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 27 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. tenglamaning ildizi qaysi oraliqda joylashgan? A) [-2;0] B) [0;2] C) [4;9] D) [2;4] 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) 4 B) 3 C) 6 D) 2 3 / 25 3. ?(?) = ?5 − 7?4 + 3?3 − ? + 2 ko‘phadni ?2 + ? ga bo‘lgandagi qoldiqni aniqlang. A) 10? + 2 B) 8? + 2 C) 4? + 2 D) 6? + 2 4 / 25 4. ?² + |? − 3| ≤ |?2 + ?| − 3 tengsizlikni yeching. A) x ≤ 3 B) x>3 C) x<0 D) 3 ≤ x 5 / 25 5. ?(? − 1) = 2?(5? + 4) va ?(2? − 1) = 4? + 4 bo‘lsa, ?(?) ni toping A) 20x+48 B) 20x+50 C) x+25 D) 0 6 / 25 6. Agar ? > 0, ? + ?² = 7,25; ?² − ? = 2 va ?² = √(? − 1) ∙ √(2 − ?) bo‘lsa, ?(√(? − 1) + √(2 − ?)) ning qiymatini toping. A) 6 B) 7 C) 5 D) 4 7 / 25 7. Tenglamani yeching: 3x+3 + 8·3x+2 = 33 A) 0 B) 1 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) 8 B) 5 C) 3 D) 2 9 / 25 9. Soddalashtiring: (4cos² 9° −3)(4cos² 27° −3)·ctg9° A) sin18° B) tg9° C) 1 D) 2cos² 9° 10 / 25 10. 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√3/12 B) 5√6/24 C) 2/5 D) 5√2/5 11 / 25 11. ABC uchburchakning AC tomonida D nuqta olingan, bunda ∠ABC = ∠BDC. Agar AD = 10, CD = 8 bo‘lsa, BC ni toping. A) 10 B) 9 C) 15 D) 12 12 / 25 12. Agar bo‘lsa, ?(0) − ?(5) ayirmani toping. A) -25 B) -26 C) -24 D) -27 13 / 25 13. Tenglamalar sistemasi nechta yechimga ega? A) 10 B) 8 C) 12 D) 6 14 / 25 14. tenglama nechta yechimga ega, agar x ∈ (0; 50)? A) 14 B) 16 C) 15 D) 17 15 / 25 15. 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 16 / 25 16. Agar A) π B) 0 C) π/2 D) 3π/2 17 / 25 17. 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) 81 C) 144 D) 36 18 / 25 18. Agar bo‘lsa, |xyz| ni toping. A) 1000 B) 500 C) 800 D) 100 19 / 25 19. bo‘lsa ? ning qiymatini toping. A) 37 B) 12 C) 25 D) 40 20 / 25 20. 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) 9 C) 15 D) 8 21 / 25 21. (?² − 2? + 3)(?² + 6? + 12) = 6 bo‘lsa, ? + ? ni toping. A) -3 B) 2 C) 3 D) -2 22 / 25 22. 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) 9 C) 8 D) 10 23 / 25 23. 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) 135° D) 150° 24 / 25 24. Agar ?1 = 6? − 6 va у2//?1 hamda у2 to‘g‘ri chiziq ?(6; 6) nuqtadan o‘tsa, ?2 ni toping. A) −6? + 42 B) 6? − 24 C) −6? + 6 D) 6? − 30 25 / 25 25. a,b,c−ABC uchburchakning tomonlari. Agar a4 + b4 + c4 + 32 = 2(a²b² + b²c² + a²c²) bo‘lsa, ABC uchburchak yuzini toping. A) √3 B) √2 C) 1 D) 2√2 0% Testni qayta ishga tushiring Tomonidan Wordpress Quiz plugin Author: InfoMaster Foydali bo'lsa mamnunmiz
