10-sinf
3-variant
ABC uchburchakning AB va BC tomonlariga tushirilgan balandlik bu tomonlardan kichik emas. Uchburchakning burchaklarini toping.
A) 60°, 60°, 60° B) 30°, 30°, 120° C) 30°, 60°, 90° D) 90°, 45°, 45° E) 45°, 60°, 75°
n ning qanday qiymatlarida cosnx - sinx ifodaning davri 3π ga teng bo'ladi?
A) -1, -3, -5, -15 B) 1, 3, 5, 15 C) n = 5k D) n = -5k E) 1, 2, 3, 4
Ushbu x2 + 1 = log3(x + 2) + 3x tenglamani nechta ildizi bor?
A) 2 B) 1 C) 3 D) ∅ E) aniqlab bo'lmaydi
Ushbu cosxcos2xcos4x=1 tenglama [-2π; 2π] kesmada nechta ildizga ega?
A) 1 B) 2 C) 3 D) 4 E) ∅
ABCDEF muntazam oltiburchak yuzasi 216 ga teng. ACF uchburchak yuzasini toping.
A) 36 B) 90 C) 72 D) 18 E) 54
Soddalashtiring: 4 28+16 3 − 6 5− 2 6 + 6 5+ 2 6
A) 3 + 3 B) 3 C) 2 + 2 D) 2 3 E) 1 +
Hisoblang: 1/sin15o + 3 /cos15o
A) 2 /4 B) 3 /2 C) 4 3 D) 1/2 E)
Hisoblang: (( 0,5 + 2 + 4,5 − 8) :(1/2)1/ 2 − 4
A) –12 B) –4 C) 2 D) –2 E) 3 9. Soddalashtiring:
1 /(2(1 + a )) + 2 / (2(1 - a )) - (a2 + 2) / (1 - a3)
A) 1 B) –a C) -1/(a2 + a + 1) D) 1- a E) (1 - a )/(1 + a )
f (x) = 12 −3x2 + ln x +1 − − x funksiyaning aniqlanish sohasini toping.
A) [-2: 2] B) [-2: 1) U (1: 2] C) [-2: -1) U (-1: 2] D) [-2: -1) U (-1: 0) E) [0: 2]
k ning qanday qiymatlarida kx2 - (k - 7)x + 9 =0 tenglama ikkita bir xil manfiy ildizga ega bo'ladi?
A) 49; 1 B) 1 C) -49; -1 D) 49 E) -1
t ning qanday qiymatlarida tx2 - 6x - 1 < 0 tengsizlik x ning barcha qiymatlarida o'rinli?
A) t < -12 B) t < -9 C) t < -13 D) t < -8 E) t < -7
Agar Sn arifmetik progressiyaning dastlabki n ta hadining yig'indisi bo'lsa, S5 - 3S4 + 3S3 - S2 ni toping.
A) 0 B) -2a1 C) 2a1 D) 3a1 E) -3a1
Faqat maxrajlarining ishorasi bilan farq qiluvchi ikkita cheksiz kamayuvchi geometrik progressiya berilgan. Ularning yig'indisi mos
ravishda S1 va S2 ga teng. Shu progressiyaning istalgan bittasining hadlari kvadratlaridan tuzilgan cheksiz kamayuvchi geometrik progressiya hadlari yi'gindisini toping.
A) S1-S2 B) S1+S2 C) |S1-S2| D) (S1+S2)2 E) S12+S22
sinα-cosα=m tenglik o'rinli bo'lmaydigan m ning qiymatlarini toping. A) [-31; 0] U (2; 31) B) (-∞;-1] U [1; ∞) C) [-∞; 0] U [2; ∞)
D) [-100; 0] U (0; 100) E) [-1; 0,5] U (2;14)
2
Agar (tgα + 3 )(tgβ + 3 ) = 4 va α, β ∈(0; π/2) bo'lsa, 9−⎛⎜α +β⎞⎟
⎝ π ⎠
ni hisoblang.
A) 0,25 B) 0,5 C) 0,36 D) 0,64 E) 0,16
cos55° - cos65° - cos175° ni hisoblang.
A) -10/8 B) - 7 /8 C) -3/8 D) - 2 - 3 /8 E) - 2 + 3 /8 18. Uchburchakning tomonlari 5; 7; 10 ga teng. Uchburchakning uchidan boshlab hisoblanganda bissektrisalar kesishgan nuqtasi katta burchakning bissektrisasini qanday nisbatda bo'ladi?
