Matematika fanidan 11-sinflar uchun Imtihon savollari to’plami

RESPUBLIKА TА’LIM MАRKАZI

11-sinf

1.                Tenglamani yeching :

2.                Funksiyaning quyidagi oraliqdagi —  eng katta qiymatini toping: y=8cos x-  x+8

3.                Quyidagi integralning b ning qanday qiymatida 1 ga teng bo’ladi ?

4.                Aylanaga tashqi chizilgan teng yonli trapetsiyaning o’rta chizig’i 5 ga teng. Shu trapetsiyaning yon tomonini toping.

5.                Hajmi 36 ga teng bo’lgan muntazam to’rtburchakli piramidaning asosidagi ikki yoqli burchagi 45⁰ . Piramida asosining tomonini toping.

1.                Ifodaning qiymatini toping :

2.                Funksiyaning quyidagi oraliqdagi  eng katta qiymatini toping: y=16 tg x- 16 x+ 4 +5

3.                Quyidagi integralning qiymatini toping :

4.                Doiraga ichki chizilgan to’g’ri to’rtburchakning tomonlari 12 va 16 ga teng. Doiraning yuzini toping.

5.                Muntazam to’rtburchakli piramidaning balandligi 6 sm , apofemasi 6,5 sm. Piramida asosining perimetrini toping.

1.                Ifodaning qiymatini toping : 11⁷ ּ  25⁵: 275⁵

2.                Ushbu f(x)=2x²-1 funksiya grafigiga abssissasi x₀=0 bo’lgan nuqtada o’tkazilgan urinma tenglamasini ko’rsating.

3.                Agar f(x)=  tg2x bo’lsa, f  ( ) ni hisoblang.

4.                Agar А(-3; у) va В(5;-4) nuqtalar orasidagi masofa 10 birlik bo’lsa, у ni toping.

5.                Asos aylanasining uzunligi 8  ga, balandligi 9 sm ga teng bo’lgan konusning hajmini toping.

1.                a= va b=  sonlarining eng kichik umumiy karralisi va eng katta umumiy bo’luvchisi ayirmasini toping.

2.                 y=6x+9 to’g’ri chiziq у=х²+7 х-6 funksiya grafigining urinmasiga parallel. Urinish nuqtasining abssissasini toping.

3.                Agar f(x)=x³+x-  va g(x)=3x²+x+ bo’lsa , f  g  (x) tengsizlikning eng kichik natural yechimini toping.

4.                va ,  )=60⁰ . k ning qanday qiymatida (  + k ) vector  vektorga perpendikulyar bo’ladi ?

5.                Ikki sfera yuzlarining nisbati 2 ga teng. Bu sferalar diametrlarining nisbatini toping.

1.                Agar  bo’lsa , sin²x+  ning qiymati qanchaga teng bo’ladi ?

2.                Funksiyaning aniqlanish sohasini toping:

y=

3.                Moddiy nuqta S(t)=e^t+cos t+5 t qonuniyat bo’yicha harakatlanayapti. Shu nuqtaning t=0 dagi tezligini toping.

4.                Teng yonli trapetiyaning yon tomoni 5 ga teng, diagonali esa o’rta chizig’ini 3 va 7 ga teng bo’lgan kesmalarga ajratadi. Trapetsiyaning yuzini toping.

5.                Uchburchakli to’g’ri prizmaning tomonlari 29sm,25 sm va 6 sm, yon qirrasi esa asosining katta balandligiga teng. Prizmaning hajmini toping.

1.                Hisoblang: ;

2.                Agar tg ( ) =  bo’lsa, tg  ni toping.

3.                Agar  va  bo’lsa,  funksiyani toping.

4.                3х+4у+7=0 va 3х+у-5=0 to’g’ri chiziqlarning kesishish nuqtasi koordinata boshidan qanday masofada joylashgan?

5.                Tekislikka og’ma va perpendikulyar tushirilgan. Og‘ma va tekislik orasidagi burchak  ga, og‘maning tekislikdagi proyeksiyasi 30 ga teng. Perpendikulyarning uzunligini toping.

1.                 ifodaning  va  bo‘lgandagi qiymatini hisoblang.

