Iii-kurslarga matematikadan olimpiada testlari


Download 368 Kb.
Sana18.12.2022
Hajmi368 Kb.
#1027372
Bog'liq
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 0 va E nuqta AC kesmaning o`rtasi uchun AE=DE va 0 bo`lsa necha gradusni tashkil qiladi?
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= , 0 , 0 , BD=13+3 bo`lsa AC ni toping.
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:




Ma'lumotlar bazasi mualliflik huquqi bilan himoyalangan ©fayllar.org 2024
ma'muriyatiga murojaat qiling