Matematika abituriyent testi №1

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Matematika abituriyentlar uchun №1

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Bir vaqtning o’zida 9,13, . . . ,405 va 15,21, . . . ,255 ketma–ketliklarning hadlari bo’lgan sonlarning eng kattasi va eng kichigining ayirmasini toping

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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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Arifmetik progressiyada a17=33  va a45=89. Progressiyaning birinchi hadi hamda ayirmasining o’rta geometrigini toping.

4 / 30

A(2;-2,5) nuqtadan y=  - 4x parabolagacha bo’lgan eng qisqa masofani toping.

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Radiusi 1 ga teng aylana uchta yoyga bo`lingan. Ularga mos markaziy burchaklar 1, 2 va 6 sonlariga proporsional. Yoylardan eng kattasining uzunligini toping.

6 / 30

Radiuslari orasidagi burchagi 36o va radiusi 5 ga teng bo`lgan sektor yoyining uzunligini toping.

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Soddalashtiring.

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Ifodani soddalashtiring.  [ln(ln x)-ln(loge10)].log10e

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Tengsizlik nechta butun yechimga ega?

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Quyidagi va  to’g’ri chiziqlarning o’zaro holatini aniqlang.

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Ushbu (y6+y3+1)(y3+1)(y3-1)-y6+y3+1 ifodani soddalashtish natijasida ko’phad hosil qilindi. Uning nechta hadi bor?

12 / 30

Parallelogrammning yuzi  213  ga, tomonlaridan biri 7 ga va o’tkir burchagi 600 ga teng bo’lsa, ikkinchi tomonini toping

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

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sistemadan x+y ning qiymatini toping.

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Ushbu  arifmetik progressiyaning manfiy hadlari yig’indisini toping.

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Agar sinx+cosx=a   bo’lsa, ning qiymatini toping.

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Tomoni 2 ga teng kvadratga tashqi chizilgan aylana uzunligini toping.

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Hisoblang

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a ning qanday qiymatlarida ushbu 7x-a-13=(a-5)(x+7) tenglama yagona yechimga ega

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y=cos(2sinx) funksiyaning qiymatlar sohasini toping.

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x2-5|x|-6=0 tenglama ildizini toping

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Hisoblang. 11+192+1993+19994+199995+1999996+19999997+199999998+1999999999

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sistemadan x+y+z ning qiymatini toping.

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Rombning yuzi 96 ga, dioganallaridan biri 16 ga teng. Romb tomonini toping.

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Hisoblang.

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sistema a ning qanday qiymatida cheksiz ko’p yechimga ega?

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bo’lsa ni toping. Bunda funksiya f(x) ga teskari funksiya.

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Tenglamaning ildizlari yig’indisi va ko’paytmasining yig’indisini toping. |x+1|.|x-4|=5

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x(t)=t2+6t+5 qonuniyat bo’yicha harakatlanayotgan moddiy nuqta harakat boshlangandan necha sekund o’tgach boshlang’ich nuqtaga nisbatan 77 metr masofaga siljiydi?

30 / 30

Ifodani soddalashtiring.

2 cos55o.cos40o.sin55o+cos110o.sin40o

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