Iii-kurslarga matematikadan olimpiada testlari
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III-kurs olimpiada test
III-kurslarga matematikadan olimpiada testlari. 1) x3+(m-1)x2+x-m+3=0 tenglamaning ildizlari arifmetik hamda geometrik progressiya hosil qilishiga ko`ra m ning qabul qilishi mumkin bo`lgan qiymati topilsin. A) -3 B) -2 C) 0 D) 2 E) 3 2) a ning qanday qiymatlarida tenglamalar sistemasining yechimi tengsizlikni qanoatlantiradi? A) B) C) D) E) TJY 3) ABCD kvadratning AD va DC tomonlarida olingan E va F nuqtalar uchun BEF muntazam uchburchak bo`lsa ni toping. A) B) C) D) E) 4) Hisoblang: arcsin(sin10) A) B) C) D) E) 10 5) a2+b2+c2=1 bo`lsa (ab+bc+ac)min ni toping. A) -1 B) C) D) E) 0 6) ABCD to`rtburchakda A) 10 B) 15 C) 20 D) 30 E) 40 7) ifodaning (max) qiymatini toping. A) B) C) D) 2 E) 3 8) ABCD qavarriq to`rtburchakda AB=10, CD= , A) 20 B) 18 C) 16 D) 14 E) 12 9) ifodaning eng kichik qiymati nechaga teng? A) B) B) D) E) TJY 10) bosh koeffitsiyenti 1 ga teng bo’lgan to’rtinchi darajali ko’phad bo’lsin. Aytaylik hamda bo’lsin. U holda nechaga teng bo’ladi? A) 122 B) 98 C) 104 D) 90 E) TJY 11) Musbat hadli geometrik progressiya uchun quyidagini soddalashtiring. A) B) C) D) 2011 E) 2012 12) parallelogrammning va DC tomonlarining o’rtalari mos ravishda nuqtalar bo’lsin. va kesmalar nuqtada kesishadi. U holda A) B) C) D) E) TJY 13) Ushbu y=log5(x2-26x+69) funksiya grafigining ikkala koordinatasi ham butun sonlardan iborat bo`lgan koordinatalari yig`indisini toping. A) 30 B) 28 C) 29 D) 31 E) TJY 14) Tub sonlar uchun x1+x2+x3=68 va x1x2+x2x3+x3x1=1121 tengliklar o`rinli bo`lsa x2 ni toping. A) 7 B) 23 C) 13 D) 19 E) 29 15) ABCD kvadratning tomoni 4 ga teng bo`lib uning ichida olingan E nuqta uchun AE=ED va AB=BE bo`lsa SBEDC -ni toping. A) B) C) D) E) 16) P(x)=x2+ax+b funksiya uchun P(-1)>0 va P( )<0 bo`lsa P(2) quydagilardan qaysi birini qabul qila olmaydi? A) B) C) D) -2 E) hech qaysisini 17) a,b,c,d,e-lar bir-biridan farqli butun sonlar (6-a)(6-b)(6-c)(6-d)(6-e)=45 bo’lsa a+b+c+d+e ? A) 5 B) 17 C) 25 D) 27 E)30 18) -Eyler funksiyasi bo`lsa ni toping. 19) Hisoblang: 20) bo’lsa x2 ni toping. 21) ABC uchburchakda AB=65,BC=33,AC=56 uchun G aylana AC,BC va ABC uchburchakka tashqi chizilgan aylanaga urinadi.G aylananing radiusini toping. 22) 2sin3x+(2sinx-1)2-2=0 tenglamani yeching 23) Hisoblang: bo`lsa a ni toping. 24) Qirrasi 8 bo`lgan kubga ichki chizilgan eng katta hajmli konusning hajmini toping. 25) Soddalashtiring: cos550cos650cos1750 Download 368 Kb. Do'stlaringiz bilan baham: |
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