Matematika abituriyent testi №1

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Matematika abituriyentlar uchun №1

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tenglamani yeching.

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

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sonning oxirgi raqamini toping.

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To’g’ri burchakli uchburchakning gipotenuzasi 13 ga, katetlaridan biri 52  ga teng. Gipotenuzaga tushirilgan balandlik uzunligini 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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Tomoni 25  ga diagonallaridan biri 4 ga teng bo’lgan rombning yuzini toping.

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x(t)=t2+7t-6 qonuniyat bo’yicha harakatlanayotgan moddiy nuqtaning tezligi harakat boshlangandan necha sekund o’tgach 87 m/s ga teng bo’ladi?

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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.

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

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ABCD kvadrat ichidan olingan O nuqtadan A, B, C uchlarigacha bo’lgan masofalar mos ravishda 3, 4, 5 ga teng bo’lsa, u holda OD kesma uzunligini toping.

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

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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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Hisoblang.

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Teng yonli trpetsiyaning asoslari 15 va 25 ga balandligi esa 15 ga teng trapetsiyaning dioganalini toping

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Tenglamaning ildizlari yig`indisini toping.

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

 

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

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Radiuslari orasidagi burchagi 36o va radiusi 5 ga teng bo`lgan sektor yoyining uzunligini 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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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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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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Ifodani soddalashtiring.  [ln(ln x)-ln(loge10)].log10e

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ifodaning qiymatini 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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tenglamalar sistemasini yeching

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Ag ar tgα=2 bo’lsa, u holda   ni hisoblang

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