Matematika abituriyent testi №1

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Matematika abituriyentlar uchun №1

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

 

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Agar    va   b-a=4   bo’lsa, a+b  ni toping.

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

7 / 30

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

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Musobaqada 5 ta ishtirokchidan 3 tasiga 1, 2, 3-o’rinlarni necha xil usulda berish mumkin?

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Ushbu  funksiyaning boshlang’ich funksiyasini toping.

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Hisoblang:

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 tenglamalar sistemasini yeching

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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.

13 / 30

Tengsizlik nechta butun yechimga ega?

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Hisoblang

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Agar arctga+ arctgb + arctgc=  bo’lsa, a+b+c ni toping.

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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?

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integralning qiymatini toping.

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Sin9x =4sin3x tenglamani yeching

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Arifmetik progressiyada a17=33  va a45=89. Progressiyaning birinchi hadi hamda ayirmasining o’rta geometrigini 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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Ifodani soddalashtiring.

2 cos55o.cos40o.sin55o+cos110o.sin40o

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Tenglamaning nechta ildizi bor? |x+1|=|2x-1|

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Tengsizlikni yeching.

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sistemadan x+y ning qiymatini toping.

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Ushbu  arifmetik progressiyaning manfiy hadlari yig’indisini 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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sin2x-cos2x=1 tenglama [-π; 2π] oraliqda nechta ildizga ega?

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y=  funktsiyaning aniqlanish sohasini toping.

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Hisoblang.

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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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