ➆
❙♦ ❭❡rt❡❵ ✐s ☞t ✏✙✕ ✒✖✚❙❡❝♦♥❞ ❣r☞✎✍ ✍☞s ❭❡rt❡❵ ☞t ✏✔✑✕ ✤✖✕ s♦
✐ts ❡q✉☞t✐♦♥ ✐s ➇ ➈➉ ➊ ➊➋ ➌ ➍ ➎ ➏➐
➑t ✎☞ss❡s t✍r♦✉❣✍ ✏✙✕ ✒✖➒ s✉➓st✐t✉t✐♥❣✐♥t♦ t✍❡ ❡q✉☞t✐♦♥ ❣✐❭❡s
➔ →➣ ↔ ↔
➣ ↕
➣ ↕
➙
➙
➙
➛ ➜ ➝ ➞
➝➞ ➞
➟
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➠
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➤ ➥➦ ➧ ➨ ➩ ➩
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➫ ➭
➭ ➭
➭ ➭
➯
➲➳ ➲
➯
➲➵ ➵ ➲
➯
➲
➵
➲
➳➯
➲
➸
➸
➸
➺ ➻♦r ✐♥t❡rs❡❝t✐♦♥ ♦❬ ➼ ➽ ➾➚ ➪ ➪➶ ➹➘ ☞♥❞
➴ ➷ ➷ ➬➮ ➱ ➱✃
❐
❒
❐
❮✃
❐❰ ✸
Ï ÐÏ Ð
Ñ Ò Ó Ñ Ñ Ò
Ñ Ò Ó Ñ Ñ Ò
Ñ Ò Ó
Ñ Ò Ó
Ñ Ñ Ó
Ó Ó
Ô Ô Ô Ô
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Ø
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Û ×Û ×Ú Ü
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ß
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❢ ✈ ✙ ✐s t✍❡ ✎♦✐♥t ♦❬ ✐♥t❡rs❡❝t✐♦♥ ☞t t✍❡❭❡rt❡❵ ✏✙✕ ✒✖ ♦❬ t✍❡ ❻rst ❣r☞✎✍✚
à♦ ❻♥❞ t✍❡ á❤❝♦♦r❞✐♥☞t❡ ♦❬ t✍❡ ♦t✍❡r
✎♦✐♥t✕ s✉➓st✐t✉t❡ âãä
å✐♥t♦ æ çè éê ë ì í✸
î ïðñò
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