1kurslar uchun olimpiada testlari

2 kurs uchun matematikadan olimpiada testlari.

1. 
   ) ifodani soddalashtiring.
   

a) 1 b) x c) -1 d) 2 e) 3

2. 
   b musbat son bo’lsa, noto’g’ri tengliklarni ko’rsating.
   

1) 2) 3)

a)1,2,3 b)1,2 c)1,3 d)2,3 e)to’g’ri javob yo’q

3. 
   bo’lsa, =?
   

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

4. 
   Ikki son yig’indisini ayirmasi va ko’paytmasini nisbati 5:1:18 kabi. Shu sonlarning kichigini toping.
   

A)1 b)2 c)3 d)4 e) to’g’ri javob yo’q

5. 
   n ning nechta natural qiymatida ifoda natural son bo’ladi?
   

A) 0 b) 1 s) 2 d) 3 e)to’g’ri javob yo’q

6. 
   tenglama ildizlari kvadratlarining teskarilari ildizlari bo’ladigan tenglamani aniqlang.
   

a) b) c)
d) e)to’g’ri javob yo’q

7. 
   Agar quyidagi sistemaning yechimalri X va Y bo’lsa, 3X+2y ni qiymatini hisoblang.
   

a)20 b) 19 c)22 d) 21 e)24

8. 
   funksiyaning aniqlanish sohasini toping.
   

a) [1;4] b)(1;4) c) [1: ) d) x 0 e) [4 : )

9. 
   To’g’ri burchakli uchburchak to’g’ri burchagi uchidan chiqqan balandligi va medianasining nisbati 40:41 bo’lsa, katetlar nisbatini toping.
   

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

10. 
    ko’phad standart ko’rinishda yozilgandagi koeffsiyentlar yig’indisini toping.
    

a) aniqlab bo’lmaydi b)2²⁰⁰² c)3²⁰⁰² d)1 e)to’g’ri javob yo’q

11. 
    Tomonlari ; 3, (3) va 5, (6) bo’lgan uchburchak perimetrini toping.
    

a)11,3 b)11,(3), c)11,(2) d)11,2
e)to’g’ri javob yo’q

12. 
    Yigirma to’rtburchakning yuzi 18 ga, unga ichki chizilgan doiraning yuzi 12 ga teng. Yigirma to’rtburchakning perimetrini toping.
    

a)16 b)12 s)18 d)6 e)18

13. 
    Silindr asosining yuzi 6 ga, yon sirtining yuzi 18 gat eng. Silindrning balandligini toping.
    

a) 9 b)6 s)1,5 d)18 e)2

14. 
    ABCD parallelogramni A va C o’tkir burchaklari uchlari qarama-qarshi tomolarning o’rtalari bilan tutashtirilgan. Bu kesmalar mos ravishda BD dioganalni E va F nuqtalarida kesib o’tadi. Agar BD=9 sm bo’lsa, EF ni toping.
    

A) 3 B) 4 C) 2,7 D) 3,6 E) 4,2

15. 
    Umumiy hadi (n ) bo’lgan ketma-ketlikning nechta hadi (1,7:2,2) oraliqqa kirmaydi.
    

a) 8 b) 10 c) 4 d) 6 e) 5

16. 
    4 = 3 + (x-2)² tenglama ildizlari ko’paytmasini toping.
    

a) -3 b) -9 c) 3 d) -15 e) 15

17. 
    tengsizlikning barcha butun sonlardagi yechimlari yig’indisini toping.
    

a) 22 b) 21 c) 24 d) 23 e) 26

18. 
    (2у – 3z)³ – (x – 3z)³ – (2y – x )³ ko’paytuvchiga ajrating.
    

a) 6 (2y – x) ( 2y – 3z) b) t. j. y.
c) Ajralmaydi d) -3 (2y – 3z) (x – 3z) (2y – x) e) 3 (2y –x ) (2y – 3z) (x – 3z)

19. 
    Agar m₁n N bo’lsa, uchun n – m ni toping.
    

a) 6 b) 4 c) 2 d) 3 e) 5

20. 
    Perimetri 24 ga, o’tkir burchagi 30⁰ ga teng bo’lgan to’g’ri burchakli trapetsiyalarning yuzining eng katta qiymatini toping.
    

