O‘zbekistоn respublikаsi хаlq

10-BILET
1. Ifodani soddalashtiring: (2 +3b)² –(2a-3b)²
2. Ushbu tengsizliklar sistemasining eng kichik butun yechimini toping.

3. 
   Agar tg =1/2 bo‘lsa, tg2 ni toping.
   
4. 
   Trapetsiya o‘rta chizig‘ining ta’rifini keltiring. Trapetsiya o‘rta chizig‘i haqidagi teoremani isbotlang.
   
5. 
   Tomoni 6 sm bo‘lgan kvadratga ichki va tashqi chizilgan aylana radiusini toping.
   

11-BILET 1.Soddalashtiring: Tenglamani yeching: │ │= 5x-x^2 Agar tgα=-1,2 va bo‘lsa, ctg2α ni toping. To‘g‘ri to‘rtburchak ta’rifini va uning xossalarini keltiring. To‘g‘ri to‘rtburchak xossalaridan birini isbotlang. Uchburchakning tomonlari mos ravishda 2 sm, 3 sm va 4 sm. Bu uchburchakning burchaklarini kosinusini toping.

12-BILET Ifodani soddalashtiring: . y=│3-x│ funksiya grafigini yasang. cosα=-0,8, bo‘lsa, tangensi va kotangensini aniqlang. Qavariq ko‘pburchak ta’rifini va uning xossalarini keltiring. Qavariq ko‘pburchak diagonallari soni haqidagi teoremani isbotlang. Teng yonli uchburchakning uchidagi burchagi 120^oga, yon tomoni 3 ga teng. Shu uchburchakka tashqi chizilgan aylana radiusini toping.

13-BILET 1. ^320011997 19982000 9 ni hisoblang {an} arifmetik progressiyada a2+a9=20 bo‘lsa, S10 ni hisoblang. Agar ctg( ^+)=2 bo‘lsa, ctgα ni toping. 4 Uchburchak o‘rta chizig‘ining ta’rifini keltiring. Uchburchak o‘rta chizig‘i haqidagi teoremani isbotlang. Rombning katta diagonali 18 sm va bir burchagi 120^0bo‘lsa, uning yuzini toping.