View topic - مرحله دوم ریاضی • Art of Problem Solving

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Author	Message
Omid Hatami Posts: 1272 Location: Tehran, Iran Blog: View Blog	Posted: Apr 22, 2009, 7:50 am • # 1 امتحان مرحله دوم فردا برگزار خواهد شد. در این قسمت می‌توانید بحث‌های خود در مورد سوالات و راه‌حل‌ها مطرح کنید _________________ No pain, no gain Last edited by Omid Hatami on Jul 11, 2009, 1:26 am, edited 1 time in total.

Kamyar1991 Posts: 99 Location: I R A N	Posted: Apr 23, 2009, 3:22 am • # 2 bashgah MASKHarsho daravorde 3 ta soal dadan 2 tash tekrari!!! farda chi mikhad beshe !!!!!!!!!! yedoonasham badihi bud biain begin chi kar kardin??????

John-Nash Posts: 11	Posted: Apr 23, 2009, 5:36 am • # 3 yeki soal ha ro bezare ma ham bebinim.

khashi70

Posts: 237
Location: Iran , Tehran
Iran, Islamic Republic of

Posted: Apr 23, 2009, 7:34 am • # 4

Soalhaye Marhale Dovvome Riazi Rooze Avval :
1- $p$ yek chandjomleyie darajeye do ast ke be ezaye $0$ , $1$ va $- 1$ ghadre motlaghe an az $1$ bishtar nist . neshan dahid baraye har $- 1\leq x \leq 1$ ghadre motlaghe $p$ az $\frac {5}{4}$ bishtar nist .
2-yek baghe morabayi shekl ra be yek shabakeye $50$ dar $50$ az ghata'ate $1$ metr dar $1$ metr taghsim kardeyim va dar bazi az ghet'e ha yek derakhte sib , anar ya holoo kashteyim . midanim mojavere har derakhte anar , daste kam yek derakhte sib va mojavere har derakhte holoo dastekam yek derakhte anar va yek derakhte sib voojood darad . be alave mojavere har gheteyi ke dar an derakhti nist , az har se no derakht voojood darad (do ghete ra mojaver migooyim agar yek zel'e moshtarak dashte bashand) .
neshan dahid tedade ghata'ate khali az $1000$ bishtar nist .
3-farz konid nimsaze dakheylie zavieye $A$ az mosalase $ABC$ zel'e $BC$ ra dar $D$ va dayereye mohitie mosalas ra dar $M$ ghat konad . az $D$ khati rasm mikonim ke do nimkhate $MB$ va $MC$ (ba shooroo az $M$ ) ra dar noghate $P$ va $Q$ ghat konad . sabet konid $\angle PAQ \geq \angle A$

navidj Posts: 57 Location: Tehran	Posted: Apr 23, 2009, 8:34 am • # 5 Yeki mishe hal soal 3 ro bezare ?

Omid Hatami

Posts: 1272
Location: Tehran, Iran
Iran, Islamic Republic of

Blog: View Blog

Posted: Apr 24, 2009, 12:16 am • # 6

‌Bebinid be rahati mitunid sabet konid ke dayere mohiti $ABD$ bar khat $MD$ momase. Pas mishe did ke:
$\angle APD\leq \angle ABD$
Be tarighe moshabeh:
$\angle AQD\leq\angle ACD$

Va khob dar akhar ham natije mishe ke:

$\angle PAQ\geq \angle A$

_________________
No pain, no gain

Last edited by Omid Hatami on Apr 24, 2009, 1:51 am, edited 1 time in total.

Amir.S

Posts: 777
Location: Islamic Republic of Iran
Iran, Islamic Republic of

Posted: Apr 24, 2009, 1:30 am • # 7

Omid Hatami wrote:

‌Bebinid be rahati mitunid sabet konid ke dayere mohiti $ABD$ bar khat $MD$ momase. Pas mishe did ke:
$\angle APD\geq \angle ABD$
Be tarighe moshabeh:
$\angle AQD\geq\angle ACD$

Va khob dar akhar ham natije mishe ke:

$\angle PAQ\leq \angle A$

albate jaye

Code:

\geq

bayad

Code:

\leq

mizashtid too hame namosavi ha.

_________________
Say: Tell me if it is from Allah; then you disbelieve in it, who is in greater error than he who is in a prolonged opposition?

Omid Hatami Posts: 1272 Location: Tehran, Iran Blog: View Blog	Posted: Apr 24, 2009, 1:51 am • # 8 Dorost migi, eshtebah kardam. _________________ No pain, no gain

Zagros Posts: 8 Location: Iran	Posted: Apr 24, 2009, 2:34 am • # 9 Emsal sakhtar bood ya parsal?

Kamyar1991 Posts: 99 Location: I R A N	Posted: Apr 24, 2009, 4:29 am • # 10 emsal be marateb sakht tar bud. akhe azmooni tasavor konin bedune HENDE3!!!!!!!!!!! vali kaf ham beyne 23-28 !!

