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. a ning qanday qiymatlarida 3 soni tenglamaning ildizlari oralig‘ida bo‘ladi? A) a>11/7 B) a>10/9 C) a>10/7 D) a<10/9 2 / 25 2. Agar x²(a²+b²+9)+2(a+b+3)x+3=0 tenglama haqiqiy yechimga ega bo`lsa, a+b ni toping. A) 3 B) 4 C) 2 D) 6 3 / 25 3. Agar bo‘lsa, ?(0) − ?(5) ayirmani toping. A) -26 B) -27 C) -24 D) -25 4 / 25 4. x, y sonlari (x² + 1)(y² + 1) + 2(x − y)(1 − xy) = 4(1 + xy) tenglikni qanoatlantiradi |1 + x| ∙ |1 − y| ni toping. A) 1 B) 3 C) 9 D) 2 5 / 25 5. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi. ?³ − 24?² + 183? − 440 = 0. Uchburchakning yuzini hisoblang. A) 4√21 B) √21 C) 35 D) 2√21 6 / 25 6. Tenglamani yeching: 3x+3 + 8·3x+2 = 33 A) -2 B) 1 C) 0 D) -1 7 / 25 7. ?² + |? − 3| ≤ |?2 + ?| − 3 tengsizlikni yeching. A) x>3 B) x<0 C) 3 ≤ x D) x ≤ 3 8 / 25 8. Tenglama nechta yechimga ega? A) 4 B) 5 C) 2 D) 3 9 / 25 9. (?² − 2? + 3)(?² + 6? + 12) = 6 bo‘lsa, ? + ? ni toping. A) -2 B) 3 C) -3 D) 2 10 / 25 10. Agar ? > 0, ? + ?² = 7,25; ?² − ? = 2 va ?² = √(? − 1) ∙ √(2 − ?) bo‘lsa, ?(√(? − 1) + √(2 − ?)) ning qiymatini toping. A) 6 B) 4 C) 5 D) 7 11 / 25 11. 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) 9 B) 10 C) 11 D) 8 12 / 25 12. Agar ni toping. A) 0.96 B) 0.81 C) 0.9 D) 0.8 13 / 25 13. 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? − 30 C) 6? − 24 D) −6? + 42 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) 5√2/5 C) 2/5 D) 5√3/12 15 / 25 15. ?(?) = ?5 − 7?4 + 3?3 − ? + 2 ko‘phadni ?2 + ? ga bo‘lgandagi qoldiqni aniqlang. A) 10? + 2 B) 8? + 2 C) 6? + 2 D) 4? + 2 16 / 25 16. Agar bo‘lsa, |xyz| ni toping. A) 1000 B) 100 C) 500 D) 800 17 / 25 17. tenglama nechta yechimga ega, agar x ∈ (0; 50)? A) 14 B) 17 C) 15 D) 16 18 / 25 18. a,b,c−ABC uchburchakning tomonlari. Agar a4 + b4 + c4 + 32 = 2(a²b² + b²c² + a²c²) bo‘lsa, ABC uchburchak yuzini toping. A) √3 B) 1 C) √2 D) 2√2 19 / 25 19. 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) 135° C) 150° D) 90° 20 / 25 20. ?(? − 1) = 2?(5? + 4) va ?(2? − 1) = 4? + 4 bo‘lsa, ?(?) ni toping A) 0 B) x+25 C) 20x+50 D) 20x+48 21 / 25 21. 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) 10 B) 8 C) 15 D) 9 22 / 25 22. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping. A) -1 B) 0 C) 1 D) 3 23 / 25 23. ABCD to‘rtburchakda АВ = CD = 9 va bu to‘rtburchakka radiusi 4 ga teng aylana ichki chizilgan. ABCD to‘rtburchak yuzini toping. A) 144 B) 72 C) 81 D) 36 24 / 25 24. ?/? kasr (?, ? −natural sonlar)— qisqarmas kasr va (7?+6?)/(3?+2?) kasr esa qisqaradi. Ushbu kasr qanday songa qisqaradi? A) 5 B) 8 C) 3 D) 2 25 / 25 25. Agar A) π/2 B) π C) 3π/2 D) 0 0% Testni qayta ishga tushiring tomonidan Wordpress Quiz plugin Matematika olimpiada, Viloyat 2021-2022 o'quv yili
