Matematika abituriyent testi №1

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Matematika abituriyentlar uchun №1

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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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To’g’ri burchakli uchburchakning gipotenuzasi 5 ga, bir katetining gipotenuzadagi proyeksiyasi 1,6 ga teng. Ikkinchi katetning kvadratini toping.

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ABCD to’gri to’rtburchak ichidan olingan O nuqtadan A, B, C, D uchlarigacha bo’lgan masofalar mos ravishda 1; 2; 1,5; 1,2 ga teng bo’ladigan barcha to’g’ri to’rtburchaklar sonini toping

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Musobaqada 5 ta ishtirokchidan 3 tasiga 1, 2, 3-o’rinlarni necha xil usulda berish mumkin?

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Soddalashtiring. (0<m<7)

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To’rtburchakli muntazam piramidaning yon qirrasidagi ikki yoqli burchak 120  ga teng. Diagonal kesimining yuzasi S ga teng bo’lsa, uning yon sirtini toping.

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Tengsizlikni yeching.

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Ushbu  arifmetik progressiyaning manfiy hadlari yig’indisini toping.

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Hisoblang.

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

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Perimetri 60 ga teng bo’lgan parallelogrammning tomonlari nisbati 2:3 ga, o’tkir burchagi esa 300 ga teng. Parallelogrammning yuzini toping.

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a(x+2)=2x+1 tenglama a ning qanday qiymatida yechimga ega emas?

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sistemada xy ning qiymatini toping.

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

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Uchburchakning balandligi 12 ga teng bo’lib, u asosni 5:16 nidbatda bo’ladi. Agar asosning uzunligi 21 ga teng bo’lsa, uchburchakning perimetrini toping

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Tengsizlik nechta butun yechimga ega?

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

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Agar f(x)=ax3-5x2+b va bo’lsa, a ni toping.

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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?

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Tomoni 6 ga teng bo`lgan teng tomonli uchburchakga tashqi chizilgan doiraning yuzini toping.

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

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To’rtburchakning uchi M (0, 4) ; N(-4,0) ; P(-3;2) uchlari berilgan. Agar  bo’lsa, Q uchining koordinatalarini toping.

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Muntazam uchburchakli piramidaning yon qirrasi asos tekisligi bilan 45o li burchak tashkil etgan bo‘lsa, u holda piramidaning yon sirti yuzining uning asosi yuziga nisbatini toping.

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Tomoni 12 ga teng bo`lgan teng tomonli uchburchakga ichki chizilgan aylana uzunligini toping.

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(-3;4) nuqtaga absissa, ordinata o’qlariga va koordinata boshiga nisbatan simmetrik bo’lgan nuqtalarni tutashtirishdan hosil bo’lgan uchburchakning eng kata tomonini toping.

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

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Soat 3:37 bo’lganda minut va soat millari orasidagi burchakni toping.

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

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