A) 2:1 B) 3:2 C) 4:3 D) 6:5 E) 5:4
19. Yuzi 9 3 ga teng bo'lgan muntazam uchburchakdan yuzi eng katta bo'lgan kvadrat qirqib olindi. Kvadratning perimetri nimaga teng?
A) 18 3 -12 B) 24-12 3 C) 64 3 -96 D) 54-16 3 E) 48 3 -72 20. Asoslari BC va AD bo'lgan ABCD trapetsiyaning diagonallari O nuqtada kesishadi. Agar DO =4, BO =2 va BOC uchburchakning yuzi 6 ga teng bo'lsa, trapetsiya yuzini toping.
A) 42 B) 48 C) 52 D) 54 E) 60 21. Hisoblang:
A) 9 D) 11 E) 10
Hisoblang : 3+ 2 2 − 3− 2 2
A) 4 2 B) 0 C) 2 D) 2 2 E) 6
Hisoblang : 3,(3) - 0,3 + 0,(2) + 0,(4)
A) 2,(3) B) 0,(6) C) 1,(4) D) 1,(6) E) 2,(6) 24. x7 = 5 - 3x tenglama nechta ildizga ega?
A) 4 B) 3 C) 2 D) 1 E) yechimi yo'q
Agar tg(α+β) = 5, tg(α-β) = 3 bo'lsa, tg2β ni toping.
A) 15 B) 8 C) 1/8 D) 1 E) 2
Hisoblang: 1 - sin92° - sin2° + 1/2 sin4°
A) 0,5 B) 0 C) 1 D) -0,5 E) -1
Geometrik progressiyada b1 + b9 = 5 и b12 + b92 = 17. b4 - b6 = ?
A) 6 B) 4 C) 3 D) 2 E) 1
Kub sirtining yuzi 24 bo'lsa, uning hajmini toping. A) 64 B) 16 C) 27 D) 2 2 E) 8
Diagonallari soni 20 ta bo'lgan ko'pburchakning nechta tomoni bor?
A) 6 B) 7 C) 8 D) 9 E) 10
Yon tomoni 2 2 , uchidagi burchagi 60о bo'lgan teng yonli uchburchakka tashqi chizilgan aylananing radiusini toping.
A) 6 B) 2 C) 4 D) 4 3 E) 3 3
Biror p sonini 3 ga bo'linganda 1 qoldiq, 4 ga bo'linganda 3 qoldiq qolsa, p ni 12 ga bo'lgandagi qoldiqni toping.
A) 9 B) 7 C) 5 D) 3 E) 1
log22x - 4log2x - 1 = 0 tenglamaning ildizlari ko'paytmasini toping.
A) 8 B) 4 C) 16 D) 1/8 E) 1/16
Quyidagi funksiyaning aniqlanish sohasiga nechta butun son kiradi: y = 7− x−2
A) 7 B) 10 C) 13 D) 15 E) 14
Agar ishchilar oyligi 20%ga oshsa, keyin yana 20%ga oshsa, hammasi bo'lib necha foizga oshgan?
A) 40 B) 50 C) 42 D) 44 E) 46
⎧x + ay =1
a ning qanday qiymatlarida ⎨ sistema yechimga ega ⎩ax + y = 2a
emas?
A) 1 B) 1; -1 C) 1; 2; -1 D) 0; 1; -1 E) a∈R 36. 982004 - 97 ayirmaning oxirgi raqamini toping.
A) 1 B) 3 C) 5 D) 7 E) 9 37. Agar |a| + b2 + c2 = 2b - 4c - 5 bo'lsa, 2a + b + c ni toping.
A) 1 B) –1 C) 4 D) 2 E) -3
Arifmetik progressiyada a3 = 5 va a2 + a6 + a7 = 0. a1 ni toping.
10 B) 15 C) 8 D) -2,5 E) -10
x2 + y2 + 4x +6y - 3 = 0 tenglama bilan berilgan aylananing radiusini toping.
A) 5 B) 4 C) 6 D) 3 E) 3,5
Agar α - to'qqizburchakning ichki burchaklari yig'indisi bo'lsa, cosα ni toping.
1 B) 1/2 C) 0 D) – 1/2 E) -1
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