10-sinf Matematika olimpiada №3 Oktabr 3, 2022Avgust 19, 2024 da chop etilgan InfoMaster tomonidan 10-sinf Matematika olimpiada №3 ga 1 fikr bildirilgan 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! Tomonidan yaratilgan InfoMaster 10-sinf Matematika olimpiada №3 2021-2022 o'quv yili viloyat bosqichida tushgan savollar. 1 / 25 1. Teng yonli uchburchakning asosi 12 sm, yon tomoni 18 sm. Yon tomonlariga bissektrisalar tushirilgan. Bissektrisalarning tomonlari bilan kesishgan nuqtalari orasidagoi masofani toping. A) 6,4 sm B) 7,2 sm C) 5,6 sm D) 8,1 sm 2 / 25 2. 2x²-2ax+1=0 kvadrat tenglama ildizlari uchun tengliko`rinlibo`lsa, a ni toping. A) -1 B) 7 C) 1 D) -3 3 / 25 3. ABCD to‘rtburchakda АВ = CD = 9 va bu to‘rtburchakka radiusi 4 ga teng aylana ichki chizilgan. ABCD to‘rtburchak yuzini toping. A) 81 B) 36 C) 72 D) 144 4 / 25 4. a,b,c−ABC uchburchakning tomonlari. Agar a4 + b4 + c4 + 32 = 2(a²b² + b²c² + a²c²) bo‘lsa, ABC uchburchak yuzini toping. A) 2√2 B) √3 C) √2 D) 1 5 / 25 5. Ayirmasi noldan farqli bo‘lgan arifmetik progressiyaning 4-hadidan boshlab 14- hadigacha bo‘lgan hadlar yig‘indisi 77 ga teng. Progressiyaning 7 ga teng bo‘lgan had nomerini toping. A) 10 B) 9 C) 8 D) 11 6 / 25 6. ABCD to‘rtburchakda А va В burchaklar- to‘g‘ri, tg∠D = 3/4 va ВС = AD/2 = АВ + 2 bo‘lsa, АС ni toping. A) 15 B) 10 C) 9 D) 8 7 / 25 7. Agar ?1 = 6? − 6 va у2//?1 hamda у2 to‘g‘ri chiziq ?(6; 6) nuqtadan o‘tsa, ?2 ni toping. A) −6? + 6 B) 6? − 24 C) 6? − 30 D) −6? + 42 8 / 25 8. Agar bo‘lsa, ?(0) − ?(5) ayirmani toping. A) -26 B) -27 C) -25 D) -24 9 / 25 9. Agar ? > 0, ? + ?² = 7,25; ?² − ? = 2 va ?² = √(? − 1) ∙ √(2 − ?) bo‘lsa, ?(√(? − 1) + √(2 − ?)) ning qiymatini toping. A) 7 B) 5 C) 4 D) 6 10 / 25 10. ABC – gipotenuzasi AB bo‘lgan to‘g‘ri burchakli uchburchak. Gipotenuzaning ikki tomon davomida AB to‘g‘ri chiziqda AK = AC va BM = BC shartlar bilan kesmalar ajratilgan. KCM burchakni toping. A) 120° B) 90° C) 150° D) 135° 11 / 25 11. (?² − 2? + 3)(?² + 6? + 12) = 6 bo‘lsa, ? + ? ni toping. A) -2 B) 3 C) 2 D) -3 12 / 25 12. Agar ni toping. A) 0.9 B) 0.8 C) 0.81 D) 0.96 13 / 25 13. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi. ?³ − 24?² + 183? − 440 = 0. Uchburchakning yuzini hisoblang. A) 35 B) √21 C) 4√21 D) 2√21 14 / 25 14. Agar cos ∠A = 1/5 va sin∠B = 1/2 bo‘lsa, АВС uchburchakning mos ravishda А va В uchlaridan tushirilgan balandliklar nisbatini toping. A) 5√6/24 B) 2/5 C) 5√3/12 D) 5√2/5 15 / 25 15. 102022 − 22021 ayirmani 24 ga bo‘lgandagi qoldiqni toping. A) 0 B) 8 C) 16 D) 12 16 / 25 16. ?(? − 1) = 2?(5? + 4) va ?(2? − 1) = 4? + 4 bo‘lsa, ?(?) ni toping A) x+25 B) 20x+48 C) 20x+50 D) 0 17 / 25 17. Tenglama nechta yechimga ega? A) 4 B) 3 C) 5 D) 2 18 / 25 18. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping. A) -1 B) 3 C) 0 D) 1 19 / 25 19. bo‘lsa ? ning qiymatini toping. A) 40 B) 37 C) 25 D) 12 20 / 25 20. Qavariq to‘rtburchakning diagonallari 3 va 4 ga teng. Agar qarama qarshi tomonlarining o‘rtalarini tutashtirishdan hosil bo‘lgan kesmalar uzunliklari o‘zaro teng bo‘lsa, qavariq to‘rtburchakning yuzini toping. A) 5 B) 7 C) 8 D) 6 21 / 25 21. x, y sonlari (x² + 1)(y² + 1) + 2(x − y)(1 − xy) = 4(1 + xy) tenglikni qanoatlantiradi |1 + x| ∙ |1 − y| ni toping. A) 3 B) 2 C) 9 D) 1 22 / 25 22. ?² + |? − 3| ≤ |?2 + ?| − 3 tengsizlikni yeching. A) x ≤ 3 B) 3 ≤ x C) x<0 D) x>3 23 / 25 23. Soddalashtiring: (4cos² 9° −3)(4cos² 27° −3)·ctg9° A) 1 B) 2cos² 9° C) sin18° D) tg9° 24 / 25 24. Tenglamani yeching: 3x+3 + 8·3x+2 = 33 A) -2 B) -1 C) 1 D) 0 25 / 25 25. Agar bo‘lsa, |xyz| ni toping. A) 800 B) 500 C) 1000 D) 100 0% Testni qayta ishga tushiring tomonidan Wordpress Quiz plugin Matematika olimpiada, Viloyat 2021-2022 o'quv yili
