Funksiyaning eng
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2015-yil math
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1. Radiusi 1 ga teng aylanaga ichki chizilgan uchburchakning tomonlari a,b,c bo`lsa, shu tomonlari kvadratlari yig`indisining eng katta qiymatini toping. A) 12 B) 16 C) 9 D) 4 9
2. O`quvchi uyidan maktabgacha bo`lgan masofaning birinchi yarim soatda 3 1
qolgan masofaning yarimini yurgach, yana 450 m masofa qoldi. O`quvchi jami qancha (m) masofani bosib o`tishi kerak? A) 1370 B) 1300 C) 1400 D) 1350 3.
2 2 2 24 24 24 24
x x x x tenglama haqiyqiy ildizlari yig`indisini toping. A) -25 B) -24 C) -23 D) -26 4. AB kesma to`g`ri chiziqqa 6 1
AA sm,
8 1 ` OA sm
va 4 1 OB sm bo`lsa, AB kesmaning uzunligini (sm) toping. A) 12 B) 15 C) 16 D) 9 5. Asoslari 2 va 6 ga teng, kichik diagonali katta yon tomoniga perpendikulyar bo’lgan to’g’ri burchakli trapetsiyaning kichik yon tomonini toping. A)
2 3 B) 3 2 C) 2 4 D) 2 2
6. Hisoblang: 5 . 1 9 . 0 4 . 0 5 . 1 4 . 1 4 . 2 4 . 1 4 . 2 7 . 0 2 . 1 7 . 0 2 . 1 4 . 2 5 . 0
A) 2 B) 1 C) 4 1 D) 2 1
7. 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
burchakni toping. A)
15 B) 30 C) 25 D) 20
8. Agar
5 4 f , 4 3 f , 3 2 f bo’lsa,
4 4 3 1 1
f f ifodaning qiymatini hisoblang. (
x f 1 funksiya
x f ga teskari funksiya) A) 35 B) 20 C) 15 D) 25 9.
4 sin 4 cos
11 cos
5 cos
2 2 ni soddalashtiring. A)
cos 2 B) 3 cos 2
C)
cos D) 8
2
10. Diagonallarining soni tomonlari sonidan 3 marta ko’p bo’lgan qavariq muntazam ko’pburchak markazidan ko’pburchak qo’shni uchlariga o’tkazilgan kesmalar hosil qilgan burchakni toping. A)
40 B) 45 C) 36 D) 30
B A E C C D O 11. 13 ag karrali, 399 dan katta bo`lmagan barcha natural sonlar yig`indisini toping. A) 6045 B) 6071 C) 6058 D) 6032 12. 5200000 sonining nechta natural bo`luvchisi bor? A) 64 B) 48 C) 56 D) 96 13.
x x x x x x 6 2 log 3 log 3 1 2 4 1 2 2 tenglamaning nechta yechimi bor? A) 1 ta B) 2 ta C) 4 ta D) 3 ta 14. x soni 0 81
36 12 16 9 x x x tenglama ildizi bo`lsa, 3x soni nechaga teng. A) 6 B) 3 C) 4 D) 2 15. 4
4 49 log 5 36 log 2 1 7 6 ni hisoblang. A) 20 B) 4 C) 10 D) 8 16.
3 1 arccos 2 sin ni hisoblang. A)
3 2 2 B) 9 2 C) 9 2 4 D) 3 2
17. Agar n ta juft son va m ta toq sonlarni qo`shganda juft son chiqsa, m ning qiymati qanday bo`ladi? A) 0 B) toq C) juft D) aniqlab bo`lmaydi. 18.
1 log
5 log
3 log
8 4 4 3 9 25 ifodaning qiymatini toping. A) 2 B) 1 C) 3 D) 0 19.
6 4 4 2 4 2 y x x x x y ni qanoatlantiruvchi yechimlar nechta? A) 3 B) 0 C) 1 D) 2 20. Diagonallarining soni tomonlarning sonidan 2 marta
kam bo`lgan qavariq muntazam ko`pburchak markazidan uning qo`shni uchlariga o`tkazilgan kesmalar hosil qilgan burchakni toping. A)
72 B) 60 C) 90 D) 108
21. Tengsizlikni yeching: . 1 3 7 2
x x
A) ; 3 B)
7 C)
; 7 4 ; 3 D) 4 ; 3
22.
028 , 0 : 3 , 0 48 , 0 : 25 , 3 75 , 4 ni
hisoblang. A) 15 B) 5 C) -5 D) -15 23. 2
1 1 2 2 2 2 x x x x x x x x tenglama ildizlarining o`rta arifmetigini toping. A) 1 B) 1,5 C) 2 D) 0,5 24.
x x x f 15 cos 9 cos
48 uchun boshlang`ich funksiyani toping. A) C
- 4sin6x
B) C cos24x
- 4cos6x
C) C cos24x - 4cos6x
D) C sin24x
4sin6x 25.
x x x y cos
2 sin
3 funksiyaning hosilasini toping. A)
x x sin 2 B) 1 cos
2
C)
1 sin
3 cos
2 x x D)
1 cos
3 sin
2 x x
26. x x y 9 cos 3 cos
3 funksiyaning hosilasini toping.
