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2015-yil math
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28-VARIANT
1.
x x x f 7 sin 6 sin
26 uchun boshlang’ich funksiyani toping.
A) 13cosx-cos13x+C B) 13sinxsin13x+C C) -13cosx-cos13x+C D) 13sinx-sin13x+C 2.
2 2 2 22 22 22 22
x x x x tenglama haqiqiy ildizlari yig’indisini yoping. A) -24 B) -23 C) -22 D) -21 3. 2
3 3 3 3 3 3 2 2 2 x x x x x x tenglamaning ildizlari ko’paytmasini toping. A) -5 B) -15 C) -10 D) -12 A A
A C B D
30 30 D B O C 4. 2 ; 2 P nuqtadan o’tuvchi va 4
6 a vektorga perpendikulyar bo’lagan to’g’ri chiziq tenglamasini toping.
A) 3x+2y-2=0 B) 3x-2y-2=0 C) 3x-2y+2=0 D) 3x+2y+2=0 5.
15 5 2 tenglama 2 ta manfiy va 2 ta musbat ildizga ega bo’ladigan barcha a lar yig’indisini toping. A)
0
B) 4,4 C) -3.4 D) 2,4 6. Radiusi 8 ga teng bo’lgan aylanaga ichki chizilgan muntazam oltiburchakning perimetrini toping. A) 56 B) 48 2 C) 48 D) 48 3 7. Diagonallarining soni tomonlarining sonidan 1.5 marta ko’p bo’lgan qavariq muntazam ko’pburchakning barcha ichki burchaklari va bitta tashqi burchagi yig’indisini toping. A)
780
B) 720 C) 900 D) 480 8. 60 km masofani bir velosipedchi ikkinchisiga qaraganda 1 soat tezroq bosib o’tadi. Agar birinchi velosipedchining tezligi ikkinchi velosipedchining tezligidan 5 km/soat kam bo’lsa, har bir velosipedchining tezligini (km/soat) toping. A) 15; 20 B) 20; 25 C) 10; 15 D) 12; 17 9.
1 2 6 3 5 2 log 2 log 4 4 4 4 x x x x x
tengsizlikning barcha butun yechimlari yig’indisining natural bo’luvchilari yig’indisi topilsin. A) 28 B) 32 C) 21 D) 24 10. 2
2 arcsin
x x tenglamani yeching. A) -1;0;1 B) 0 C) 1 D) -1 11.
2 2 2 1 cos
1 cos
sin 1 sin
tg if odani soddalashtiring. A) sin 2 cos
B) 1 C) 5 D) 3 12. Ifodani qiymatining oxirgi raqamini toping:
2014 2015
5 2014
2013 A) 6 B) 2 C) 4 D) 8 13. 144 va 128 sonlarining umumiy bo’luchisi yig’indisini toping. A) 35 B) 32 C) 31 D) 33 14. Tenglamani yeching:
3 log
1 4 log 3 2 log 4 2 2 4 x x x
A) 14 B) 13 C) 10 D) 12 15. y=5cos6x-3cos10x funksiyaning hosilasini toping. A)
x x 8 sin 2 cos
60 B) x x 8 cos 2 sin
60
C) x x 8 cos 2 cos
60 D) x x 8 sin 2 sin
60
16.
5 : 15 3 : 12 ni hisoblang. A) -5 B) 0,2 C) -0,2 D) 1 17.
10 lg 2 1 10 ni hisoblang. A) 10 B) 0,01 C) 0,1 D) 1 18.
0 4 2 3 1 2 3 2 x x x x x tengsizlikning eng katta manfiy butun yechimining eng kichik musbat butun yechimiga nisbatini toping. A) 4
B) 5 1
C) 3 1 D) 2 1
19.
