Test-2019 1-Variant
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2019 yil 30 ta lik variant
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- GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI
- 27 – Variant.
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25 – Variant.
1. Agar sin 17° = 𝑥 va cos 17° = 𝑦 bo’lsa, cos 56° ni 𝑥 va 𝑦 orqali ifodalang. A) 2𝑥𝑦 B) 2𝑥 + 𝑦 C) 𝑥𝑦 C) 4𝑥𝑦
2. Agar sin 𝑥 = 𝑎 𝑏 bo’lsa,cos 2𝑥 ni toping. A) 𝑏 2 −2𝑎 2 𝑏 2 B) 𝑎 2
2 𝑎 2 C)
2𝑎 2 −𝑏 2 𝑏 2 D) 2𝑏 2 −𝑎 2 𝑏 2
3. Agar 𝑓(𝑥) = lg(lg 𝑥 4 )
′ ( 1 100 )
ni toping. A) −
25 𝑙𝑛 2 10 B) − 𝑙𝑔 2
100
C) 𝑙𝑔 2 𝑒 100
D) − 50 𝑙𝑛 2 10
4. Agar 𝑎 + 𝑏 + 𝑐 = 0 bo’lsa, 𝑎+𝑏
𝑐 + 𝑎+𝑐 𝑏 + 𝑎 𝑏+𝑐 ning qiymatini toping. A) – 3 B) – 1 C) 3 D) 0
5. Agar (2𝑥 2 − 3𝑦)
𝑛 ifoda yoyilganda, birhadlaridan biri 𝐴𝑥 6 𝑦 5 ga teng bo’lsa, n ning qiymatini toping. A) 11 B) 8 C) 9 D) 10
6. Aniqmas integralni hisoblang: ∫ 𝑑𝑥 𝑥 2 +4𝑥+20
A)
1 4 ∙ 𝑎𝑟𝑐𝑡𝑔 𝑥 4 + 𝐶 B) 1 4 ∙ 𝑎𝑟𝑐𝑡𝑔 𝑥+2
4 + 𝐶
C) 4 ∙ 𝑎𝑟𝑐𝑡𝑔 𝑥+2 4
D) 4 ∙ 𝑎𝑟𝑐𝑡𝑔 𝑥 4 + 𝐶
7. {𝑎 𝑛 } arifmetik progressiya berilgan. 𝑎 1 + 𝑎 2 + 𝑎 3 = 3
va 𝑎 1 3 + 𝑎 2 3 + 𝑎 3 3 = 9
bo’lsa, 𝑎 3 ni toping. A) 1 B) 2 C) 3 D) 4
8. Aniq integralni hisoblang: ∫ [𝑥 − [𝑥]]𝑑𝑥 10 0 A) 0 B) 10 C) 1 D) 5
9. Agar −3 < 𝑥 < −2 bo’lsa, √𝑥 2 − 5𝑥 + 11 + √𝑥 2 + 4𝑥 + 4
ni toping. A) 𝑥 − 3 B) 𝑥 + 3 . C) −𝑥 − 3 D) 3 − 𝑥
10. Agar 1 𝑥
1 𝑧
1 𝑦 bo’lsa, |𝑥 − 𝑦| + |𝑧 − 𝑦| + |−𝑥|
A) z B) 2x – z C) z – 2x D) z – 2y
11. Ko’paytuvchilarga ajrating: (𝑥 − 𝑦) 2 ∙ (𝑦 − 𝑧) + (𝑦 − 𝑥) ∙ (𝑧 − 𝑦) 2
A) (𝑥 − 𝑦) ∙ (𝑦 − 𝑧) ∙ (𝑥 − 𝑧) B) (𝑥 − 𝑦) ∙ (𝑦 − 𝑧) ∙ (𝑥 + 𝑧 − 2𝑦) C) (𝑥 − 𝑦) ∙ (𝑦 − 𝑧) ∙ (𝑧 − 𝑥) D) (𝑥 − 𝑦) ∙ (𝑦 − 𝑧) ∙ (𝑥 − 𝑧 + 2𝑦)
12. Agar 𝑥 = √2019 3 bo’lsa, (𝑥 + 1) 3
2 + 3𝑥 + 5
ni toping.
A) 2022 B) 2021 C) 2020 D) 2019
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 13. n natural son uchun 𝐸𝐾𝑈𝐾((𝑛+2)!; 𝑛!) 𝐸𝐾𝑈𝐵((𝑛+1)! ;𝑛!) = 30 o’rinli bo’lsa, n ni toping. A) 3 B) 4 C) 5 D) 7
14.
