Matematika abituriyent testi №1

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Matematika abituriyentlar uchun №1

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

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

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Tengsizlikni yeching.

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

6 / 30

Ifodani soddalashtiring.

2 cos55o.cos40o.sin55o+cos110o.sin40o

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

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

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Tenglamaning ildizlari yig`indisini toping.

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

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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.

12 / 30

Bog’bon uch kun davomida o’nta daraxt ko’chati o’tqazishi lozim. Agar bog’bon bir kunda eng kamida bitta ko’chat o’tqazadigan bo’lsa, u shu ishni kunlar bo’yicha necha xil usul bilan taqsimlashi mumkin?

13 / 30

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

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Quyidagilardan qaysi biri barcha  lar uchun ma’noga ega (aniqlangan)?

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

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Agar  f(x)=sin2x  va  g(x)=cos2x  bo’lsa, u holda  f(g(x)) funksiyaning hosilasini toping.

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tenglamani yeching.

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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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Tenglamani yeching.

|x2-11x+10|=x2-11x+10

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sistemadan x+y ning qiymatini toping.

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

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ifodaning qiymatini toping.

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sistemada xy ning qiymatini toping.

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Tengsizlikni yeching.

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

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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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a ning 7x-a-13=(a-5)(x+7) tenglama yechimga ega bo’lmaydigan qiymatining natural bo’luvchilar sonini toping.

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Soddalashtiring. (0<m<7)

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qonuniyat bo’yicha harakatlanayotgan moddiy nuqta harakatning 200- metrida qanday tezlikka (m/s) erishadi?

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Ushbu  arifmetik progressiyaning manfiy hadlari yig’indisini toping.

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