Matematika abituriyent testi №1

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Matematika abituriyentlar uchun №1

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

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“Tutgan balig‘ining og‘irligi qancha?” degan savolga baliqchi: “Baliqning dumi 3 kg, boshi uning dumi hamda tanasi yarmining og‘irligiga teng, tanasi esa boshi va dumining og‘irligiga teng”, deb javob berdi. Baliqning og‘irligini (kg) toping.

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

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n ning qanday qiymatida ushbu

81 .82 .83 ..8n=51222 tenglik o’rinli bo’ladi?

5 / 30

tenglamani yeching.

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 tenglamalar sistemasini yeching

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Ikki burchagi graduslari yig’indisi uchinchi burchagi gradusidan katta bo’lgan uchburchaklar sonini toping.

 

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|x2-5x-14|+20≥5|x+2|+4|x-7| tengsizlikni yeching.

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sistemadan x+y ning qiymatini toping.

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

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

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

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

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Ushbu  arifmetik progressiyaning manfiy hadlari yig’indisini toping.

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Hisoblang.

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bo’lsa, ni x orqali ifodalang.

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

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a=sin 1; b=sin 2; c=sin 3; d=sin 4 va  e=sin 5  sonlarni kamayish tartibida joylashtiring.

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sistema yagona yechimga ega bo’ladigan a ning barcha qiymatlari to’plamini toping.

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sistemadan x+y+z ning qiymatini toping.

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Ifodani soddalashtiring.

2 cos55o.cos40o.sin55o+cos110o.sin40o

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Markazi  nuqtada bo‘lgan aylanaga  va  urinmalar o‘tkazilgan bo’lib,  va  nuqtalar urinish nuqtalari bo’lsin. Aylanadagi Q nuqtadan o‘tkazilgan uchinchi urinma  va  kesmalarni X va Y nuqtalarda kesib o‘tadi. Agar  uchburchakning perimetri 48 va aylana radiusi 7 ga teng bo‘lsa, u holda  kesma uzunligini toping

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ABCD to’gri to’rtburchak ichidan olingan O nuqtadan A, B, C, D uchlarigacha bo’lgan masofalar mos ravishda 3, 4, 5, 6 ga teng bo’lsa, u holda AB tomon uzunligini toping.

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x2-5|x|-6=0 tenglama ildizini 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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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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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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Tomoni 6 ga teng bo`lgan teng tomonli uchburchakga tashqi chizilgan doiraning yuzini toping.

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