1kurslar uchun olimpiada testlari

1-bosqich olimpiada testlari

1. 
   ko’rinishdagi 36 ga qoldiqsiz bo’linadigan besh xonali sonlardan eng kattasidan eng kichigining ayirmasini toping.
   

A) 900 B) 396 C) 432 D) 504 E) 540

2. 
   bo’lsa, =?
   

A) 8 B) 11 C) 13 D) 15 E) 18

3. 
   y = (2a² – 19a - 21)x + a – 7 va y = (a² – 4a + 7) x + a² – 1 to’g’ri chiziqlar parallel bo’ladigan a paarmetrning barcha qiymatlari yig’indisini aniqlang.
   

A) – 12 B) 15 C) 12 D) 8 E) 18

4. 
   Muntazam to’rtburchakli prizmaning yon siriti 160 ga, to’la sirti 232 ga teng. Shu prizma asosining dioganalini toping.
   

A) B) C) 8 D) 6 E) 9

5. 
   a va b natural sonlar va a + b = 24 bo’lsa, eng katta x ni toping.
   

A) 20 B) 25 C) 30 D) 35 E) 40

6. 
   (a -5) (a - 3) (a + 6) ( a + 8) ga qanday enh kichik butun sonni qo’shganda hosil bo’lgan yig’indi a ning har qanday haqiqiy qiymatida musbat bo’ladi?
   

A) 841 B) 121 C) 140 D) 122 E) 842

7. 
   To’g’ri burchakli uchburchakka tashqi chizilgan aylana radiusiga nisbati 5 : 2 kabi. Kichik katet uzunligining katta katet uzunligiga nisbatini aniqlang.
   

A) 2:3 B) 2:5 C) 1:2 D) 3:4 E) 3:7

8. 
   y = ln³ (1 + cosx) bo’lsa , ni toping.
   

A) B) C)
D) E)

9. 
   x² + (m + 3) x + m – 1 = 0 tenglamaning turli ishorali ikki haqiqiy ildizi bo’lishi uchun m qaysi oraliqda bo’lishi kerak?
   

A ) (-3; ) B) (- ;-3) C) (3; ) D) (- ; 1) E) O

10. 
    2185¹⁰ ni 59 ga bo’lgandagi qoldiqni toping
    

A) 57 B) 43 C) 35 D) 5 E) 21

11. 
    Rasmda BD=2, DC =6, CA = 8, AD =4. AB ni toping.
    

A) 4 B) 5 C) 2 D) 7 E) 3

12. 
    ning eng kichik qiymatini toping.
    

A) 2 B) 6 C) 4 D) 8 R) 16

13. 
    Uchburchakli piramida asosining tomonlari 9, 10 va 11 ga teng. Piramidaning yon qirralari asos tekisligi bilan 60⁰li burchak tashkil etadi. Piramidaning balandligini toping.
    

A) B) C) D) E)

14. 
    (x + 3)² + ( y - 5)² = 45 aylananing A (0;11) nuqtasiga o’tkazilgan urinmaning burchak koeffitsiyentini toping.
    

A) B) – 2 C) D) 2 E)

15. 
    Ushbu funksiyaning eng kichik qiymatini toping.
    

A) B) C) D) - E) 1

16. 
    Nechta son bir vaqtning o’zida 5, 8 …, 302 va 7 , 12, …, 202 arifmetik progressiyalarning hadlari bo’ladi?
    

A) 13 B) 12 C) 11 D) 10 E) 14

17. 
    Ushbu funksiyaning aniqlanish sohasiga tegishli x ning butun qiymatlari nechta?
    

A) 3 B) 4 C) 5 D) 2 E) 1

18. 
    Sin (arcsin + arcsin ) ni hisoblang.
    

A) B) C) D) E)

19. 
    Tenglamani [ - 180⁰; 180⁰] oraliqdagi eng katta va eng kichik yechimlari ayirmasini toping:
    

sin ( -x) + ctg ( ) =
A) 360⁰ B) 240⁰ C) 135⁰ D) 90⁰ E) 120⁰

20. 
    a = cos1, b = sin 5, c = cos sonlarni o’sish tartibida yozing.
    

A) b,a,c B) b,c,a C) a,b,c D) a,c,b E) c,a,b

21. 
    log_x-2­ (2x-7) < 1 tengsizlikni yeching.
    

A) (3;7) B) (4;5) C) (3,5;5) D) (4;9) E) (3,5;7)

22. 
    Agar radiusi 1 bo’lgan sfera asosi uchburchakli muntazam prizmaning barcha yonlariga urinsa, uning asosi qirrasining uzunligini toping.
    

A) 3 B) 2 C) 4 D) 6 E) 5

23. 
    a ning qanday qiymatlarida a²x² – ax – b = 0 kvadrat tenglamaning har ikkala ildizi modul jihatdan birdan katta bo’ladi?
    

A) (-2;0) B) (-2;2) C) (-2;0) D) (0;2) E) (-1;0) (0;1)

24. 
    Qomusiy lug’atning varaqlarini nomerlashda 6869 ta raqam ishlatildi. Lug’atning betlar sonini aniqlang.
    

A) 1884 B) 1994 C) 2994 D) 2884 E) 1995

25. 
    (-3;1;4) , (-2;3;-7) va (5;-1;4) lar ABCD to’rtburchakning tomonlari bo’lsa, shu to’rtburchakning dioganallaridan iborat vektorlar skalyar ko’paytmasining modulini toping.
    