1 0 4 dx x ni hisoblang. A) 7
B) 5 1 C) 6 5 D) 8 3 20. P(x) ko’phadni 6 5
x ga bo’lganda qoldiq 3x-4 bo’ladi. P(x) ko’phadni x-3 ga bo’lgandagi qoldiqni toping. A) x+3 B) -4 C) 5 D) 4 21. ABCD trapetsiya AB yon tomonining o’rtasidagi E nuqtadan CD tomonga paralell qilib AD katta asos bilan G nuqtada uchrashguncha to’g’ri chiziq o’tkazilgan. Agar AG=5 dm va GD=2,5 m bo’lsa, trapetsiyaning asoslarini (m) toping. A) 2,2 B) 3,2 C) 2,1 D) 3,1 22. Aylanaga tashqaridagi P nuqtadan PA urinma o’tkazilgan. P nuqta va aylananing O markazini tutashtiruvchi kesma aylanani B nuqtada kesib o’tadi. Agar PA=7, PB=5 ga teng bo’lsa, aylana radiusini toping. A) 2,7 B) 2,6 C) 2,5 D) 2,4 23.
2 3 2 3 2 3 2 3 2 ni hisoblang A) 3 B) 1 C) 2 D) 0 24. Radiuslari bir xil 3 sm ga teng bo’lgan ikki aylana rasmdagidek ABCD trapetsiyaga ichki chizilgan. Agar uning AD va BC asoslari mos ravishda 15 sm va 10 sm bo’lsa, uning yon tomonlari AB va CD lar uzunliklari yig’indisi topilsin.
A) 12 sm B) 19 sm C) 13sm D) 25sm 25. 729
9 1 2 3 y x y x ,tenglamalar sistemasini yeching. A)
2 ; 1 B) 5 , 1 ; 5 , 1 C) 1
2 D) 2
2
26. 10 10 9 2 lg lg
x x tenglamaning ildizlari ko’paytmasini toping. A) 1 B) 2 C) 2 D) 0 27. Kollejda 4 ta guruhda 126 ta o’quvchi bor. Birinchi guruhda jami o’quvchilarning 14 3 qismi, ikkinchi guruhda 21 5 qismi, uchunchi guruhda 42 11 qismi, qolganlari to’rtinchi guruhda o’qiydi. Har bir guruhda qanchadan o’quvchi bor? A) 27; 30; 33; 36 B) 36; 33; 30; 27
C) 30; 27; 36; 33 D) 33; 30; 27; 36 28. To’g’ri burchakli uchburchakning bir burchagi 38
tushirilgan bissektrisa va mediana orasidagi burchakni toping. A)
B) 7 C) 10 D) 17 29.
3 3 76 76 8
x tenglamani yeching. A) 2209 B) 0 C) 2304 D) 2401 30. Ifodani soddalashtiring: 25 ,
2 1 5 2 5 1 2
A) 0 B) 1 C) 2 D) 3 31. Agar tasvirdagi raqamlar oq, qorq, och kulrang yoki to’q kulrang bo’lsa, bitta nuqtaning rangini kodlash uchun necha bit kerak bo’ladi? A) 3 B) 4 C) 8 D) 2 32. Bir sanoq sistemasida berilgan sonning boshqa sanoq sistemasidagi ko’rinishini aniqlang:
16 9EF7
. A) 2 111101
1110001100
B)
2 110101
1000101101
C)
2 000100
1100011100
D)
2 110111
1001111011
33. HTML teglari necha turga bo’linadi? A) 3-turga: ochiq teglar, yopiq teglar va ichma-ich teglar B) 2-turga: uzun teglar va qisqa teglar C) 2-turga: juft teglar va juft emas teglar D) 2-turga: sodda teglar va murakkab teglar 34. Ikkilik sanoq sistemasida 10111 sonni 101 songa ko’paytiring: A) 1111011 B) 1010011 C) 1110111 D) 1110011 35. MS Excel 2003 dasturida berilgan =Если(Степень(3;4)>80; Степень(“Avto”; “bus”);MAKC(15;30;4)) formulaning natijasini aniqlang. A) AFTOBUS B) 81 C) Avtobus D) 30 36. Paskal tilida quydagi dastur qismining bajarilishi natijasida ekranga chiqariladigan axborotlarni aniqlang: a:=’informatika’; n:=Length(a); write(n). A) n=11 B) informatika C) 13 D) 11
29-VARIANT 1. 0 2 1 3 x x tenglamaning ildizlari ko’paytmasini toping. A) 2 B) 3 C) 1 D) 4 2. Bir ayol bog’ga olma tergani kirdi. Bog’da u 4 ta eshik orqali chiqishi kerak edi. Har bir eshik oldida qorovul turgan bo’lib, ayol birinchi qorovulga tergan olmalarining yarmini berdi. Ikkinchi qorovulga esa qolgan olmalarning yarmini berdi. Uchinchi va to’rtinchi qorovullarni ham xuddi shunday siyladi. Oxirida o’zida 10 ta olma qoldi. Ayol bog’dan necha dona olma uzun? A) 210 B) 150 C) 160 D) 180 3. Agar 6 ; 3 2 ; 27 a va 2 6 ; 6 ; 20 b berilgan bo’lsa, 3 2 a b ni toping. A) 2 B) 1 C) 5 D) 3 4. Agar
1 x x f va
1 2
x g funksiyalar uchun
b f g a f g tenglik o’rinli bo’lsa,
a ni
a . A) -2 B) 0 C) 2 D) aniqlab bo’lmaydi. 5.
