Matematika
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MAT Test
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Kanal: “AEXA” MATH Tuzuvchi: Xolmurodov Sunnatulla
25 MATEMATIKA 1. Ikki sonning yig’indisi 10,8 ga teng. Ulardan biri ikkichisidan 3 marta kichik. Shu sonlarning kichigini toping. A) 2,7 B) 1,2 C) 5,4 D) 4,8
2. Quyidagi sonlarning qaysi biri 76 17 ga teng emas? A) 323
38 1 B) 19 4 17 C) 17 38 1 D)
19 17 2 1
3. x
2 -14x+54 parabola uchining koordinatalari yig’indisini toping. A) -12 B) 12 C) -35 D) 35
4. p ning qanday qiymatlarida 7x-6p=5 tenglama musbat ildizga ega? A)
p 6 5 B)
p − 6 5 C) p< 6 5 D) p< 6 5 −
5. Ildizlari x 2 -22x+112=0 tenglamaning ildizlaridan ikki marta katta bo’lgan kvadrat tenglama tuzing. A) x
2 +44x+448=0 B) x 2 -44x+448=0 C) x 2 -44x-448=0 D) x 2 +44x-448=0
6. Quyidagi tengsizliklardan qaysilari x ning barcha qiymatlarida noto’g’ri? 1) (x+6)(x+3)>(x+5)(x+4) 2) (x+3)(x-7)>(x-5)(x+1) 3) (x-5)(x-6)>(x-3)(x-8) 4) x
2 +17>-8x
A) 2; 4
B) 3; 4 C) 1;2 D) 1; 3
7. Quyida keltirilgan tasdiqlardan qaysilari noto’g’ri? 1) arifmetik progressiyaning ayirmasi uchun ) 1 ( 1 1 − + = n n a a d n munosabat o`rinli; 2) ),
+ cos sin va
) sin(
− sonlar arifmetik progressiyaning ketma-ket keladigan hadlari bo`ladi. 3) arifmetik progressiya dastlabki n ta hadining yig`indisi uchun
− − = 2 ) 1 ( 2 1 formula o`rinli; 4) cheksiz kamayuvchi geometrik progressiyaning yig`indisi
− = 1 1 ga teng; 5) geometrik progressiya dastlabki n ta hadining yig`indisi ) 1
1 ) 1 ( 1 − − = q q q b S n n formula bilan hisoblanadi; A) 2;3;4 B) 1;3;5 C) 2;4;5 D) 1;3;4
8. Hosilalar uchun formulalarning qaysilari to’g’ri? 1) ) (x p =px p-1 ;
2) ) (a x = ; ln a a x
3) cosx ) (sinx = ; 4) ; cos 1 - ) (tgx 2
=
5) ) (e b kx + =ke
kx+b ; A) 1; 3; 5 B) 1; 3; 4 C) 1; 4; 5 D) 2; 3; 5 9. Boshlang’ich funksiyani topish uchun quyidagi keltirilgan formulalardan qaysilari to`g`ri? 1) f(x)=x p , p≠-1 F(x)= 1 1 + + p x p +C
2) f(x)= x 1 , x>0 F(x)= 2 1
− +C
3) f(x)=e kx+b
, k≠0 F(x)= k 1 e kx+b +C
4) f(x)=sin(kx+b), k≠0 F(x)=-kcos(kx+b)+C 5) f(x)=
3 cos
2 x e x − , F(x)= 2 1 3 cos 3 2 x e x − +C A) 1; 2; 3 B) 1; 3; 5 C) 1; 2; 5 D) 3; 4; 5
10.
3 9 ) 4 ( log 9 − x tengsizlikni yeching. A) x≤7 B) 4
11. To’g’ri burchakli uchburchakning o’tkir burchagi 60 0 ga, gipotenuzasiga tushirilgan balandligi 15 ga teng. Berilgan uchburchakning katta katetini toping. A) 3 5 B)
2 3 15 C) 3 10 D) 30
12. Quyidagi tasdiqlarning qaysilari noto’g'ri? 1) o’hshash bo’lgan ikk ita jism hajmlarining nisbati ularning mos chiziqli o’lchovlari kvadratlarining nisbatiga teng. 2) silindrning hajmi asosining yuzi bilan balandligi ko’paytmasining teng. 3) konisning hajmi asos yuzi bilan balandligi ko’paytmasining uch barabariga teng. 4) asosining radiusi R ga, yasovchisi l ga teng konus yon sirtinig yuzi πRl ga teng. 5) raduisi R ga, segmentining balandligi H ga teng bo’lgan shar segmentining hajmi 3 2
2 H ga teng. A) 2; 3; 5 B) 1; 3; 4 C) 1; 3; 5 D) 2; 4; 5
13. 2cos3x+1=0 tenglamani yeching. A)
Z k k k + − , 3 9 2 ) 1 (
B) Z k k + , 3 2 9 2
C) Z k k k + − , 3 18 ) 1 ( D)
Z k k + − , 3 2 18
14. Uchta sonning nisbati 1:2:6 ga, ularning yig’indisi esa 468 ga teng. Shu sonlardan eng kattasini va eng kichigining ayirmasini toping. A) 255
B) 240 C) 260 D) 230
15. Ikkita buyumning birgalikdagi bahosi 16110 so’m turadi. Agar birinchi buyumning bahosi 10 kamaytirilsa, ikkinchisiniki esa 20 orttirilsa, ular Kanal: “AEXA” MATH Tuzuvchi: Xolmurodov Sunnatulla
26 birgalikda 17658 so’m turadi. Birinchi buyumning dastlabki bahosini toping. A) 10430 B) 5580 C) 15583 D) 6138 16.