A) x x 6 cos 3 cos
18 B) x x 6 sin 3 cos
18 C)
x x 6 cos 3 sin
18 D) x x 6 sin 3 sin
18 27.
a ax x 15 5 2 tenglama a ning qanday qiymatlarida 3 ta musbat ildizga ega? A) 2,4 B) 3 C) D) 4 , 2 ; 0
28. M,N,P nuqtalar mos ravishda ABC uchburchakning AB,BC va AC tomonlarida yotadi. Bunda MN║AC, NP║AB. Agar AC=15 sm, AB=10 sm va MN:PN=3:2 bo`lsa, MA va AP ning uzunligini (sm) toping. A) 5,5;6 B) 4;5 C) 5;7,5 D) 10;12 29.
3 2 3 2 3 2 1 3 1 1 2
x x tenglamaning ildizlari quydagi oraliqlarda qaysi birida joylashgan? A)
2 ; 1 B) 3 ; 2 C) 0 ; 1 D)
1 ; 0 30. Yig’indisi 6 ga teng, birinchi 5 ta hadining yig’indisi esa 16 13 5 ga teng bo’lgan cheksiz kamayuvchi geometrik progressiyaning uchinchi hadini toping. A) 0.5 B) 1.5 C) 0.75 D) 3 31. Agar axborot hajmi 2097152 bit bo’lsa, uning hajmini Kbaytda aniqlang. A)
12 2 B) 8 2 C) 10 2
7 2
32. Sakkizlik sanoq sistemasidagi 123 sonini o’nlik sanoq sistemasidagi 2 ga ko’paytirganda hosil bo’ladigan sonni o’n oltilik sanoq sistemasida ko’rsating. A) A10 B) 246 C) 106 D) A6 33. Ikkilik sanoq sistemasida arifmetik amalning to’g’ri javobini toping: 10.101+11.111 A) 1100.11 B) 110.1 C) 110.011 D) 100.111 34. MS Excel 2003 dasturida berilgan
17 ; 16 ; 15 1415 . 3 СРЗНАЧ ДЛСТР formulaning natijasini aniqlang. A) 22 B) 20 C) 21 D) 23 35. HTML tilida jadvaldagi ustunlarni birlashtirish uchun tegida qanday parametr qo’llaniladi?
| A) COLSPAN B) CAPTION C) ROWSPAN D) BORDERCOLOR 36. Agar a=16, b=2 va c=49 bo’lsa, trunc(sqr(a mod b)+sqrt(c)) ifodaning natijasini toping. (Paskal dasturlash tilida) A) 7 B) 10 C) 8 D) 9 15-VARIANT 1. Tenglamani yeching: 2 log 4 2 log 5 log
3 1 3 3 x x x
A) 7 B) 8 C) 6 D) 5.5 2. 4 4 5 3 1 1 2
x x x y funksiyaning aniqlanish sohasini toping.
A) 2 ; 1 1 ; 0 1 ; B)
2 ; 1 1 ; 0 1 ; C) 2 ; 0 1 ;
D)
2 ; 1 1 ; 0 0 ; 1
3. Sistemani yeching: 1 0 9 3 2 2 2 y x e xy y x y x
A)
3 ; 3 3 ; 3 B) 1 ; 1 1 ; 1 C)
4 ; 4 4 ; 4 D) 2 ; 2 5 . 1 ; 5 . 1
4. x ning qanday eng kichik qiymatida 354 5 3 x
yig’indini 3 ga qoldiqsiz bo’linadi? A) 1 B) 5 C) 4 D) 6 5.
0 8 2 x x tenglamaning haqiqiy ildizlari yig’indisini toping. A) 12 B) 1 C) 9 D) 8 6.
sin
1 sin
tengsizlikni yeching. A)
Z k k k , 2 ; 4
B) Z k k k , 2 4 ; 2 2 C)
Z k k k , 4 ; 2 D)
Z k k k , 2 2 ; 2 4
7. 2 5 5 2 1 1 ni hisoblang. A) -1 B) 0 C) 1 D) 2 8. 0
32 3
x x tenglamaning haqiqiy ildizlari ko’paytmasini toping. A) 1 B) 3 C) 4 D) 2 9. Teng yonli trapetsiyaning perimetri 52 ga, unga ichki chizilgan aylananing radiusi 4 ga teng. Shu trapetsiyaning yuzini toping. A) 100 B) 104 C) 102 D) 107 10. Bir odam shunday vasiyat qildi: “Naqd 10 dirhan pulim bor. Bir kishiga qarz ham berganman. Qarzning miqdori o’g’lim oladigan merosga teng. Ikkala o’g’lim barobar meros ilishsin. Ukamga jami merosning 5 1
qismini va yana 1dirham beringlar”. U kishining o’g’illari necha dirhamdan meros olishga? A) 6
B) 6 C) 6 35 D) 3 25 11.