A) 2 B) 12 C) 9 D) 5 E) 16

26. 
    ko’patmaning eng kichik qiymatini toping. A)9 B)-25 C)-16 D)-9
    
27. 
    tenglamaning ildizlarining yig’indisini toping. A)6 B)5 C)3 D) 7
    
28. 
    tengsizlikni butun yechimlari nechta? A) 3 B) 5 C) 2 D) 4
    
29. 
    tenglamaning ildizlari qarama-qarshi sonlar bo’ladigan k ning barcha qiymatlari yig’indisini aniqlang. A) 1,4 B) 1,2 C) 1,8 D) 1,6
    
30. 
    tenglamani yeching. A) B) C) D)
    

26. 
    tengsizlikning butun sonlardan iborat yechimi nechta? A)5 B)13 C)10 D)12
    
27. 
    1 dan 126 gacha bo’lgan sonlar orasida 2 ga ham, 7 ga ham bo’linmaydiganlari nechta? A) 64 B) 54 C) 45 D) 50
    
28. 
    Birinchi son 80 ga teng . Ikkinchi son birinchi sonning 80% ini, uchunchisi esa birinchi va ikkinchi son yig’indisining 50% ini tashkil qiladi. Bu sonlarning o’rta arifmetigini toping. A) 64 B) 80 C) 54 D) 72
    
29. 
    ni hisoblang. A) B) C) D)
    
30. 
    Raqamlarining yig’indisidan 8 marta katta, raqamlari kvadratlarining yig’indisi esa 53 ga teng bo’lgan ikki xonali sonning kvadratini toping. A)729 B)5184 C) 6561 D) 529
    
31. 
    Nechta butun son tenglamani qanoatlantiradi? A)8 B) 10 C) 24 D) 16
    
32. 
    Uchlari A(-2;3), B(-1;-2) va C(1;1) nuqtalarda bo’lgan uchburchakning A va C burchaklarini toping?
    

A)45⁰,90⁰ B) 90⁰,45⁰ C) 30⁰,90⁰ D) 60⁰,90⁰ E) 90⁰,30⁰

26. 
    6^log₆^cosx + 5 tenglamasini yeching.
    

A) B)
C) D)

26. 
    f(x)=e^sin2x f¹(x)=?
    

A) B) C) D)

26. 
    y= funksiya ning qanday qiymatlarida aniqlang?
    

A) B)
C) D)

26. 
    Muntazam to’rtburchakli kesik piramida asoslarining tomonlari 3;7 sm ; dioganali 10sm, uning balandligini toping?
    

A) 5 B) 5 C) 4 D) 4

26. 
    Konus asosining radyusi ga teng. Konusning yasovchi asos tekisligi bilan qanday burchak tashkil qilganda konusning yon sirti yuzi ga teng bo’ladi.
    

A) arccos B) arccos C) 30⁰ D) 60⁰

26. 
    Agar 2ⁿ = 5 bo’lsa , lg2 ni n orqali ifodalang.
    

A) B) n C) D)

26. 
    tekislik va uni kesib o’tmaydigan AB=13 kesma berilgan. Agar kesmaning uchlaridan tekislikkacha bo’lgan masofalar AA₁=5, BB₁= 8sm bo’lsa , AB kesma yotuvchi to’g’ri chiziqlarning tekislik bilan tashkil qilgan burchak kosinusini toping.
    

A) B) C) D)

26. 
    B(4;2;0) nuqta a (-2;3;-1) vektorning oxiri bo’lsa , bu vektor boshining koordinatasini toping.
    

A) (-6;1-1) B) (6;-1;1) C) (6;-1;-1) D) (-6;-1;1)

26. 
    y= , x=-3,x=0,y=0 to’g’ri chiziqlarlar bilan chegaralangan figurani absissalar o’qi atrofida aylantirishdan hosil bo’lgan jismning hajmini toping.
    

A) 2 B) 3 C) 4 D) 5

26. 
    Konus asosining raddusi 0,5 ga teng.Konus yasovchi bilan uning asos
    

tekisligi orasidagi burchak qanday bo’lganda konus yon sirtining yuzi 0,5 ga teng bo’ladi?
A) B) 60⁰ C) D)

26. 
    a ning qanday qiymatlarida tengsizlikning yechimlari to’plami oraliqdan iborat bo’ladi?
    

A) a<0 B) a>0 C) D) a=0 E)

26. 
    tengsizlikning butun sonlardan iborat yechimlaridan eng kattasi va eng kichigining ko’paytmasini toping?
    

A) 42 B) -117 C) -140 D) -130 E) aniqlab bo’lmaydi

26. 
    Teng yonli uchburchakning uchidagi burchagi 30⁰ ga, asosiga tushirilgan balandligi 6 ga teng. Uchburchakning yon tomoniga tushirilgan balandligini toping. A) 6cos15⁰ B)12sin15⁰ C) D)