1 ) 5 3 3 37 8 5 1 4 8 5 4 ( − − ni hisoblang. A)
5 2 1 B) 5 3 1 C)
3 2 1 D) 4 3 1
17. a ning qanday qiymatlarida y=9x 2 -12x-17,5a parabola abssissalar o’qi bilan ikkita umumiy nuqtaga ega bo’ladi?. A) a< 35
B) a > 35 8 − C) a<
35 18 D) a> 35 4
18. k ning qanday qiymatida 3x 2 +5x+3k=0 tenglamaning x 1 va x 2 ildizlari orasida 6x 1 +8x
2 =-14
munosabat o’rinli bo’ladi?
A) 3 2 − B)
3 2 C) 3 5 − D) 3 5
19. = = + − 9 23 9 484
2 2 2 xy y xy x bo’lsa, |x+y| ni hisoblang.
A) 6 B) 7 C) 8 D) 5
20. Uchburchak burchaklarining kattaliklari nisbati 1:1:2 kabi, katta tomonining uzunligi esa 12 ga teng. Uchburchakning katta tomoniga tushirilgan balandligini toping. A) 6 B) 2 4
21.
) 2 ; 0 ; 3 (− AB va
) 2 ; 6 ; 9 ( −
bektorlar ABC uchburchakning tomonlaridir. Shu uchburchakning AN medianasi uzunligini toping.
A) 1,5 B) 2 3
C) 2 3 D) 6 3
22. 2 6 sin 5 , 0 3 cos
93 cos
0 0 0 + + ni hisoblang. A) 1 B) 2 1 C) 2 D) 0
23. 0 cosx
- ctgx
sin2x = tenglamani yeching.
A)
Z k k + , 2
B) Z k k , 2
C)
D)
Z k k , 2
24. Matematikadan o’tkazilgan imtihonda o’quchilarning 10% i birorta ham masalalarni yecha olmadi, 312 ta o’quvchi masalalarni yechishda xatolikka yo’l qo’ydi. Agar barcha masalalarni to’liq yechgan o’quvchilarning masalalarini umuman yecha olmagan o’quvchilarga nisbati 5:2 kabi bo’lsa, qancha o’quvchi imtihon topshirgan?
A)370 B) 480 C) 680 D) 690 25. k ning qanday qiymatlarida
= + + + − = + + 0 5 5 , 2 ) 3 ( 0 2 2
x k k k y x
sistemaning birorta ham yechimi bo’maydi? A) -5 va 6 B) 2 va -1 C) 6 D) -1 26.
2 6 5 | 3 | 2 + − −
x x tengsizlikni yeching. A) ( 4
2 5 ) B) [ 2 ; 2 3 ) C) [-10; 10] D) yechimi yo’q
27. Geometrik progressiyaning oltinchi va birinchi hadi ayirmasi 186 ga, maxraji 2 ga teng. Shu progressiyaning dastlabki oltita hadi yig’indisini toping. A) 378 B) 1820 C) 910 D) 360 28.
108 log
6 =
bo’lsa, 3 log 2 ni a orqali ifodalang. A)
+ − 3 2 B) a a + + 3 2 C) a a − − 3 2 D) a a + − 3 2
29. Pombning kichik diogali va tomoni 3 16
Rombga ichki chizilgan aylananing radiusini toping. A) 12 B) 13,5 C) 3 12 D) 3 8
30. Agar 85 | | = a , | | b a + =20 va
| |
a − = 2 9 bo’lsa, | | b ni toping. A) 15 B)
2 7 C) 12 D) 14 31. Teng yonli uchburchakning perimetri 48 ga teng. Asosi yon tomonidan 1,2 marta katta. Uchburchakning yuzini toping.
A) 96 B) 48 C) 108 D) 54
32. 4)
1; (-2;
a vektor va M(2; 21 23
; 3 19 − ) nuqta berilgan. Agar 0
2 = + NM a bo’lsa, N nuqtaning koordinatalarini toping. A)
3 11 ; 3 7 ; 3 2 − − B)
3 5 ; 3 2 ; 3 1 − C)
3 11 ; 3 2 ; 3 7 − − D) 3 11
7 3 ; 3 2 − −
33. Mumtazam uchburchakli piramidaning balandligi 4 ga, asosining balandligi esa 6 3 ga teng. Piramidaning yon qirrasini toping. A) 8 B) 6 C) 9 D) 5
teng. Piramidaning barcha yon yoqlari asos tekisligi bilan 45 0 li burchak tashkil etsa, uning hajmini toping. A) 36 B) 24 C) 21 D) 32
35. sinx= b b − − 4 3 2 tenglama b ning nechta butun qiymatida yechimga ega bo’ladi? A) 1 B)4 C)3 D) 2
36. 3 4 7 3 3 9 3 3 9 + − − − + ni soddalashtiring. A) 1+
3 B) 2- 3 C) 2+ 3 D) 1 3 −
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