2. funksiyaning eng katta qiymati nechaga teng

1-variant

1. y=x² va y=|x| funksiyalar grafiklarining OX o‘qida yotmaydigan kesishish nuqtalari orasidagi masofani toping.

A)2 B)2,5 C)2,3 D)1,5 E)1,8

2. funksiyaning eng katta qiymati nechaga teng?

A)–1,6 B)–1,2 C)–1,4 D)–0,8 E)–1,8

3. y=x²–8 (x≥0) funksiyaga teskari bo‘lgan funksiyaning aniqlanish sohasini toping.

A)(–8;∞) B)[–8;∞) C)(–8;8) D)[–8;8] E)(–8;8]

4. funksiyalardan qaysilari juft funksiya?

A)y₁ B)y₂ C)y₁;y₂ D)y₁;y₃ E)y₁;y₄

5. 2^|x–5|+2x=64 tenglamani yeching.

A)1,5 B)1 C)2 D)0,5 E)1,8

6. 2^3x+7+5^3x+4+2^3x+5–5^3x+5=0 tenglamani yeching.

A)1 B)0 C)–1 D)2 E)1/3

7. tenglama ildizlarining yig‘indisini toping. A)2 B)3 C)4 D)5 E)7

8. Agar 2^a=5 va 20^b=125 bo‘lsa, a ni b orqali ifodalang.

A) B) C) D) E)

9. Nechta natural son (0,7)^2+4+6+…+2n>(0,7)⁷² tengsizlikni qanoatlantiradi?

A)7 B)8 C)9 D)10 E)12

10. funksiyaning aniqlanish sohasini toping.

A)(8;9] B)[8;9] C)(–∞;0)U[8;9] D)(8;9)E)(–∞;0)U(8;9]

11. f(x)=x²+bx+c funksiyaning nollari 2 va 3 bòlsa, b ni toping. A.-6 B.6 C.5 D.-5

12. y=3x²-6x+7 kvadrat funksiyaning eng kichik qiymatini aniqlang. A.4 B.7 C.5 D.1

13. y=x² parabolani vektor bo‘yicha parallel ko‘chirganda, uning tenglamasi qanday bo‘ladi?

A)y=x²+6x+1 B)y=x²+5

C)y=x²–1 D)y=x²+9 E)y=x²+4x–9

14. f(x)=–4x²+2x–1 funksiyaning grafigi koordinatalar tekisligining qaysi choraklarida joylashgan?

A)III;IV B)I;II;III C)I;III D)II;IV E)I;II;III;IV

15. Agar bo’lsa, f(3) ni toping. A) 6 B) 12 C) 17 D) 9

16. tenglama ildizlari o’rta arifmetigini toping.

1. 
   1 B) 2 C) 3 D) 4
   

17. tengsizlikni qanoatlantiradigan eng kichik butun sonni toping.

1. 
   1 B) 2 C) 3 D) 4
   

18. Uchburchakning burchaklari 1:2:3 kabi nisbatda. Uchburchak katta tomonining kichik tomoniga nisbatini toping.A)1 B)2 C)3 D)4 E)5

19. To‘g‘ri burchakli uchburchakning katetlari 9 va 12 ga teng. Kichik katetining gipotenuzadagi proyeksiyasini toping.

A)6 B) C)5,4 D)4,8 E)

20. 20. a||b bo’lsa, x=?

x

126^o



b



43^o

A) A)87^o B) 97 ^o C) 77 ^o D)107 ^o

21. Kichik tomoni ga teng bo‘lgan uchburchakning burchaklari 1:2:3 kabi nisbatda bo‘lsa, uchburchakning perimetrini toping.

A) B) C) D) E)

22. Uchburchakning tomonlari a, b va c ga teng. Bu uchburchakning tomonlari orasida a²=b²+c²+bc munosabat o‘rinli bo‘lsa, uzunligi a ga teng tomon qarshisidagi burchakni toping.

A)60⁰ B)150⁰ C)120⁰ D)90⁰ E)135⁰

23. Teng yonli uchburchakning uchidagi burchagi β ga, asosiga tushirilgan balandligi m ga teng. Uchburchakning yon tomoniga tushirilgan balandligini aniqlang.

