ÐÏࡱá>þÿ (*þÿÿÿ'wÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿì¥Á€ø¿î/bjbjöàöà.<”Š”Š÷ ÿÿÿÿÿÿ·––ëëëëëÿÿÿÿÿÿÿÿ<;,ÿ¦øgØ????ž¢@ 8Eë���ëë??Û`¹¹¹�"ë?ë?¹�¹¹¹?ÿÿÿÿ`@Hm�Îÿ±~¹v0¦¹x /Hx ¹x ë¹LLf6¹œ,ÈÇwB¦����ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿx – ±:Kombinatorika, pravdpodobnost, statistika  TEST 1) Jestli~e aritmetický promr dvanácti rozných pYirozených ísel je 12, potom nejvtaí z tchto ísel mo~e být nejvýae rovno íslu: A  42 B  54 C  66 D  78 E  90 2) Test psalo 25 ~áko. 5 nejlepaích získalo ze 100 mo~ných bodo promrn 76,4 bodu, 5 nejhoraích ~áko získalo promrn 22,8 bodu. Jaký byl promrný bodový zisk zbývajících 15 ~áko, jestli~e vaech 25 ~áko získalo promrn 47,8 bodu? A  42,8 B  46,6 C  50,8 D  52,8 E - 54,8 3) Deset kamarádo dosáhne v roce 2013 vku 18 let: Karel a Petr v lednu, Jan a Zdenk v únoru, Michal v dubnu, Jaroslav v kvtnu, Milan v  ervenci, OndYej a Lukáa v záYí a Pavel v Yíjnu. Po ítejme jejich stáYí na celé msíce. Ve kterém msíci bude promrný vk chlapco pYesn 18 let? A - v bYeznu B  v dubnu C - v kvtnu D - v ervnu E - v ervenci 4) Z pti úse ek délek 2 cm, 3 cm, 5 cm, 7 cm a 11 cm náhodn vybereme tYi. Pravdpodobnost, ~e z vybraných úse ek lze sestrojit trojúhelník je A -  EMBED Equation.3  B -  EMBED Equation.3  C -  EMBED Equation.3  D -  EMBED Equation.3  E -  EMBED Equation.3  5) Xeaením rovnice  EMBED Equation.3  je íslo z intervalu: A -  EMBED Equation.3  B -  EMBED Equation.3  C -  EMBED Equation.3  D -  EMBED Equation.3  E -  EMBED Equation.3  6) V pizzerii pYidávají na základní pizzu podle pYání zákazníka ~ampiony, nivu, olivy, sardelky, cibuli, klobásu, aunku, papri ky nebo ananas. Po et rozných zposobo ochucení pizzy alespoH jednou pYísadou je: A  506 B  511 C  518 D  523 E - 530 VXbdfr t € † ˆ Œ   ª ¼ Æ Ö â Ê Ì Þ ä è ì þ   ( > H \ ^ ` Ú œž ¼ÂÎÐÚÜàâ(024~€ˆŠ°²´¶ÂÒÔúüöïöïèäàäàäàäàäàäàäàÜàÜàÜàÜàÜàÜäàäÜäàÜàÜàÜàÜàÜàÜàÜàÜàÜÔÜŸÔàÜÔÜ©j˜©tU hÞîCJUVaJjhÞîhÞîEHèÿUjn©tU hÞîCJUVaJjhÞîUhÞîh˜kÒh<Ÿ h˜kÒ5�>* h<Ÿ5�>*h<Ÿh<Ÿ5�>*?dfr t ò ô ö Ê Ì ^ ` b ž RTV~€æèêrt¼¾b÷÷òòòòòòòòòòòòíòòòòíííííííígdÞîgd<Ÿ$a$gd<ŸüþDFHJN\fhŽ�’”–¦²´ÚÜÞà>@BDrt~€¦òêæâæêæÓÆêæâæêæ·ªêæâæê曎êæêærêæâæjfhHuÅjhHuÅUjd hÞîhHuÅEHâÿUjªtU hHuÅCJUVaJjOhÞîhÞîEHèÿUj©tU hÞîCJUVaJj:hÞîhÞîEHèÿUj±©tU hÞîCJUVaJj'hÞîhÞîEHèÿUj¡©tU hÞîCJUVaJh˜kÒhÞîjhÞîUjhÞîhÞîEHèÿU%¦¨ª¬ºÂÄêìîðòø,.024<HJprtvz‚ŒŽ´¶¸ºðãÛ×ÓÛÏÀ³ÛÓ×ÓÛϤ—ÛÓ×ÓÛψ{ÛÓ×Ós×dWsj<h˜kÒh˜kÒEHòÿUjR«tU h˜kÒCJUVaJjh˜kÒUjhHuÅhHuÅEHòÿUj «tU hHuÅCJUVaJjÖhHuÅhHuÅEHòÿUjöªtU hHuÅCJUVaJj£hHuÅhHuÅEHòÿUjܪtU hHuÅCJUVaJhHuÅhÞîh˜kÒjhHuÅUjq hHuÅhHuÅEHòÿUjÁªtU hHuÅCJUVaJ"ºz|~€šž¾Àâä"”#˜#š#ª#¬#®#°#$V$X$f$j$n$r$t$š$œ$ž$ $¢$¤$¨$ð$ò$%%%%"%&%t%üõüñüñüñüñüñüïüëçÝÖÝÖçÒçÝÖÊçÂ糦Â碚¢’¢ƒv’¢š¢jlhx:Uhx:UEHöÿUjY'uU