2 1 3 y ax x a parabolaning uchi y o’qi ustida bo’lsa, a ni toping. A) 1 B) 3 C) 0 D) 2 12. Sinfda jami 36 ta o’quvchi bor. Jami o’quvchilarning 0,(5) qismi matematika to’garagiga, 0,6(6) qismi ingliz tili to’garagiga, 0,(4) qismi ikkala to’garakga ham qatnashmaydi o’quvchilar sonini toping. A) 7 B) 8 C) 6 D) 9 13. a ning qanday qiymatida
0 3 2 x ax a
tenglama yagona ildizga ega A) a=0 B) a=12 C) a=0; a=12 D) a=0; a=-12
14. 1 11 x x tenglamani yeching. A) 5 B) -2 C) D) 5; -2 15. a=2 bo’lganda, S soha yuzini toping.
A) 52 B) 48 C) 40 D) 44 16. Rasmda berilgan ma’lumotlarga ko’ra, EC ning qiymatini toping. Bu yerda,
va
BD=7, AD=5, AE=6.
A) 3 B) 4 C) 5 D) 2 17.
x x x f 12 cos 8 sin
40 uchun boshlang’ich funksiyani toping. A) -5sin4x-cos20x+C B) 5sin4x-sin20x+C C) 5sin4x+sin20x+C D) 5cos4x-cos20x+C 18.
2 0 sin 2 sin
cos ni hisoblang. A) e-1 B) e+1 C) 1 2 1 e D)
2 1 e
19. Rasmdagi ADC uchburchakda AD-ichki, CD- tashqi bissektrissa bo’lib, AC=CD va 80
bo’lsa,
AEC ning qiymatini toping.
A) 135 B) 120 C) 150 D) 160
20. 1 1 1 1 1 1 1 1 1 5 8 4 2
x x x x x x
Tenglamaning haqiqiy ildizlari yig’indisini toping. A A A A C B D B D C A E A) 2 B) 1 C) -1 D) 0 21.
a a a a a 1 5 20 5 2
A) a+1 B) a-1 C) 2a D) 2 22. Rasmda
` funksiya grafigi berilgan.
x f y funksiya ekstemum nuqtalari nechta? 2 ; 4 x
A) 2 B) 5 C) 4 D) 3 23. Tengsizliklar sistemasini yeching.
6 3 arcsin
0 33 28 4 2 x x x
A) 4 ; 5 . 3 B)
; 5 . 3 C)
; 5 . 3 D)
; 5 . 3
24. 3 6 : 3 24 ni hisoblang. A) 7 B) 3 C) -7 D) -3 25. Agar
, 0 ; 5 , 0 ; 1 , 0 a va 8 , 0 ; 4 , 0 ; 2 , 0
b a ni toping. A) 81
B) 81 50 C) 27 26 D) 27 25 26. Tenglama ildizlari modullari yig’indisini toping. 0
log 3 2 2 2
x
A) 12 B) 10 C) 9 D) 8 27. 1 8 2 3 4 bx ax x x ko’phad biror ko’phadning kvadrati bo’lsa, a va b koeffitsiyentlarning barcha qiymatlari yig’indisini toping. A) 48 B) 26 C) 27 D) 32 28. 639 sonini 2:3:4 kabi nisbatda bo’ling. A) 142; 215; 282 B) 142; 213; 284 C) 171; 239; 259 D) 171; 142; 326 29.
15 5 2 tenglama a ning qanday qiymatlarida 2 ta haqiqiy ildizga ega? A)
; 5 . 2 B) ; 4 . 2 C)
5 2 2 ; 0 D) 5 . 2 ; 0
30. Diagonallarining soni tomonlari sonidan 3.5 barobar ko’p bo’lgan qavariq muntazam ko’pburchakning barcha ichki burchaklari va bitta tashqi burchagi yig’indisini toping. A)
1285 B) 1440 C) 1476 D) 1300
31. Sonlarni o’sish tartibida joylashtiring: 1)
2 111011 ; 2)
8 114
; 3)
16 3A
A) 2, 3, 1 B) 3, 2, 1 C) 3, 1, 2 D) 2, 1, 3 32. Quyidagi ikkilik sanoq sistemasidagi sonni o’n oltilik sanoq sistemasida tasvirlang: 10101111110111101010101 A) 55EA05 B) 52BC35 C) 57FF75 D) 57EF55 33. MS Excel dasturida absolyut murojatlarni ifodalashda qanday belgi ishlatiladi? A) # B) ! C) $ D) @ 34. MS Excel 2003 dasturida berilgan
17 ; 16 ; 15 1415 . 3 СРЗНАЧ ДЛСТР formulaning natijasini aniqlang. A) 23 B) 22 C) 20 D) 21 35. Faqat arxivlash dasturlari to’g’ri berilgan qatorni toping.. A) Opera, Chrome, Firefox B) The hat, Outlook express C) Nod32, AVP Kasperskiy, DrWeb D) WinRar, WinZip, 7z 36. Paskal. Quyidagi dasturning ekrandagi natijasini aniqlang. Var a, b, s: integer; Begin a:=-2; s:=0; for b:=-10 to 6 do s:=s+a*b; Writeln(s); end. A) 68 B) 54 C) 52 D) 60 2 1 -1
1 -1 -2
-3 -4
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