I. Burchaklar

XIV. Takrorlash

1. Uchburchak o`tkir burchakli bo`lishi uchun uning α, β va γ burchaklari orasida qanday munosabatlar o`rinli bo`lishi kerak? (00–5–52)
A) γ≥α+β B) γ≤α+β C) β<α+γ D) γ<α+β E) α<β+γ, β<α+γ, γ<α+β
2. a ning qanday qiymatida istalgan ABC uchburchak uchun cosA+cosB+cosC≤a tengsizlik hamisha o`rinli bo`ladi? (00–5–67)
A) 1 B) 2 C) D) E) 3
3. Agar A, B va C lar uchburchakning burchaklari bo`lsa, nimaga teng? (00–8–62)

4. Uchburchakning ikkita burchagi yig`indisining kosinusi ga teng. Uchinchi burchagining kosinusini toping. (96–12–35)

5. sinα – ? (96–3–95)


6. tgα – ? (96–12–95)


7. Aylananing O markazi to`g`ri burchakli ABC uchburchakning AC gipotenuzasida yotadi. Uchburchakning katetlari aylanaga urinadi. Agar OC kesmaning uzunligi 4 ga, C nuqtadan CB katetning aylana bilan urinish nuqtasigacha bo`lgan masofa 3 ga teng bo`lsa, CB nin toping.
(99–1–32)
A) B) 7 C) 8 D) 6 E)
8. ABC uchburchakning AB, BC va AC tomonlari mos ravishda 4; 5 va 6 ga teng. AB va BC tomonlarga urinadigan aylananing markazi AC tomonda yotadi. Aylananing markazi AC tomondan ajratgan kesmalarning uzunliklari ko`paytmasini toping.
(00–9–54)

9. Rasmda tasvirlangan shaklning shtrixlangan qismini p perimetri va S yuzasini aniqlang. Bunda ABCD kvadratning tomoni 4 sm ga teng (π=3 ga teng deb olinsin). (96–3–11)

A) P=10 sm, S=18 sm² B) P=10 sm, S=10 sm²
C) P=22 sm, S=22 sm² D) P=18 sm, S=10 sm²
E) P=16 sm, S=10 sm²
10. Rasmda tasvirlangan shaklning shtrixlangan qismini p perimetri va S yuzasini aniqlang. Bunda ABCD kvadratning tomoni 6 sm ga teng (π=3 ga teng deb olinsin). (96–11–12)

A)P=33 sm, S=22,5 sm² B)P=27 sm, S=22,5 sm²
C)P=27 sm, S=27 sm² D)P=22,5 sm, S=12,5 sm²
E) P=22,5 sm, S=33 sm²
11. Muntazam uchburchakli piramidaning balandligi 4 ga, asosining balandligi esa 4,5 ga teng. Piramidaning yon qirrasini toping. (97–12–61)
A) 6 B) 6,5 C) 5 D) 5,5 E) 5,3
12. Muntazam piramidaning asosi ichki burchaklarining yig`indisi 720<sup>0</sup> ga, tomoni 6 ga teng bo`lgan ko`pburchakdan iborat. Agar piramidaning yon qirrasi 10 ga teng bo`lsa, piramidaning balandligini toping. (99–8–61)
A) 8 B) 6 C) 9 D) 7 E) 6,2
13. Muntazam to`rtburchakli piramidaning balandligi 24 ga, asosining tomoni 14 ga teng. Uning apofemasini toping. (98–11–47)
A) 18 B) 27 C) 25 D) 32 E) 28
14. Qirrasi 1 ga teng bol`gan kub yoqlarining markazlari tutashtirildi. Hosil bo`lgan jismning hajmini toping. (98–4–36)

15. Qirrasi 4 ga teng bo`lgan muntazam tetraedrning to`la sirti qanday yuzaga ega bo`ladi? (00–2–42)
16. Diagonallari 12 va 16 ga teng bo`lgan rombga ichki chizilgan aylananing radiusini toping.
(00–6–40)
A) 9,6 B) 8 C) 6 D) 3,6 E) 4,8
17. y=|x+2|, x = –3 , x=0 va y=0 chiziqlar bilan chegaralangan figurani abstsissalar o`qi atrofida aylantirish natijasida hosil bo`lgan jismning hajmini toping. (96–11–55)
A) 2π B) 3π C) π D) 4π E) 5π
18. y=|x–1|, x = –1 , x=2 va y=0 chiziqlar bilan chegaralangan figurani abstsissalar o`qi atrofida aylantirish natijasida hosil bo`lgan jismning hajmini toping. (96–12–57)
A) 3π B) 4π C) 5π D) π E) 2π
19. y=|x+1|, x = –3 , x=0 va y=0 chiziqlar bilan chegaralangan figurani abstsissalar o`qi atrofida aylantirish natijasida hosil bo`lgan jismning hajmini toping. (96–3–53)
A) π B) 2π C) 3π D) 4π E) 5π