sepehr ahmadzadeh Posts: 173 Location: tehran	Posted: Apr 24, 2009, 8:27 am • # 11 yani vaghan nazARet ine ke az parsal sakhttar bode???? marhale 2 az emsal asoontar faghat sale 86 bood ke dg hame midoonan bashgah che gandi zade bud..!! khashi???? khabari niss azataaa dg yadet raft maro??? TST keye??? beterekooniaa ! darzEmn be Ramtin BEGOO age nare IOI ........ ...... .......!!!!!!(khodet befahm dg))

khashi70

Posts: 237
Location: Iran , Tehran
Iran, Islamic Republic of

Posted: Apr 24, 2009, 8:36 am • # 12

Rooze Dovvom :
4- $n(n+2)$ sarbaze taze kar dar $n$ sootoone barabar kenare ham va be faseleye yek ghadam istade and . ba farmane farmande , har sarbaz ya sare jayash mi istad ya be yeki az chahar jahat yek ghadam bar midarad . pas az jabejayi sarbazha dar $n+2$ sootoone barabar , be shekle monazzam gharar gerefte and , be nahvi ke do satre avvalo akhar hazf va do sootoon be chap va rast ezafe shode ast . neshan dahid $n$ zoj ast .
5-adade tabiyie $a_{1}<a_{2}<\cdots<a_{n}$ daraye in khassiat hastand ke baraye har $i$ va $j$ motemayez :
$a_{i}-a_{j}|a_{i}$ . neshand dahid baraye har $i<j$ :
$ia_{j}\leq ja_{i}$
6- $11$ nafar dore yek mize dayereyi shekl be shekle monazzam (!) nesheste and va $11$ kart ba shomarehaye $1$ ta $11$ beyne anha pakhsh shode ast , momken ast barkhi karti nadashte bashand va barkhi bish az yek kart dashte bashand . dar har marhale yek nafar mitavanad yeki az karthaye khod ra be farde mojaverash bedahad dar soorati ke agar shomareye an kart $i$ bashad , ghabl va bad az in amal , makane se karte $i-1$ , $i$ va $i+1$ tashkile yek mosalase hade nadahand ( manzoor az karte shomareye $0$ karte shomareye $11$ va manzoor az karte shomareye $12$ karte shomareye $1$ ast )
Farz konid dar ebteda karthaye $1$ ta $11$ be tartib dar jahate aghrabe haye saat , be afrad dade shode bashad . sabet konid hichgah kartha dar daste yek nafar jam nakhahad shod .

khashi70

Posts: 237
Location: Iran , Tehran
Iran, Islamic Republic of

Posted: Apr 24, 2009, 8:57 am • # 13

Be nazare man vaghean emtehane badi bood . vaghean comite che fekri karde $3$ ta tarkibiat gozashte too emtehan mage computere ?
Har kasi ke soalaye IMO e chand sale akhiro dide bashe mifahme ke IMO dare mire be samte inke tarkibiat bi tasir she va jabr tasiresh ziad she . tooye $7$ , $8$ sale gozashte too IMO faghat ye sal tarkibiat $2$ ta boode . hala ma nemigim comite kheyli az khodesh ebtekar bezane o az in harfa , $2$ ta tarkibiat moshkeli nadare vali vaghean $3$ ta tarkibiat fajeast !

Toxic_Frog Posts: 64	Posted: Apr 24, 2009, 10:02 am • # 14 kaf beine 4,5 va 5e oonayi ke migan kaf payintare fekre ghabulie khodeshunan vagarna gheire soale 6 baghie soala sakht nabud vaghean baraye comtie (az bala ta paeen) moteassefam , manam ke bayad gajamo bekharam . _________________ $6 \times 7 = 42$

sepehr ahmadzadeh Posts: 173 Location: tehran	Posted: Apr 26, 2009, 7:08 am • # 15 na sakht bood..!! alaki nagoo 4 5 ghabulie bishtar az 24 nemire emkan nadare soale 6 kheli sakht bood .. bashgaham ke ozash kheli kharabe mese inkkee

goodgirl_2278 Posts: 52 Location: iran	Posted: Apr 27, 2009, 1:55 am • # 16 vaghan bashgah gand zad ba in emtehanesh....rasman olamp comp gereft dg....hala age soalash tekrari nabood baz ye chizi!! har sal haghe ye edde zaye mishod,emsal sigmaye hameye salaye ghabl haghe mellat zaye shod!!! aghaye hatami nazare shoma raje be kaf chie?

Omid Hatami Posts: 1272 Location: Tehran, Iran Blog: View Blog	Posted: Apr 28, 2009, 9:35 am • # 17 نمی‌دونم، بستگی داره ولی حدس می‌زنم بین ۲۱ تا ۲۵ باشه _________________ No pain, no gain

vandermond

Posts: 26
Location: I.R.IRAN (IRI) is the excellent country
Iran, Islamic Republic of

Posted: May 02, 2009, 10:17 am • # 18

Hi............

رياضي رو بايد براي خودش خوند نه براي المپياد و هرچي ديگه. البته درسته اينا هم در كنار اون هدف ممكنه بدست بيان ديگه.
من با اين كه خيلي اميد داشتم و فقط براي المپياد(استعاره از رياضي) وقت گذاشته بودم و خيلي كار كرده بودم و براي مرحله هاي بالاتر مي خوندم ، اين آزمون (مرحله $2$ ) رو خيلي بد دادم و حالا ديگه مطمئن هستم كه قبول نميشم. الان هم دارم براي كنكور شروع ميكنم. ولي رياضي رو هيچ وقت ول نميكنم.
شايد اين يكي از بزرگترين و مهمترين شكست هاي زندگيم بوده باشه ولي مطمئن هستم كه ميتونم با تلاش و پشتكار اين رو بزرگترين تجربه زندگيم كنم
اين نظر منه كه طي اين 10 روز خيلي فكرا (حتي ...) به سرم زده بود
موفق باشيد

Bye.......

_________________
Vandermonde's identity : $\displaystyle \sum_{i=0}^{k}\dbinom{m}{i} \dbinom{n}{k-i}}$ $= \dbinom{m+n}{k}$ :wow:

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مرحله دوم ریاضی

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