A) aniqlab bo’lmaydi B) 24 C) 12 D) 24 E) 18

21. 
    To’g’ri burchakli uchburchakning ikki tomoni 5 va 12 bo’lsa, uchinchi tomonini toping.
    

A) B) 13 C) 13 yoki D) 17 E) 7

22. 
    To’g’ri burchakli uchburchakka ichki chizilgan aylana radiusi 1,5ga va tashqi chizilgan aylana radiusi 3 ga teng bo’lsa, katetlar yig’indisini toping.
    

A) bunday uchburchak mavjud emas B) 9 C) 4,5 D) 8 E) 4

23. 
    ?
    

a) b) c)2 d)0,5 e)to’g’ri javob yo’q

24. 
    ni soddalashtiring.
    

a) b) 3 - c) 2 - d) 2 + e) 1+

25. 
    > tengsizlikni yeching.
    

a) b) s) (1;1,5) d) (2;5) e)

26. 
    Hisoblang: A) 2 B)3 C) 4 D) 5
    
27. 
    Hisoblang: A) 1 B) 2 C) 3 D) 4
    
28. 
    Hisoblang: A) 1 B) 2 C) 3 D) 4
    
29. 
    ketma-ketlikning dastlabki n ta hadining yig’indisini toping. A) B) C) D) aniqlab bo’lmaydi.
    
30. 
    Cheksiz kamayuvchi geometrik progressiyaning yig’indisi 9 ga , maxraji esa ga teng. Uning A) B) C) D)
    
31. 
    Olti haddan iborat geometrik progressiyaning dastlabki 3 ta hadining yig’indisi 168 ga, keyingi 3 tasiniki esa 21 ga teng. Shu progressiyaning 1-hadini toping. A)96 B)86 C)126 D)0,5
    
32. 
    Ikkinchi hadi 6 ga teng, birinchi 3ta hadining yig’indisi 26 ga teng o’suvchi geometric progressiyaning to’rtinchi va ikkinchi hadining ayirmasini toping. A) 16 B) 32 C) 48 D)36
    
33. 
    tenglamaning barcha ildizlari ko’paytmasini toping. A) B) C) D)
    
34. 
    ni soddalashtiring. A) B) C) D)
    
35. 
    ayirma qanday raqam bilan tugaydi? A)2 B)0 C)6 D)4
    
36. 
    Agar bo’lsa, ni soddalashtiring. A) B) 0 C) D)
    
37. 
    tengsizlikning eng katta va eng kichik butun yechimlari ayirmasini toping. A) 4 B) 3 C) 2 D) 5
    
38. 
    funksiyaning aniqlanish sohasini toping. A) B) C) D)
    
39. 
    tenglamaning ildizlari manfiy bo’ladigan k ning barcha butun musbat qiymatlari yig’indisini toping. A) 13 B) 10 C) 8 D)11
    
40. 
    tenglamaning yechimga ega bo’lmaydigan k ning butun qiymatlari o’rta arifmetigini toping. A) -2 B) -3,5 C) -3 D) -4
    
41. 
    Massasi 54 kg bo’lgan mis va rux qotishmasining tarkibida 45% mis bor. Qotishma tarkibida 60%mis bo’lishi uchun unga yana necha kg mis qo’shish kerak? A)24 B)13,5 C)25 D)20,25
    
42. 
    m ning qanday qiymatlarida kvadrat uchhadni to’la kvadrat shaklida tasvirlash mumkin? A)-17 B)-17;3 C)3 D)2
    
43. 
    k ning qanday qiymatlarida tenglama x=1 yechimga ega? A)1;-3 B) 1;3 C) -2;3 D) -1;3
    
44. 
    tenglamalar sistemasi x=3, y=2 yechimga ega bo’lsa, a ning qiymatini toping. A) 5 B) 4 C) 2 D) 3
    
45. 
    Agar va bo’lsa, y-x ning qiymatini hisoblang. A) -6 B) -9 C) 9 D) -15
    
46. 
    Tengsizlikni yeching.
    

A) B) C) D)

26. 
    P(0;3) nuqtani koordinata boshi atrofida 90⁰ ga burganda hosil bo’lgan nuqtaning koordinatalarini toping. A) (0;-3) B) (3;0) C) (3;3) D) (-3;0)
    
27. 
    a ning qanday qiymatlarida va to’g’ri chiziqlar kesishadi? A) B) C) D)
    
28. 
    bo’lsa, x-y=?
    

A) 0;4 B) 3;-1 C) 1;5 D) -2;4

26. 
    ni soddalashtiring. A) B) C) D)