Uy » Online olimpiada » Matematika olimpiada » 9-sinf Matematika olimpiada №6 Matematika olimpiadaTuman 2023-2024 o'quv yili 9-sinf Matematika olimpiada №6 InfoMaster Avgust 19, 2024 587 Ko'rishlar 0 SaqlashSaqlanganOlib tashlandi 0 0 Savollar 123456789101112131415161718192021222324252627282930 Vaqtingiz tugadi! Yaratilgan Aprel 07, 2025 Tomonidan InfoMaster 9-sinf Matematika olimpiada №6 2023-yil 21-oktyabr: 2023-2024 o'quv yili tuman bosqichida tushgan savollar! 1 / 30 𝑥, 𝑦, 𝑧 −haqiqiy sonlar 𝑥𝑦 + 𝑦𝑧 + 𝑧𝑥 = 0 tenglikni qanoatlantirsa, yig‘indini hisoblang. Tekshirish 2 / 30 𝐴𝐵𝐶 uchburchakning 𝐴𝐶 tomonida 𝐷 nuqta olingan. Agar 𝐴𝐶 = 𝐷𝐵 va ∠𝐶𝐵𝐷: ∠𝐵𝐴𝐷: ∠𝐴𝐶𝐵 = 2: 3: 4 bo‘lsa, ∠𝐴𝐵𝐷 ni toping. (Javobni gradusda yozing) Tekshirish 3 / 30 tengsizlikning butun yechimlari o’rta arifmetigini toping. A) 3,5 B) 2, (6) C) 3, (3) D) 2,5 4 / 30 Soddalashtiring: A) D B) A C) B D) C 5 / 30 𝑎 + 𝑏 + 𝑐 = 0 bo‘lsa, yig‘indini toping. A) 0 B) -1 C) 1 D) -2 6 / 30 tenglamani yeching. A) -1/6 B) -1 C) -7/4 D) 0 7 / 30 funksiyaning aniqlanish sohasini toping A) [−2; 1] B) [−2; 0) ∪ (0; 2] C) [−2; 1) ∪ (1; 2] D) [−2; 2] 8 / 30 Agar ni toping. Tekshirish 9 / 30 Hisoblang: A) 6 B) 2√3 C) 4 D) 2√6 10 / 30 Tenglamaning eng katta va eng kichik ildizlari ayirmasini toping. |𝑥² − 3𝑥 + 1| = |2𝑥 − 3| A) 5 B) 3 C) 4 D) 2 11 / 30 50 − 51 + 52 − 53 + 54−. . . −599 + 5100 ni 10 ga bo‘lgandagi qoldiq nimaga teng? Tekshirish 12 / 30 BM = MN = CN = 2bo’lsa BA² +CA² − MA² − NA² ni toping. Tekshirish 13 / 30 А va В punktlardan bir paytda bir biriga qarab ikkita poyezd yo‘lga chiqdi. Birinchi poyezdning tezligi ikkinchisidan 10km/soat ortiq. Poyezdlar AB yo’lning o‘rtasidan 28 km masofada uchrashishdi. Agar birinchi poyezd A punktdan ikkinchi poyezdga qaraganda 45 minut kech chiqqanda edi poyezdlar yo‘lning o‘rtasida uchrashgan bo‘lar edi. А va В punktlar orasidagi masofani toping. (km da yozing javobni) Tekshirish 14 / 30 𝑏𝑐 = 49, 𝑐a = 9 va 𝑏a = 7 bo‘lsa, 𝑐𝑐ni toping. A) 63 B) 7 C) 3 D) 81 15 / 30 7𝑥² − 78𝑥 ≤ 0 tengsizlikning barcha butun yechimlari o‘rta arifmetigini toping. A) 5 B) 5,5 C) 6 D) 6,5 16 / 30 𝐴𝐵𝐶 to‘g‘ri burchakli uchburchak. 𝐶𝐷 = 1/√3, 𝐴𝐵 = 2 bo‘lsa, ∠𝐴𝐵𝐶 ni toping. A) 45° B) 15° C) 60° D) 30° 17 / 30 𝑥² − 2𝑎𝑥 + 2𝑎 − 1 = 0 tenglama roppa-rosa 2 ta turli ildizga ega bo‘ladigan 𝑎 parametrning barcha qiymatlarini toping. A) 𝑎 < 1 B) 𝑎 > 1 C) 𝑎 ≠ ±1 D) 𝑎 ≠ 1 18 / 30 Haqiqiy ildizlarga ega tenglamani ko’rsating. A) A B) B C) C D) D 19 / 30 (3³ + 1)(2³ − 1) sonining nechta natural bo‘luvchisi mavjud? A) 9 B) 8 C) 6 D) 12 20 / 30 Agar ning qiymatini toping. A) 2 B) −2,5 C) 1 D) -1 21 / 30 𝑛 −natural son va 𝐸𝐾𝑈𝐾(7; 𝑛) + 𝐸𝐾𝑈𝐵(7; 𝑛) = 351 bo‘lsa, 𝐸𝐾𝑈𝐵(2𝑛 − 1; 𝑛 + 71) ni toping. Tekshirish 22 / 30 Tomonlari 5,6,8 ga teng bo‘lgan uchburchak eng kichik burchagining kosinusini toping. A) 53/80 B) 17/40 C) 25/32 D) -1/20 23 / 30 2, 3, 5, 6, 9, 0 raqamlari yordamida nechta toq olti xonali son tuzish mumkin? Bunda, har bir hosil qilingan olti xonali sonda berilgan raqamlar takrorlanmaydi. Tekshirish 24 / 30 Hisoblang: A) −0,072 B) 0,072 C) 0,252 D) −0,148 25 / 30 𝐴𝐵𝐶𝐷 −kvadrat va 𝐴𝑄 = 𝐷𝑄 = 𝐶𝑃 = 𝐷𝑃 = 2 bo‘lsa, 𝐴𝑇 ni toping. Tekshirish 26 / 30 𝑥, 𝑦 natural sonlari 49𝑥 + 51𝑦 = 602 tenglikni qanoatlantiradi. 3𝑥 − 2𝑦 ayirmani toping. A) 1 B) 9 C) 11 D) 5 27 / 30 tenglamalar sistemasi yechimga ega bo‘ladigan 𝑎 parametrning barcha musbat qiymatlarini toping. A) 5 < 𝑎 < 6 B) 0 < 𝑎 < 5 C) 0 < 𝑎 < 2 D) 4 < 𝑎 < 6 28 / 30 Agar 𝐴𝐵 = 𝐶𝐷, 𝐵𝐷 = 𝐷𝐸, ∠𝐴BD = ∠EDC = 3 ∙ ∠ECD = 3𝛼 bo‘lsa, 𝛼 burchakni toping. (Javobni gradusda kiriting) Tekshirish 29 / 30 𝑥1 va 𝑥2 sonlari 2𝑥² + (𝑎 − 1)𝑥 + 4 = 0 tenglamaning ildizlari bo‘lib, 𝑥²1𝑥2 = 4 tenglikni qanoatlantirsa, 𝑎 parametr qiymatini toping. A) − 6 B) − 5 C) − 4 D) − 7 30 / 30 Tengsizlikni yeching: A) D B) C C) B D) A 0% Author: InfoMaster Foydali bo'lsa mamnunmiz
