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MATEMATIKA.
1. Ifodaning qiymatini toping: 26·25−25·24+24·23−23·22−12·8
A)106 B)1 C)54 D)8 E)0
2. 3, 6, 7 va 9 raqamlaridan ularni takrorlamasdan mumkin bo’lgan barcha 4 xonali sonlar tuzilgan.
Bu sonlar ichida nechtasi 4 ga qoldiqsiz bo’linadi?
A) 2 B) 4 C) 6 D) 8 E) 12
3. Ifodani 6 ga bo’lgandagi qoldig’ini toping. 7+69+671+6673+66675
A) 1 B) 4 C) 3 D) 5 E) 2
4. 10 dan boshlab 75 dan katta bo’lmagan barcha natural sonlarni ko’paytirish natijasida hosil bo’lgan
sonning oxirida nechta nol qatnashadi?
A) 15 B) 16 C) 17 D) 18 E) 14
5. Sonlarni o’sish tartibida joylashtiring?
a = ; b = ; c =
A) a < c < b B) b < c < a C) c < a < b D) b < c < a E) a < b < c
6. Agar a + 1/a = 3 bo’lsa, a4+1/2a2 ning qiymati nimaga teng?
A) 3,5 B) 4 C) 5,5 D) 7 E) 10
7. (a+b+c)(ab+bc+ac)−abc ni ko’paytma shaklida yozing.
A) (a+b)(b+c)(a+c) B) a2 +b2 +c2 C) (a+b)(b+c)(a−c) D) a2 +b2 –c2 E) 0
8. Hisoblang. *(3+ )( )
A) 8 B) 4 C) 10 D) 1 E) 2
9. Kvadrat uchhadni chiziqli ko’paytuvchilarga ajrating. X2 +X−2
A) (x−1)(x−2) B) (x−1)(x+2) C) (1−x)(x+2) D) (x+1)(x−2) E) (x+1)(x+2)
10. k ning qanday qiymatida k(k +6)x = k +7(x+1) tenglama yechimga ega bo’lmaydi?
A) 1 va 7 B) 1 C) 7 D) 1 va −7 E) −7
11. a ning qanday qiymatlarida x2 +3x+a+0,75 = 0 tenglamaning ikkala ildizi ham manfiy bo’ladi?
A) 0,5 < a < 2 B) −0,75 < a < 1,5 C) 0,6 < a < 1,8 D) 0,8 < a < 1,2 E) 0,9 < a < 1,4
12. Nechta natural sonlar jufti x2 –y2 = 105 tenglikni qanoatlantiradi?
A) 3 B) 4 C) 2 D) 5 E) 8
13. Ushbu f(x) = funksiyan ing aniqlanish sohasini toping.
A) [−3;0)∪(0;2)∪(2;4] B) (0;2) C) [−4;3) D) (−∞;3]∪[4;∞) E) (−∞;0)∪(2;∞)
14. Ushbu (x+3)(x−2)2(x+1)3(x−5)4 ≤0 tengsizlikning barcha butun yechimlari yig’indisini toping.
A) 1 B) 2 C) 3 D) 4 E) 5
15. (m−3)(m−7) ifodaning qiymati m ning harqanday qiymatida musbat bo’lishi uchun, unga qanday
eng kichik butun sonni qo’shish kerak?
A) 4 B) 8 C) 3 D) 6 E) 5
16. a =√1996+√1998 va b = 2·√1997 ni taqqoslang.
A) a > b B) a < b C) a = b D) a = b+1 E) a = b−1
17. Tenglamaning ildizlari ko’paytmasini toping? |x−1|2 −8 = 2|x−1|
A) 15 B) −3 C) 5 D) −8 E) −15
18. Arifmetik progressiyaning dastlabki n ta hadining yig’indisi 91 ga teng. Agar a3 = 9 va a7−a2 = 20
ekanligi ma’lum bo’lsa, n ni toping.
A) 7 B) 5 C) 3 D) 9 E) 8
19. Oltita haddan iborat geometrik progressiyaning dastlabki uchta hadining yig’indisi 168 ga, keyingi
uchtasiniki esa 21 ga teng. Shu progressiyaning maxrajini toping.
A) 1 4 B) 1 3 C) 1 2 D) 2 E) 3
20. Sinfdagi 35 ta o’quvchidan 28 tasi suzish sektsiyasiga, 14 tasi voleybol sektsiyasiga qatnashadi.
Agar har bir o’quvchi hech bo’lmaganda bitta sektsiyaga qatnashsa, ikkala sektsiyaga qatnashadigan
o’quvchilar necha foizni tashkil etadi?