hx:UCJUVaJjhx:UUhÎ*hx:U5�hx:Uj›hsc„hx:UEHèÿUj¦&uU hx:UCJUVaJjhsc„UhÎ*hsc„5�hÎ* hsc„5�>*hsc„hsc„5�>*hsc„hÞîUhw¨ h˜kÒh˜kÒh˜kÒ-bdüþþ"#”#–#˜#š#°#¼#¾#Ê#Ì#Ø#Ú#æ#è#ô#ö#$$$$$$úúúúúúúúõõíèèèèèèèèèèèèèèèègdsc„$a$gdsc„gd<ŸgdÞî7) Klí ivost semen nového druhu okurek je 94%. Pravdpodobnost, ~e z 30 zasazených semen jich vyklí í práv 28 je pYibli~n: A - 11% B  18% C - 25% D - 28% E - 32% VÝSLEDKY: 1) D 2) B 3) C 4) B 5) B 6) B 7) D XE`ENÍ: 1)  EMBED Equation.3  2) x& . promrný bodový zisk 15 ~áko  EMBED Equation.3  3) Kladný msíc je x-tým msícem roku 2013. Proto~e sou et odchylek od promru je roven nule, musí platit: 2(x -1) + 2(x-2) + (x-4) + (x-5) + (x-7) + 2(x-9) + (x-10) = 0 x = 5 4) Z daných úse ek mo~eme vybrat 10 trojic s tmito hodnotami délek: (2,3,5), (2,3,7), (2,3,11), (2,5,7), (2,5,11),  EMBED Equation.3 (2,7,11), (3,5,7), (3,5,11), (3,7,11), (5,7,11) Trojúhelníkovou nerovnost splHují pouze dv z tchto trojic: (3,5,7), (5,7,11) Pravdpodobnost je tedy  EMBED Equation.3 , tj.  EMBED Equation.3  5)  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 & . Podmínkám vyhovuje pouze n2 = 5 6) Je mo~né pYidat bu jednu, nebo dv,& nebo vaech devt z devíti pYísad. Celkový po et mo~ností je tedy:  EMBED Equation.3  = 9 + 36 + 84 + 126 + 126 + 84 + 36 + 9 + 1 = 511 7) Pravdpodobnost vyklí ení semena je 0,94, pravdpodobnost, ~e toto semeno nevyklí í je 0,06. Ze 30 semen má vyklí it práv 28. Takových skupin je  EMBED Equation.3 . Hledaná pravdpodobnost je:  EMBED Equation.3  ZDROJE: - ZHOUF, Jaroslav a kol. Sbírka testových úloh k maturit z matematiky. Praha: Prometheus, 2002, ISBN 80-7196-249-X. $$$$$ $"$$$&$($*$,$.$0$2$4$6$8$:$<$>$@$B$D$F$H$J$L$N$P$úúúúúúúúúúúúúúúúúúúúúúúúúúúúúgdsc„P$R$T$V$X$h$j$¢$¤$î$ð$ %"%ú%x&6'8'Ä'2(Ð(Ò(v)x)**P*R*úúúúòòúúúúúúúúúúúííííííííå$a$gdx:Ugdx:U$a$gdsc„gdsc„t%²%8'<'2(4(Z(\(^(`(H)t)v)ª)¬)Ò)Ô)Ö)Ø)æ)è)****** *"*H*J*L*N*P*R*T*z*üøðøèäÕÈèøäøäè乬èäèä��èäˆäèäylèeøèä hsc„h{bjr$h{bh{bEHúÿUj®*uU h{bCJUVaJhÎ*h{b5�j_"h{bh{bEHèÿUjÍ)uU h{bCJUVaJjJ h{bh{bEHèÿUj¸)uU h{bCJUVaJj#h{bh{bEHúÿUj�*uU h{bCJUVaJh{bjh{bUhÎ*hx:U5�hx:UhªA=$z*|*~*€*‚*„*ª*¬*®*°*²*´*Ú*Ü*Þ*à*â*ä* + +++++:+<+>+@+B+D+j+l+ðãÛ×ÛÓÄ·ÛÓÛÓ¨›ÛÓÛÓŒÛÓÛÓpcÛÓÛÓTj!,uU h2PCJUVaJjÇ2h{bh{bEHúÿUjû+uU h{bCJUVaJjA0h{bh{bEHöÿUjÚ+uU h{bCJUVaJj?-h{bh{bEHèÿUj”+uU h{bCJUVaJj¥)h{bh{bEHäÿUj×*uU h{bCJUVaJh{bhx:Ujh{bUj˜&hÞîh{bEHâÿUjªtU h{bCJUVaJR*‚*²*â*+B+¶+¸+N,Ž,À,$-&-„.î.ð.//ì/î/ýýýýýýýýýýýýýýýýýøýgd˜N1l+n+p+r+ª+¬+´+¶+¸+¼+L,N,Ž,�,¶,¸,º,¼,&-*-R.T.z.|.~.€.¾.À.æ.è.ê.ì./4/Ž/î/òêæâÝâæâÕÑâÑÉѺ­ÉÑÕÑÉÑž‘ÉÑÉÑ‚uÉÑqjq h˜N16�]�h˜N1j¼=hÎ*hÎ*EHâÿUj21uU hÎ*CJUVaJjo;hÎ*hÎ*EHâÿUj 1uU 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