Uy » Online olimpiada » Matematika olimpiada » 10-sinf Matematika olimpiada №3 Matematika olimpiadaViloyat 2021-2022 o'quv yili 10-sinf Matematika olimpiada №3 InfoMaster Avgust 19, 2024 115 Ko'rishlar 1 izoh SaqlashSaqlanganOlib tashlandi 0 0 Savollar 12345678910111213141516171819202122232425 Vaqtingiz tugadi! Tomonidan yaratilgan InfoMaster 10-sinf Matematika olimpiada №3 2021-2022 o'quv yili viloyat bosqichida tushgan savollar. 1 / 25 1. Hisoblang: A) -1 B) -0,5 C) 2 D) 1 2 / 25 2. trigonometrik tenglamani yeching. A) π/12+2πk; k∈Z B) π/12+πk/2; k∈Z C) π/6+πk; k∈Z D) π/12+πk; k∈Z 3 / 25 3. tenglama nechta yechimga ega, agar x ∈ (0; 50)? A) 14 B) 15 C) 16 D) 17 4 / 25 4. Tenglamani yeching: 3x+3 + 8·3x+2 = 33 A) -1 B) 1 C) 0 D) -2 5 / 25 5. ?(? − 1) = 2?(5? + 4) va ?(2? − 1) = 4? + 4 bo‘lsa, ?(?) ni toping A) 0 B) 20x+50 C) x+25 D) 20x+48 6 / 25 6. 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) 1 C) √2 D) √3 7 / 25 7. (?² − 2? + 3)(?² + 6? + 12) = 6 bo‘lsa, ? + ? ni toping. A) 3 B) 2 C) -3 D) -2 8 / 25 8. 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) 8 B) 11 C) 9 D) 10 9 / 25 9. ?(?) = ?5 − 7?4 + 3?3 − ? + 2 ko‘phadni ?2 + ? ga bo‘lgandagi qoldiqni aniqlang. A) 4? + 2 B) 10? + 2 C) 6? + 2 D) 8? + 2 10 / 25 10. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping. A) 1 B) 3 C) 0 D) -1 11 / 25 11. 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) 135° B) 120° C) 150° D) 90° 12 / 25 12. Agar A) 0 B) π C) 3π/2 D) π/2 13 / 25 13. 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) 144 C) 72 D) 36 14 / 25 14. 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 15 / 25 15. Agar bo‘lsa, |xyz| ni toping. A) 100 B) 1000 C) 800 D) 500 16 / 25 16. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi. ?³ − 24?² + 183? − 440 = 0. Uchburchakning yuzini hisoblang. A) 35 B) 4√21 C) √21 D) 2√21 17 / 25 17. Agar ni toping. A) 0.9 B) 0.96 C) 0.8 D) 0.81 18 / 25 18. Agar ?1 = 6? − 6 va у2//?1 hamda у2 to‘g‘ri chiziq ?(6; 6) nuqtadan o‘tsa, ?2 ni toping. A) 6? − 30 B) −6? + 6 C) 6? − 24 D) −6? + 42 19 / 25 19. Soddalashtiring: (4cos² 9° −3)(4cos² 27° −3)·ctg9° A) 2cos² 9° B) tg9° C) 1 D) sin18° 20 / 25 20. 102022 − 22021 ayirmani 24 ga bo‘lgandagi qoldiqni toping. A) 8 B) 12 C) 0 D) 16 21 / 25 21. bo‘lsa ? ning qiymatini toping. A) 40 B) 12 C) 37 D) 25 22 / 25 22. Tenglama nechta yechimga ega? A) 3 B) 4 C) 2 D) 5 23 / 25 23. ABC uchburchakning AC tomonida D nuqta olingan, bunda ∠ABC = ∠BDC. Agar AD = 10, CD = 8 bo‘lsa, BC ni toping. A) 15 B) 10 C) 9 D) 12 24 / 25 24. ?/? kasr (?, ? −natural sonlar)— qisqarmas kasr va (7?+6?)/(3?+2?) kasr esa qisqaradi. Ushbu kasr qanday songa qisqaradi? A) 5 B) 3 C) 2 D) 8 25 / 25 25. ?² + |? − 3| ≤ |?2 + ?| − 3 tengsizlikni yeching. A) x<0 B) x ≤ 3 C) x>3 D) 3 ≤ x 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
