Matematika abituriyent testi №1

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Matematika abituriyentlar uchun №1

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ifodaning qiymatini toping.

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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?

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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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Tenglamaning ildizlari yig`indisini 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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Hisoblang

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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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Agar funksiya berilgan bo’lsa, u holda M=ning qiymatini toping.

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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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Sin9x =4sin3x tenglamani yeching

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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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tenglamalar sistemasini yeching

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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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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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sistemadan x+y+z ning qiymatini toping.

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

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Tenglamani yeching. (x+2)+(x+4)+(x+6)+…+(x+100)=2800

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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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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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Agar bank qo`yilgan pulga 40% yillik foyda bersa, qo`yilgan 5000 so`m pul bir yildan keyin qancha bo`ladi ?

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

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O’qishni bilmaydigan bola alifbening A,A,A, N,N, S- 6 ta harflarini ixtiyoriy ravishda terib chiqadi. Bunda ANANAS so’zining hosil bo’lish ehtimolini toping.

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

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

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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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Fazoda (1;2;3) nuqtalardan o’tuvchi to’g’ri chiziq tenglamasini tuzing.

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Soddalashtiring.

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Soddalashtiring. (0<m<7)

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To'g'ri javob uchun 3,1 ball.

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