Matematika abituriyent testi №1

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Matematika abituriyentlar uchun №1

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y=  funktsiyaning aniqlanish sohasini toping.

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

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

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Konsert zalining birinchi qatorida 40 ta o’rindiq bor. Har bir keyingi qatordagi o’rindiqlar soni oldingi qatordan 4 ga ko’p. Agar konsert zalida jami 40 ta qator bo’lsa, u holda shu zaldagi barcha o’rindiqlar sonini toping.

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n ning qanday qiymatida ushbu

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

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sistemadan x+y+z ning qiymatini toping.

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Tengsizlikni yeching.

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

11 / 30

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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To’g’ri burchakli uchburchakning gipotenuzasi 13 ga, katetlaridan biri 52  ga teng. Gipotenuzaga tushirilgan balandlik uzunligini toping

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m ning qanday eng katta butun qiymatida y=2x-mx-5+m funksiyaning grafigi 1,3,4 –choraklarda yotadi?

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ifodaning qiymatini toping.

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

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Tengsizlik nechta butun yechimga ega?

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Parallelogrammning tomonlari nisbati 3:5 kabi. Agar parallelogrmmning perimetri 48 ga burchaklaridan biri 1200 ga teng bo’lsa, uning yuzini toping.

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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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sistemada xy ning qiymatini toping.

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Ostki asosining yuzi 16π ga va ustki asosining yuzi 4π ga teng bo‘lgan kesik konus berilgan. Agar kesik konusga shar ichki chizilgan bo‘lsa, u holda sharning hajmini toping.

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

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

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

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Ifodani soddalashtiring.

2 cos55o.cos40o.sin55o+cos110o.sin40o

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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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Hisoblang

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

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 tenglamalar sistemasini yeching

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