11-sinf Matematika olimpiada №6

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Yaratilgan Tomonidan InfoMaster

11-sinf Matematika olimpiada №6

2023-yil 21-oktyabr:

2023-2024 o'quv yili tuman bosqichida tushgan savollar!

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ko‘paytmani 1000 ga bo‘lgandagi qoldiqni toping.

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𝐴𝐵𝐶 uchburchakda, ∠A=2·∠B=2·x, AC=3, BC=4 boʻlsa, u holda cosx ni toping.

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Soddalashtiring: 

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Tenglamaning eng katta va eng kichik ildizlari ayirmasini toping ||𝑥² − 𝑥| − 𝑥²| = 4

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Agar 𝑎 + 2/b=26 va 𝑎𝑏 = 11 bo‘lsa, 𝑎 ni toping.

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AB-aylana diametri. bo‘lsa, AB ni toping.

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AB/BC ni toping.

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tenglama nechta haqiqiy ildizga ega? (bunda [𝑥] − 𝑥 sonining butun qismi)

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funksiyalar grafiklari bilan chegaralangan shakl yuzini toping. (Necha π ekanligini yozing. Masalan: 8 yoki 9)

10 / 30

qavsni ochganda 𝑥 ishtirok etmagan hadni toping.

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𝐴𝐵 = 𝐵𝐶 = 𝐶𝐷, ∠𝐴𝐵𝐶 = 90°, ∠𝐵𝐶𝐷 = 150° bo‘lsa, ∠𝐴𝐷𝐶 ni toping. (Javobni gradusda kriting)

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𝑚 = 𝑐𝑡𝑔 175º; 𝑛 = sin 105º; 𝑝 = 𝑡𝑔 175º va 𝑞 = cos 75º sonlarini taqqoslang.

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𝐴𝐵𝐶 −to‘g‘riburchakli uchburchak. Agar 𝐴𝐸 = 𝐸𝐹 = 𝐹𝐷 = 𝐷𝐵 = 2 bo‘lsa, 𝐶𝐸² + 𝐶𝐹² + 𝐶𝐷² yig‘indini toping.

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Hisoblang: cos²21° + cos²69° ∙ ctg²25°

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Juft funksiyani ko‘rsating.

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f(x) = x2 − x − 1 bo‘lsa, f(0, (1)) − f(0, (2)) + f(0, (3)) − f(0, (4)) + f(0, (5)) − f(0, (6)) + f(0, (7)) − f(0, (8)) ni hisoblang.

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Taqqoslang:

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Soddalashtiring:

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Arifmetik progressiyada 𝑎1 + 𝑎3 + 𝑎5 = 36 va 𝑎²3 − 𝑎1 = 128 bo‘lsa, 𝑎1 ni toping.

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𝐴𝐵𝐶 uchburchakda ∠𝐴 = 90°, ∠𝐵 = 30°. Agar 𝐴𝐷, 𝐵𝐹 − uchburchakning ichki bissektrisalari bo‘lsa, 𝐵𝐹: 𝐴𝐷 ni toping.

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bo‘lsa, |𝑥 + 𝑦| ni hisoblang.

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to‘g‘ri chiziqqa perpendikulyar va 𝐴(−5; 3) nuqta orqali o‘tuvchi to‘g‘ri chiziq tenglamasini ko‘rsating.

 

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𝑥² − 2𝑥 + 𝑎 = −1 tenglama [-4;3] oraliqda ildizga ega bo‘ladigan 𝑎 parametrning barcha qiymatlarini toping?

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𝐴𝐶 = 𝐵𝐷, ∠𝐴 = 80° , ∠𝐵 = 20°, ∠𝐴𝐷𝐶 burchakni toping. (Javobni gradusda kiriting.)

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funksiyaning eng katta qiymatini toping.

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   bo‘lsa, N ni toping. (n! = 1 ∙ 2 ∙ 3 ∙ … ∙ n)

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Tomonlari 8, 15, 17 bo‘lgan uchburchakka ichki chizilgan aylana radiusini toping.

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Hisoblang:

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𝑎, 𝑏 < 0 bo‘lsa,   ni soddalashtiring.

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Ifodani soddalashtiring:

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