A) B) C)2mcosβ D)mtgβ E)

24. Uchburchak ikki tomonining nisbati 2:3 kabi. Uchinchi tomonining uzunligi 40 ga teng. uchinchi tomon qarshisidagi burchak bissektrisasi shu tomondan ajratgan katta qismining uzunligini toping.

A)25 B)22 C)26 D)28 E)24

25. Uchburchakning asosi 22 ga, yon tomonlari 13 va 19 ga teng. Asosiga tushirilgan medianasini toping.

A)18 B)12 C)16 D)13 E)14

26. O‘tmas burchakli uchburchakning tomonlari butun sonlardan iborat va ular ayirmasi 5 ga teng bo‘lgan arifmetik progressiyani tashkil etadi. Shu uchburchak eng kichik tomonining eng katta qiymati nechaga teng bo‘lishi mumkin?

A)5 B)10 C)15 D)14 E)16

27. Agar uchuburchakning asosi 20 % uzaytirilib, balandligi 20 % qisqartirilsa, uning yuzi qanday o‘zgaradi?

A)o‘zgarmaydi B)4 % kamayadi C)4 % ortadi D)6 % kamayadi E)6 % ortadi

28. Yuzi 48 ga teng bo‘lgan ABC uchburchakning AC tomoni D nuqtada AD:DC=1:7 kabi nisbatda bo‘linadi. ABD uchburchakning yuzini aniqlang.

A)4 B)6 C)5,5 D)8 E)12

29. Uchburchakning ABC tomonlari MN||AC to‘g‘ri chiziq bilan kesildi. ABC va MBN uchburchaklarning perimetrlari 3:1 kabi nisbatda. ABC uchburchakning yuzi 144 ga teng. MBN uchburchakning yuzini toping.

A)16 B)48 C)32 D)64 E)56

30. ABC uchburchak, unga AD va CE bissektrisalari tushirilgan.Agar uchburchak ABC orasisagi burchak 108° bòlsa,

A.36° B.28° C.34° D.38°

2-variant

1. Koordinata boshidan y=x² va y=1/x funksiyalarning grafiklari kesishgan nuqtagacha bo‘lgan masofani aniqlang. A)2 B)1,5 C) D) E)1

2. funksiyaning qiymatlar sohasini toping.

A)[1,6;5] B)[1,6;4] C)[1,4] D)(1;4] E)(0;5]

3. funksiyaga teskari bo‘lgan funksiyani aniqlang.

A) B)

C) D) E)

4. Quyidagilardan qaysilari o‘suvchi funksiyalar hisoblanadi?

1)y=3^x 2) 3) 4) 5)

A)1;2;4 B)1;2;3 C)3;4;5 D)2;3;4 E)1;4;5

5. 3^x+1·27^x–1=9⁷ tenglamaning ildizi 10 dan kancha kam? A)5 B)4 C)8 D)6 E)7

6. 2^5x+6–7^5x+2–2^5x+3–7^5x+1=0 tenglamani yeching.

A)1 B)2 C)3 D)0 E)0,2

7. x soni tenglamaning ildizi bo‘lsa, x+3 soni nechaga teng?

A)5 B)4 C)6 D)7 E)3

8. Agar 2^a=5 va 20^b=125 bo‘lsa, b ni a orqali ifodalang.

A) B) C) D) E)

9. 3^3x–2+3^3x+1–3^3x<57 tengsizlikni yeching.

A)x>1 B) C)x<1 D) E)

10. f(x)=log₂(64^–x–8^1–x) funksiyaning aniqlanish sohasini toping.

A)(–∞;0) B)(–∞;–1) C)(–∞;–2) D)(1;∞) E)(2;∞)

11. f(x)=x²+bx+ c funksiyaning nollari 2 va 3 bòlsa, c ni toping. A.-6 B.5 C.6 D.-5

12. y=3x²-12x+15 kvadrat funksiyaning qiymatlar tòplamini aniqlang. A.[7;+ ∞) B.[-1;+ ∞) C.[3;+ ∞) D.[2;+ ∞)

13. y=x²–4x+7 parabolani vektor yordamida parallel ko‘chirishdan hosil bo‘lgan kvadrat funksiyani yozing.