2.                Tengsizlikni yeching: ;

3.                Funksiya hosilalasini toping: ;

4.                Rasmda ,  uchburchakning perimetri 42 sm,  uchburchakning perimetri 84 sm.  uchburchakning yuzi 44  bo’lsa,  uchburchak yuzini ( ) toping.

5.Uzunligi 15 m bo’lgan telefon simi yerdan balandligi 8 m bo’lgan simyog’ochdan uyga qarab 20 m balandlikka tortilgan. Sim osilib turmagan deb faraz qilib, simyog’ochdan uygacha masofani toping.

1.                 , va  sonlardan qaysilari musbat?

2.                Quyidagi ,  ni hisoblang.

3.                Tenglamani yeching:

4.                 Parallelogrammning burchaklaridan biri 150⁰ ga teng. Uning 6 ga teng bo’lgan diagonali tomoniga perpendikulyar. Parallelogrammning perimetrini toping.

5.                Muntazam to‘rtburchakli piramidaning balandligi 24ga, asosining tomoni 14 ga teng. Uning apofemasini toping.

1.                 ni soddalashtiring.

2.                Tengsizlikni yeching: .

3.                Absissasi  nuqtada bo’lgan nuqtadan  funksiyaga o’tkazilgan urinma OY o’qi bilan qanday burchak tashkil etadi?

4.                 Agar  va  vektorlar berilgan bo’lsa,  va  vektorlar orasidagi burchakni toping.

5.                Muntazam to’rtburchakli prizmaga silidr ichki chizilgan. Silindr hajmining prizma hajmiga nisbatini toping.

1.                 funksiyasining (6;2) nuqtadan o’tuvchi boshlang’ich funksiyasini toping.

2.                 tenglamani yeching.

3.                 va  vektorlarda yasalgan parallelogrammning diagonallari orasidagi burchakni toping.

4.                Aylananing AB vatari uning radiusiga teng. Katta AB yoyning ixtiyoriy nuqtasidan qaraganda AB vatar qanday burchak ostida ko’rinadi?

5.                Hajmi 8  ga teng bo’lgan muntazam tetraedrning balandligini toping.

1.                 funksiyaga teskari funksiyani aniqlang.

2.                 tengsizlik  ning  oraliqqa tegishli qanday qiymatlarida o’rinli bo’ladi?

3.                Agar  va  bo’lsa,  ning qiymati qancha bo’ladi?

4.                АВС uchburchak  tekislikni B₁ va C₁ nuqtalarda kesib o’tadi.

Agar AB₁: BB₁=2:3 ,BC=15 sm, BC B₁C₁ bo’lsa , B₁C₁ kesma uzunligini toping.

5.                 va  vektorlar perpendikular bo’lsa,  ning qiymati qanchaga teng bo’ladi?

1.                Hisoblang:

2.                {a_n}-arifmetik progressiyada bo‘lsa  ning qiymati nechaga teng bo‘ladi?

3.                Agar  bo‘lsa  va  ni toping.

4.                AB, AC, AD to’g’ri chiziqlar juft-jufti bilan o’zaro perpendikulyar. Agar BD=9 sm, BC=16 sm, AD=5 sm bo’lsa, CD kesma uzunligini toping.

5.                Uchlari  va  nuqtalarda bo‘lgan teng yonli uchburchakning asosidagi burchagini toping.

1.                ni hisoblang.

2.                Agar  va  bo‘lsa,  ning qiymatini qaysi oraliqqa tegishli bo‘ladi?

3.                Tenglamani yeching: , agar  bo’lsa.

4.                 aylananing absissa o‘qidan ajratgan kesma uzunligini toping.

5.                Diagonal kesimi kvadrat bo’lgan silindr yon sirtining yuzi 64  ga teng. Uning radiusini toping.

1.                 kvadrat funksiyaning nollari yig‘indisini toping.

2.                 ni hisoblang.

3.                Integralni hisoblang:

4.                Aylanaga yon tomoni 10ga, asosi  ga teng bo‘lgan teng yonli uchburchak ichki chizilgan. Aylana radiusini toping.

5.                ABCD A₁ B₁ C₁ D₁ kubning qirrasi 8 sm bo’lsa, AB₁C uchburchak perimetri va DAC₁ uchburchak yuzini toping.

1.                 ni soddalashtiring.