4 log
5 log
8 log
6 6 27 5 4 3 ifodaning qiymatini toping. A) 1 B) 2 C) 3 D) 0 6.
50 5 5 log log
3 3 x x tenglamani yeching. A) 5 B) 3 C) 9 D) 25 7.
6 4 5 yx yz xz xy z y x tenglamalar sistemasining nechta yechimlari uchligi bor? A) 2 ta B) 4 ta C) 3 ta D) 1 ta 8. 48
2 2 3 bx ax x ko’phad
6 2 x x ga qoldiqsiz bo’linsa, a va b ni toping. A) 4; 11 B) 6; 11 C) 6; 8 D) 4; 8 9. Tenglamani yeching: 0 1
4 sin
2
A)
Z k k k , 24 2 1 B)
Z k k , 4 24
C)
Z k k k , 4 24 24 1
D)
Z k k k , 6 6 1 10. Teng yonli uchburchakka ichki chizilgan aylananing markazi uning asosiga tushirilgan balandligini, ichidan boshlab hisoblaganda, 5 va 3 ga teng kesmalarga ajratadi. Uchburchakning yuzini toping. A) 54 B) 48 C) 52 D) 50 11. 1
9 10 2 2
x x tengsizlikni qanoatlantiruvchi eng kichik butun sonni toping. A) 1 B) 2 C) 0 D) 4 12.
7 5 log
1 log
4 2 4 4 4
x x x tengsizlikni yeching. A)
2 ; 3 3 ; 4 B) ; 4 . 1 C) 0 D)
; 1 1 ; 13. Tengsizlikning eng katta butun va eng kichik musbat butun yechimlar yig’indisini toping: 1 2 2 2 2 2 3 2 3 5 6 5 3
x x x x x
A) 4 B) 1 C) 5 D) 6 14. x ning qanday qiymatlarida ifoda ma`noga ega? 100
... 4 3 2 1 50 A) x<0 B) x=0 C) x>0 D) R x
15. Tengsizlikni yeching: 3 3 7 7 2 3 1 5
x x
A) ; 1 25 47 ; 2 7 B) 1 ; 2 7
C) 1 ; 25 47 D) 25 47 ; 2 7
16. Teng yonli trapetsiyaning diagonali o’rta chizig’ini 1.5 va 7.5 ga teng kesmalarga ajratadi. Agar trapetsiyaning yon tomoni 10 ga teng bo’lsa, balandligini toping. A) 7 B) 8 C) 10 D) 6 17. Agar A(-4,5;5) va B(3,5;3,5) nuqtalar berilgan bo`lsa, AB kesma o`rtasining koordinatasini toping. A) (-3,75;4,25) B) (-3,75;8,5) C) (-1;8,5) D) (-0,5;4,25) 18.
