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 49 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. Agar ikki xonali sonning o‘ng tomoniga 6 raqami yozib qo‘yilsa, berilgan sonning yarmi bilan 500 ning yig‘indisiga teng son hosil bo‘ladi. Bu qanday ikki xonali son? A) 52 B) 60 C) 30 D) 43 2 / 25 2. Agar f(g(x))=x²-6x+6 va f(x)=x−3 funksiyalar berilgan bo`lsa, g(x) funksiya ko`rinishini aniqlang. A) x²-12-3 B) (x+3)² C) x²+12x+3 D) (x-3)² 3 / 25 3. Agar ? > 0, ? + ?² = 7,25; ?² − ? = 2 va ?² = √(? − 1) ∙ √(2 − ?) bo‘lsa, ?(√(? − 1) + √(2 − ?)) ning qiymatini toping. A) 7 B) 6 C) 5 D) 4 4 / 25 4. Agar ni toping. A) 0.9 B) 0.81 C) 0.8 D) 0.96 5 / 25 5. (?² − 2? + 3)(?² + 6? + 12) = 6 bo‘lsa, ? + ? ni toping. A) -2 B) 2 C) -3 D) 3 6 / 25 6. 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) 2/5 C) 5√6/24 D) 5√2/5 7 / 25 7. Soddalashtiring: (4cos² 9° −3)(4cos² 27° −3)·ctg9° A) 2cos² 9° B) tg9° C) 1 D) sin18° 8 / 25 8. 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) 8 B) 5 C) 7 D) 6 9 / 25 9. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi. ?³ − 24?² + 183? − 440 = 0. Uchburchakning yuzini hisoblang. A) 2√21 B) √21 C) 35 D) 4√21 10 / 25 10. ABC uchburchakning AC tomonida D nuqta olingan, bunda ∠ABC = ∠BDC. Agar AD = 10, CD = 8 bo‘lsa, BC ni toping. A) 10 B) 15 C) 9 D) 12 11 / 25 11. 102022 − 22021 ayirmani 24 ga bo‘lgandagi qoldiqni toping. A) 16 B) 12 C) 8 D) 0 12 / 25 12. Tenglamalar sistemasi nechta yechimga ega? A) 12 B) 8 C) 6 D) 10 13 / 25 13. Tenglamani yeching: 3x+3 + 8·3x+2 = 33 A) -2 B) -1 C) 0 D) 1 14 / 25 14. ?(?) = ?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 15 / 25 15. Agar bo‘lsa, ?(0) − ?(5) ayirmani toping. A) -24 B) -25 C) -27 D) -26 16 / 25 16. bo‘lsa ? ning qiymatini toping. A) 25 B) 40 C) 12 D) 37 17 / 25 17. 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 18 / 25 18. 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) 9 C) 1 D) 2 19 / 25 19. 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) 10 C) 8 D) 9 20 / 25 20. Agar A) π/2 B) 0 C) 3π/2 D) π 21 / 25 21. tenglama nechta yechimga ega, agar x ∈ (0; 50)? A) 16 B) 15 C) 17 D) 14 22 / 25 22. 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 23 / 25 23. ?/? kasr (?, ? −natural sonlar)— qisqarmas kasr va (7?+6?)/(3?+2?) kasr esa qisqaradi. Ushbu kasr qanday songa qisqaradi? A) 5 B) 8 C) 2 D) 3 24 / 25 24. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping. A) -1 B) 0 C) 1 D) 3 25 / 25 25. Agar bo‘lsa, |xyz| ni toping. A) 500 B) 1000 C) 100 D) 800 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