2.                 ning qanday qiymatlarida  va  to‘g‘ri chiziqlarning kesishish nuqtasi musbat ordinataha ega?

3.                 tenglama  oraliqda nechta ildizga ega?

4.                а (-1< a < ) ning qanday qiymatlarida uzunliklari mos ravishda 1+а, 1-2а va 2 ga teng bo’lgan kesmalardan uchburchak yasash mumkin?

5.                 va  vektorlarning skalyar ko‘paytmasini hisoblang.

1.                 funksiyaning o‘sish oralig’ini aniqlang.

2.                Soddalashtiring:

3.                Agar  bo‘lsa,  tengsizlikni yeching.

4.                 M nuqta tomoni 60sm bo’lgan muntazam ABC uchburchakning har bir uchdan 40 sm masofada joylashgan. ABC uchburchak tekisligidan M nuqtagacha bo’lgan masofani toping.

5.                Agar shar sektori asosi aylanasining radiusi 60 sm ga, sharning radiusi esa 75 sm ga teng bo‘lsa shar sektorining hajmini toping.

1.                Tenglama ildizlarining ko‘paytmasini

toping:

2.                 funksiyaning boshlang‘ich funksiyasini toping.

3.                Tenglamani yeching:

4.                O’tkir burchagi 60⁰ ga teng bo’lgan teng yonli trapetsiyaning asoslari 1:2 nisbatda. Trapetsiyaning perimetri 50 ga teng bo’lsa, uning katta asosini toping.

5.                Muntazam oltiburchakka tashqi chizilgan aylananing uzunligi  ga teng. Shu ko‘pburchakning yuzini toping.

1.                 ning qanday qiymatlarida  tengsizlik o‘rinli bo’ladi?

2.                 funksiyaning grafigiga  nuqtada o‘tkazilgan urinma va koordinata o‘qlari bilan chegaralangan yuzani toping.

3.                Agar  bo‘lsa,  ni hisoblang.

4.                Rombning diagonallari 32 va 4 sm ga teng bo’lsa, uning katta burchagining kotangensini toping.

5.                Muntazam piramidaning yon sirti to‘la sirtining 60% ini tashkil etadi. Piramidaning yon yoqlari va asos tekisligi orasidagi burchakni toping.

1.                Tenglamaning ildizlari ko‘paytmasini toping:

2.                 funksiya  funksiyaning boshlang‘ich funksiyasi,  funksiyaning hosilasini toping.

3.                 tenglama  kesmada nechta ildizga ega?

4.                Teng yonli trapetsiyaning asoslari 8 va 12 ga teng. Uning diagonallari o’zaro perpendikulyar. Teng yonli trapetsiyaning yuzini toping.

5.                Konusning yasovchisi  ga teng va u asos tekisligi bilan li burchak hosil qiladi. Konusning hajmini toping.

1.                Ifodani qiymatini toping:

2.                 funksiyani o‘sish va kamayish oralig‘ini toping.

3.                 ga teng bo‘lsa,  qiymatini toping.

4.                Rombning tomoni 6 sm, yuzi 18 ga teng bo’lsa , uning o’tmas burchagini toping?

5.                To’rtburchakli muntazam prizmaning diagonali 3,5 sm ga teng, yon yog‘ining diagonali 2,5 sm ga teng. Prizmaning hajmini toping.

1.                 yig‘indi ko‘rinishida tasvirlang va hisoblang.

2.                 va  funksiya grafiklari bilan chegaralangan yuzani hisoblang.

3.                Agar{a _n} –arifmetk progressiyada  bo‘lsa,  ni toping.

4.                To’g’ri burchakli uuchburchakning katetlaridan biri 12 sm, gipotenuzasi boshqa katetidan 6 sm katta. To’g’ri burchakli uuchburchakning yuzini toping.

5.                To’rtta nuqta berilgan.  va  vektorlar orasidagi  burchakning kosinusini toping.

1.                Ifodaning qiymati ratsional son ekanligini isbot qiling:

2.                Sistemani yeching:

3.                Hisbolang:

4.                 Ikkita o’xshash uchburchaklarning perimetrlari 18 va 36. Yuzalarining yig’indisi 30 ga teng. Katta uchburchakning yuzini toping.