2 2 5 4 arccos
4 x x x x tengsizlikni yeching. A)
5 ; 1 B) C) 3 ; 2 D) {2} 19. Diagonallarining soni tomonlari sonidan 3 marta ko’p bo’lgan qavariq muntazam ko’pburchakning har bir uchidan bittadan olingan tashqi burchagi va bitta ichki burchagining yig’indisini toping. A)
496
B) 504 C) 480 D) 500 20. Katta idishga 15
30 C li 11 litr suv aralashtirildi. Natijada idishdagi suvning harorati
C qanday bo’ladi? A) 21.6 B) 25.4 C) 45 D) 22.5 21. Teng yonli trapetsiyaning asoslari 4 va 12 bo`lsa, unga ichki chizilgan doira yuzini toping. A)
8 B) 16 C) 18 D) 12
22. 2 2 2 25 25 25 25
x x x x
tenglama haqiqiy ildizlari yig’indisini toping. A) -24 B) -26 C) -27 D) -25 23.
6 20 2 2 x y y x xy y x tenglamalar sistemasini yeching. A) (2;3)(3;2) B) (16;1)(1;16) C) (9;1)(1;9) D) (1;4)(4;1) 24.
0 1 3 cos 3 2 sin 2 1 x x tengsizlik x ning qanday qiymatlarida o’rinli? 2 ; 0 x
A) 4 7 ; 2 4 3 ; 2 arctg arctg
B) 2 ; 4 3 arctg C)
4 7 ; 2 arctg
D)
4 3 ; 2 arctg
25. 13 6 2 1 18 1 15 2 45 7 9 2 : 18 1 8 1 18 1 125
, 0
A) -1 B) 0 C) 1 D) 2 1 26. Aylana tashqarisidagi O nuqtadan aylanaga kesuvchi ikkita to’g’ri chiziq o’tkazildi. O burchak tortib turgan yoylar 5:3 kabi. Bu burchaklar yig’indisi butun aylana yoyining 3 1
qismiga teng bo’lsa, O burchakni toping. A)
30 B) 15 C) 25
20
27.
x x x f 12 cos 12 8 sin 40 uchun boshlang’ich funksiyani toping. A)
20 sin
4 sin
5 B) C x x 20 cos 4 cos
5
C)
20 cos
4 cos
5 D) C x x 20 sin
4 sin
5
28. 4 2 1 dx x ni hisoblang. A) 12 B) 4 C) 6 D) 8 29.
2014 2011
1 10 7 1 7 4 1 4 1 1 ni
hisoblang. A) 3 B) 3 1
3 1 2014 D) 3 2014
1
30. Rasmda
x f y ` funksiya grafigi tasvirlangan.
x f y va x f y ` funksiyalarning grafiklari mos ravishda 3 0
x va
2 1 x abssissali nuqtalarida o’tkazilgan urinmalari orasidagi burchak a bo’lsa, cos ni toping.
A) 4 1 B) 4 1
31. Quyidagi mantiqiy ifodaga teng kuchli ifodani aniqlang: B A A A)
B A B) B A C) B A D) B A
32. Quyidagi to’plamning Paskal tilida yozilishini aniqlang: 0 , 0 , 2 2 2 x y R Y X
A) (x*x+sqr(y) B) (sqr(x)+sqr(y) C) (x*x+sqr(y) D) (X*X+Y*Y) 33. MS Excel 2003 dasturida berilgan
30 30 ; 10 ; 15 ; 80 4 ; 3 MAKC СТЕПЕНЬ ИЛИ
formulaning natijasini aniqlang. A) ЛОЖЬ B) 0 C) ИСТИНА D) 1 34. Bir sanoq sistemasida berilgan sonning boshqa sanoq sistemasidagi ko’rinishini aniqlang :
8 37672
. A)
8 1111
1101101110
B)
2 1111
1010111011
C)
2 1010
1111111011
D)
2 1101
1011011001
35. Quyidagi axborot uzatish o’lchov birliklari keltirilgan. Ular o’sish tartibida joylashishi uchun mos tartiblari to’g’ri yozilgan javobni aniqlang. 1) 1 Mbayt/sekund; 2) 1Kbyt/sekund; 3) 1bod; 4) 1Kilobit/sekund. A) 3, 4, 2, 1 B) 3, 2, 4, 1 C) 4, 3, 2, 1 D) 3, 4, 1 36. Elektron pochta bilan ishlash dasturini aiqlang. A) OutLook Express B) Dreamweawer C) Flash Plater D) Smoltok Express
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