A)y=x²–8x+22 B)y=2x²–6x+10 C)y=x²–6x+10 D)y=x²–8x+7 E)y=x²–6x–10

14. y=–2x²+4x–8 funksiyaning grafigi qaysi choraklarda joylashgan?

A)II,III,IV B)I,II,III,IV C)I,III,IV D)I,II,III E)III,IV

15. funksiyalar berilgan. tenglamani yeching.

A) x=0 B) C) x=1 D) Ø

16. tenglamani yeching.

1. 
   x=1 B) x=-1 C) x=0,5 D) 2
   

17. tengsizlikni yeching

1. 
   ( ) B) C) D)
   

18. Tomonlari 10; 8 va 6 bo‘lgan uchburchakning katta tomoniga o‘tkazilgan medianasini toping.

A)7 B)6 C)3 D)4 E)5

19. To‘g‘ri burchakli uchburchakning katetlari 9 va 12 ga teng. Kichik katetining gipotenuzadagi proyeksiyasini toping.

A)6 B) C)5,4 D)4,8 E)

A) 102 ^o B) 112 ^o C) 122 ^o D)130 ^o

20. 20.a||b bo’lsa, α=?

A) A)63^o B) 45 ^o

C) 72 ^o D)77 ^o

21. ABC uchburchakda AD mediana AB va AC tomonlar bilan mos ravishda 30⁰ va 60⁰ li burchak hosil qiladi. AB= bo‘lsa, AC ni toping.

A)1 B) C) D) E)

22. Uchburchak tomonlarining uzunliklari m; n va k. tenglikni qanoatlantiradi. Uzunliklari m ga teng tomon qarshisidagi burchakni toping.

A)45⁰ B)150⁰ C)120⁰ D)90⁰ E)135⁰

23. Teng yonli uchburchakning uchidagi burchagi β ga, yon tomoniga tushirilgan balandligi h ga teng. Uchburchakning asosini toping.

A) B) C) D) E)

24. ABC uchburchakning bissektrissasi AC tomonni 28 va 12 ga teng bo‘lgan kesmalarga ajratadi. Agar AB–BC=18 bo‘lsa, berilgan uchburchakning perimetrini toping. A)42 B)80 C)85 D)72 E)75

25. Tomonlari 11, 12 va 13 ga teng bo‘lgan uchburchakning katta tomoniga tushirilgan medianasi uzunligini toping. A)10 B)9 C)8,5 D)9,5 E)8

26. O‘tkir burchakli uchburchak tomonlarining uzunliklari natural sonlardan iborat va ular ayirmasi 4 ga teng bo‘lgan arifmetik progressiyani tashkil qiladi. Shu uchburchak kichik tomonining eng kichik qiymati nechaga teng bo‘lishi mumkin?

A)8 B)15 C)14 D)12 E)13

27. Uchburchakning yuzi 6 ga teng. Shu uchburchakning 3 va 8 ga teng tomonlari orasidagi burchakni toping.

A)30⁰ B)45⁰ C)60⁰ D)60⁰ yoki 120⁰ E)30⁰ yoki 150⁰

28. ABC uchburchakda medianalar kesishgan nuqtadan AB tomongacha bo‘lgan masofa 1 ga teng. Agar AB=8 bo‘lsa, ABC uchburchakning yuzini toping.

A)12 B)16 C)9 D)13 E)10

29. ΔABC ning AB tomoni MN||AC to‘g‘ri chiziq yordamida BM=2 va AM=4 bo‘lgan kesmalarga ajratildi. Agar ΔMBN ning yuzi 16 ga teng bo‘lsa, ΔABC ning yuzi qanchaga teng bo‘ladi?

A)48 B)96 C)80 D)144 E)128

30. Uchburchakning ikkita burchagi mos ravishda 38° va 52° ga teng. Uchinchi burchak uchidan tushirilgan bissektrisa va mediana orasidagi burchakni toping.

A.10° B.14° C.7° D.17°