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 9 Ko'rishlar 1 izoh SaqlashSaqlanganOlib tashlandi 0 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! 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) 5,6 sm B) 8,1 sm C) 6,4 sm D) 7,2 sm 2 / 25 2. tengsizlik yechimi bo`la oladigan tub sonlar nechta? A) 5 B) 4 C) 3 D) 2 3 / 25 3. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping. A) 1 B) 3 C) 0 D) -1 4 / 25 4. 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) 11 B) 8 C) 10 D) 9 5 / 25 5. Agar ? > 0, ? + ?² = 7,25; ?² − ? = 2 va ?² = √(? − 1) ∙ √(2 − ?) bo‘lsa, ?(√(? − 1) + √(2 − ?)) ning qiymatini toping. A) 7 B) 4 C) 5 D) 6 6 / 25 6. ?² + |? − 3| ≤ |?2 + ?| − 3 tengsizlikni yeching. A) x<0 B) x>3 C) x ≤ 3 D) 3 ≤ x 7 / 25 7. 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) 1 D) √2 8 / 25 8. ?/? kasr (?, ? −natural sonlar)— qisqarmas kasr va (7?+6?)/(3?+2?) kasr esa qisqaradi. Ushbu kasr qanday songa qisqaradi? A) 2 B) 8 C) 5 D) 3 9 / 25 9. (?² − 2? + 3)(?² + 6? + 12) = 6 bo‘lsa, ? + ? ni toping. A) -3 B) 3 C) -2 D) 2 10 / 25 10. ABCD to‘rtburchakda АВ = CD = 9 va bu to‘rtburchakka radiusi 4 ga teng aylana ichki chizilgan. ABCD to‘rtburchak yuzini toping. A) 72 B) 36 C) 144 D) 81 11 / 25 11. Agar bo‘lsa, |xyz| ni toping. A) 100 B) 800 C) 1000 D) 500 12 / 25 12. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi. ?³ − 24?² + 183? − 440 = 0. Uchburchakning yuzini hisoblang. A) √21 B) 35 C) 2√21 D) 4√21 13 / 25 13. 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 14 / 25 14. Tenglamani yeching: 3x+3 + 8·3x+2 = 33 A) 1 B) -2 C) 0 D) -1 15 / 25 15. Soddalashtiring: (4cos² 9° −3)(4cos² 27° −3)·ctg9° A) sin18° B) 2cos² 9° C) 1 D) tg9° 16 / 25 16. ?(?) = ?5 − 7?4 + 3?3 − ? + 2 ko‘phadni ?2 + ? ga bo‘lgandagi qoldiqni aniqlang. A) 6? + 2 B) 4? + 2 C) 8? + 2 D) 10? + 2 17 / 25 17. ABC uchburchakning AC tomonida D nuqta olingan, bunda ∠ABC = ∠BDC. Agar AD = 10, CD = 8 bo‘lsa, BC ni toping. A) 12 B) 15 C) 10 D) 9 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? + 6 B) −6? + 42 C) 6? − 24 D) 6? − 30 19 / 25 19. Tenglamalar sistemasi nechta yechimga ega? A) 12 B) 10 C) 6 D) 8 20 / 25 20. 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) 90° D) 150° 21 / 25 21. Agar ni toping. A) 0.96 B) 0.81 C) 0.9 D) 0.8 22 / 25 22. Tenglama nechta yechimga ega? A) 3 B) 4 C) 5 D) 2 23 / 25 23. Agar A) 0 B) π/2 C) 3π/2 D) π 24 / 25 24. 102022 − 22021 ayirmani 24 ga bo‘lgandagi qoldiqni toping. A) 0 B) 8 C) 16 D) 12 25 / 25 25. 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) 2 C) 9 D) 3 0% Testni qayta ishga tushiring Tomonidan Wordpress Quiz plugin Author: InfoMaster Foydali bo'lsa mamnunmiz