5.                Silindr asosining radiusi 2 m, balandligi 3 m ga teng. O‘q kesimining diagonalini toping.

1.                Kasrni qisqartiring:

2.                 geometrik progressiyaning birinchi hadi  va maxraj  ma’lum. Agar  bo‘lsa  ni toping.

3.                Funksiyaning [-4;1] oralig‘idagi eng katta va eng kichik qiymatini toping :

4.                Uchburchakning birinchi tomoni x (х  ) sm, ikkinchi tomoni undan 4 sm qisqa, uchinchi tomoni esa birinchisidan 4 sm uzun. Shu uchburchakning perimetrini toping.

5.                To‘g‘ri burchakli parallelepiped o‘lchovlari 15 m, 50 m va 36 m. Unga tengdosh hubning qirrasini toping.

1.                Kasrni qisqartiring:

2.                Tengsizlikni yeching:

3.                Integralni hisoblang:

4.                 Rombning tomoni 4 ga, o’tmas burchagi 120⁰ ga teng. Rombning yuzini toping.

5.                Kesik konus asoslarining radiuslari 3 m va 6 m balandligi 4 m. Yasovchisini toping.

1.     Ifodani soddalashtiring: .

2.     Tenglamani yeching:

3.      integralni hisoblang.

4.     Teng yonli uchburchakning yon tomoni b ga, uchidagi burchagi 2  ga teng. Unga ichki chizilgan aylananing radiusini toping?

5.     Kubning har bir qirrasi 2 sm orttirilsa, uning hajmi 98  ortadi. Kubning qirrasi qanchaga teng?

1.                Funksiyani aniqlanish sohasini toping:

2.                Boshlang’ich funksiyani toping, agar

3.                Tenglamani yeching:

4.                 to‘g‘ri chiziq  aylanani kesib o‘tmasligini isbotlang.

5.                Ichki burchaklarini har biri  ga teng bo‘lgan muntazam ko‘pburchak nechta tomoni bor?

1.                 ifodani qiymatini 120 ga bo‘linishini isbot qiling.

2.                Funksiya hosilasini toping:

3.                 tenglama bilan berilgan aylana markazini toping.

4.                AOB burchak 40⁰, BOC burchak 80⁰. Bu ikki burchak bissektrissalari orasidagi burchakni toping.

5.                Tomoni 3,2 sm va qalinligi 0,7 sm bo’lgan muntazam sakkizburchak shaklidagi yog’och plitkaning massasi 17,3 gr. Yog’ochning zichligini toping.

1.                Tenglamani yeching:

2.                 qonuniyat bilan harakatlanayotgan moddiy nuqtaning t=2 dagi tezlik va tezlanishini hisoblang.

3.                Quyidagi chiziqlar bilan chegaralangan figura yuzini toping.

va x=e.

4.                Bir-biridan 3,4 m uzoqlikda bo‘lgan vertikal ustunlarning yuqori uchlari to‘sin bilan tutashtirilgan. Ustunlarning balandliklari 5,8 m va 3,9 m bo‘lsa, to‘sin uzunligini toping.

5.                α tekislik ABC uchburchakning AB va AC tomonlarini  va  nuqtalarda kesib o‘tadi. Agar  bo‘lsa, BC kesmaning uzunligini toping.

1.     Quyidagi ifodaning eng kichik qiymatini toping:

2.     Ushbu  funksiyaning grafigiga  nuqtada o‘tkazilgan urinmaning burchak koeffitsientini toping.

3.      funksiyaning qiymatlar sohasini topimg.

4.     Quyidagi  (parabola) va  (to’gri chiziq) larning kesishgan nuqtalari orasidagi masofani toping.

5.     Piramidaning barcha yon yoqlari muntazam uchburchaklardan iborat. Agar piramidaning to’la sirti  ga teng bo’lsa, uning yon yoqlari markazlari orasidagi masofani toping.

1.     Hisoblang:

2.     Agar  ga teng bo’lsa,  ni hisoblang.

3.      funksiyaning qiymatlar sohasini toping.

4.      va  chiziqlarning kesishish nuqtasi markazi koordinata boshida bo’lgan aylanada yotadi. Shu aylana radiusini toping.

5.     To’gri burchakli paralellelepipedning diagonali 13 sm, yon yoqlarining diagonallari  va  sm ga teng. To’gri burchakli paralellelepipedning hajmini toping.