A) 20 B) 18 C) 25 D) 15 E) 21
21. Hisoblang.
A) 4 B) 3 C) 5 D) 6 E) 2
22. Agar tgα = 2 bo’lsa , – ning qiymatini hisoblang.
A) 3/4 B) 4/5 C) 6/7 D) 7/8 E) 8/9
23. Soddalashtiring.
sin3α/sinα −cos3α/cosα
A) 2cosα B) 2 C) 2sinα D) 1 E) 0,5
24. Ushbu cosx·cos2x = cos3x tenglama [0;2π] oraliqda nechta ildizga ega?.
A) 5 B) 4 C) 3 D) 2 E) 1
25. Ushbu y = sin(sinx) funksiyaning hosilasini toping.
A) sin(sinx)·cosx B) cos(cosx)·cosx C) sin(cosx)·sinx D) cos(sinx)·sinx E) cos(sinx)·cosx
26.
dx
ni hisoblang. A) 1/8 B) 8/15 C) 17/ 24 D) 24/41 E) 12/29
27. )Uchburchakning birinch itomoni x(x > 5)sm, ikkinchi tomoni undan 2sm qisqa, uchunchi tomoni esa
birinchisidan 3 sm uzun. Shu uchburchakning perimetrini toping.
A) (3x−1) sm B) (3x+2) sm C) (3x−2) sm D) (3x+3) sm E) (3x+1)sm
28. )Teng yonli uchburchakning yon tomoni 25 ga teng. Asosiga tushirilgan balandligi asosidan 25 ga kam.
Shu uchburchakning asosini toping.
A) 44 B) 30 C) 35 D) 40 E) 48
29. To’g’riburchakliuchburchakto’g’riburchagining bissektrisasi gipotenuzani 1 : 5 nisbatda
bo’ladi. Uchburchakning balandligi gipotenuzani qanday nisbatda bo’ladi?
A) 25 : 1 B) 1 : 25 C) 1 : 5 D) 5 : 1 E) 1 : 6
30. Uchburchakning ikki tomoni uzunliklari 6 va 3 ga teng. Agar butomonlarga o’tkazilgan balandliklar
uzunliklari yig’indisining yarmi uchunchi tomonga o’tkazilgan balandlikka teng bo’lsa, uchunchi tomon uzunligini aniqlang.
A) 6 B) 5 C) 3 D) 4 E) 7
31. Kvadratga ichki chizilgan to’rtburchakning uchlari kvadrat tomonlarining o’rtalarida yotadi. Agar to’trburchakning yuzi 36 ga teng bo’lsa, kvadratning yuzi qancha bo’ladi?
A) 70 B) 74 C) 77 D) 72 E) 76
32. Ikki ta o’xshash romblartomonlarining nisbati 3 ga teng. Ularning yuzlarining nisbatini hisoblang.
A) 7 B) 8 C) 10 D) 11 E) 9
33. Parallelogramm o’tkirburchagining bissektrisasi uning diagonalini uzunliklari 3,2 va 8,8 bo’lgan
kesmalarga ajratadi. Agar parallelogrammning perimetri 30ga teng bo’lsa, uning kata tomonini toping.
A) 8 B) 9 C) 12 D) 11 E) 10
34. Trapetsiyaning yon tomoni uchta teng qismga bo’lingan, bo’linish nuqtalaridan ikkinchi yon
tomoniga asosga parallel kesmalar o’tkazilgan. Trapetsiyaning asoslari 2 va 5 ga teng bo’lsa, bu kesmalarning
uzunliklarini toping.
A) 3;4 B) 2,5;3,5 C) 3,5;4,5 D) 2,5;4 E) 3;4,5
35. BC va AD trapetsiyaning asoslari; O− AC va BD diagonallarning kesishish nuqtasi. BOC va AOD uchburchaklarning yuzlari mos ravishda 4 va 9 ga teng. Trapetsiyaning yuzini toping.
A) 16 B) 25 C) 26 D) 30 E) 36
36. . Muntazam oltiburchak tomonining uzunligi 1 ga teng. Shu oltiburchak tomonlarining o’rtalari
ketma - ket tutashtirildi, so’ngra hosil bo’lgan oltiburchak tomonlarining o’rtalari yana ketma - ket tutashtirildi va h.k. Hosil bo’lgan barcha oltiburchaklar yuzlarining yig’indisini toping.
A) 3√3 B) 2√6 C) 2√3 D) 3√6 E) 6√3
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