Matematika abituriyent testi №1

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Matematika abituriyentlar uchun №1

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integralning qiymatini toping.

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Anvar tub son o’yladi va o’ylagan sonini 5 ga ko’paytirib, 8 ni ayirgan edi, yana tub son hosil bo’ldi. Anvar qanday son o’ylagan?

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Agar geometrik progressiyaning ketma–ket dastlabki uchta hadining yig’indisi 62 ga, ularning o’nli logarifmlari yig’indisi 3 ga teng bo’lsa, shu geometrik progressiyaning birinchi hadini toping.

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tenglamani yeching.

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bo’lsa, ni x orqali ifodalang.

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Ikki burchagi graduslari yig’indisi uchinchi burchagi gradusiga teng bo’lgan uchburchak qanday uchburchak deyiladi?

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Hisoblang

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a ning 7x-a-13=(a-5)(x+7) tenglama yechimga ega bo’lmaydigan qiymatining natural bo’luvchilar sonini toping.

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sistemadan x+y ning qiymatini toping.

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Soddalashtiring.

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Ostki asosining yuzi 16π ga va ustki asosining yuzi 4π ga teng bo‘lgan kesik konus berilgan. Agar kesik konusga shar ichki chizilgan bo‘lsa, u holda sharning hajmini toping.

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Teng yonli uchburchakning tomonlari 5, 5 va 6 ga teng. Bu uchburchakning bissektiritsalari va medianalari kesishgan nuqtalar

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Qaysi javobda faqat juft funksiyalar ko’rsatilgan?

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Bog’bon uch kun davomida o’nta daraxt ko’chati o’tqazishi lozim. Agar bog’bon bir kunda eng kamida bitta ko’chat o’tqazadigan bo’lsa, u shu ishni kunlar bo’yicha necha xil usul bilan taqsimlashi mumkin?

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Rombning balandligi 8 ga dioganallarining ko’paytmasi 80 ga teng. Rombning perimetrini toping

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Hisoblang.

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To’g’ri to’rtburchakning perimetri 50 ga teng. Bir tomoni boshqa tomonidan 5 ga ko’p. To’g’ri to’rtburchakning yuzini toping.

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Radiusi 25 bo’lgan doirada 48 ga teng vatar o’tkazilgan. Doira markazidan shu vatargacha masofani toping.

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y=\sqrt{2x^{2}-4x}  funksiyaning aniqlanish sohasini toping

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Tenglamani yeching.

|x2-11x+10|=x2-11x+10

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Ostki asosining yuzi 32π va ustki asosining yuzi 18π ga teng bo‘lgan kesik konus berilgan. Agar kesik konusga shar ichki chizilgan bo‘lsa, u holda sharning sirtini toping.

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Agar f(x)=4x3-6x2-2x+3x .log3e bo’lsa, u holda  ni toping.

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AA1A2A3A4A5A6 muntazam oltiburchakli piramidaning hajmi  ga va balandligi 2 ga teng bo‘lsa, u holda AA2A6 kesim yuzini toping.

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Tomoni 25  ga diagonallaridan biri 4 ga teng bo’lgan rombning yuzini toping.

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Ushbu  arifmetik progressiyaning manfiy hadlari yig’indisini toping.

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funktsiyaning aniqlanish sohasini toping.

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Agar x,y sonlar (x+5)2+(y-12)2=142 tenglikni qanoatlantirsa, x2+y2  ifodaning eng kichik qiymatini toping.

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7 sonini uchta natural sonlar yig’indisi ko’rinishida necha xil usulda yozish mumkin?

 

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Tengsizlikni yeching.

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