𝑥 2 +9𝑦 2 𝑥𝑦 = 6 ga ko’ra, 𝑥+2𝑦
𝑥−𝑦 ni toping. A) 3 B) 1 C) 2,5 D) 2
15. Agar 𝑓(𝑥 − 𝑎) = 3𝑥 + 5 va 𝑓(−1) = 20 bo’lsa, 𝑓(𝑎 − 5) ni toping. A) 29 B) 26 C) 25 D) 24
16. Agar 𝐴 = 2 2 + 2
4 + 2
6 + ⋯ + 2
22
bo’lsa, 2 + 2 3 + 2
5 + ⋯ + 2
17 ni A orqali ifodalang. A)
𝐴−8 32 B) 𝐴−12 32
C) 𝐴−20
32 D) 𝐴+12 32
17. Soddalashtiring: 𝑥 + 𝑥 2
3 + ⋯ + 𝑥
19 𝑥 −1 + 𝑥 −2 + 𝑥 −3 + ⋯ + 𝑥
−19
A) 𝑥 −20 B) 𝑥 20 . C) 𝑥 −20
+ 1 D) 𝑥 20 − 1
18. Agar (𝑥 + 2) 2 = 4 ∙ (𝑥 + 3) bo’lsa, (𝑥 + 3)
2 + 1 (𝑥+3) 2 ning qiymatini toping. A) 28 B) 32 C) 34 D) 36
19. Agar 𝑥 2 + 𝑥 + 1 = 0 bo’lsa, 𝑥 99 + 𝑥 98 + ⋯ + 𝑥 + 1 ning qiymatini toping.
A) x+1 B) 0 C) 1 D) 1 – x
20. 𝑓(𝑥) = 3𝑥 2 − 1 𝑥 + 7
va 𝑔(𝑥) = ∫ 𝑓(𝑥)𝑑𝑥
funksiyalar berilgan. Agar 𝑔(1) = 12 bo’lsa, 𝑔(𝑥) ni toping. A) 𝑥
3 − ln|𝑥| + 7
B) 𝑥
3 − ln|𝑥| + 7𝑥 + 4
C) 𝑥
3 + ln|𝑥| − 7𝑥 + 7
D) 𝑥
3 − ln|𝑥| + 7𝑥 − 4
21. Ikkita qo’shni burchaklar ayirmasi 30° ga teng bo’lsa, burchaklardan kichikini toping.
A) 84 ° B) 75° C) 96° D) 108°
22. Uchlari A(2;0). B(0;1) va C(0;0) nuqtalarda bo’lgan uchburchakning CM bisektrissasi o’tkazilgan bo’lsa, M nuqtaning koordinatasini toping. A) (
2√2 3 ; 2√2 3 ) B) ( 3 2√2 ; 3 2√2 )
C) ( 2 3 ; 2 3 ) D) ( 3 2 ; 3 2 )
23. Teng yonli trapetsiyaning diogonali o’tkir burchagining bisektrissasi bo’lib, katta asosi 21 ga, perimetri 54 ga teng bo’lsa, o’rta chizig’ini toping. A) 15 B) 17 C) 16 D) 18
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 24. Uchburchakli piramida asosining ikki tomoni uzunligi 9 dm va 10 dm ga teng. Ular orasidagi burchak 45°. Yon qirrasi uzunligi 20 dm ga teng. Agar yon qirrasi va asos tekisligi orasidagi burchak 30° ni tashkil etsa, piramidaning hajmini toping. A) 58√3
3 B) 30√2 C)105√2 D) 75√2
konus ichki chizilgan. Piramidaning yon yoqlari bilan asosi 60° li burchak hosil qiladi. Agar piramidaning asosiga ichki chizilgan aylananing radiusi 16 ga teng bo’lsa, konusning yon sirtini toping. A) 512𝜋 B) 256𝜋 C) 300𝜋 D) 450𝜋
18 bo’lgan uchburchakning katta tomonida va u kichik tomonlariga urinadi. Aylananing radiusini toping. A)
40√5 11 B) 40√3 11 C) 40√2 11 D) 20√5 11
27. r radiusli aylanaga tashqi chizilgan to’g’ri burchakli trapetsiya kichik tomoni
3𝑟 2 ga teng bo’lsa, trapetsiya yuzini toping. A)
9𝑟 2 4 B) 9𝑟 2 2
C) 9𝑟 2 5 D) 9𝑟 2
28. Teng tomonli uchburchak balandligi tomonidan 3 sm kichik bo’lsa, uchburchakning tomonini toping. A) 2√3 B) 6 + 2√3 C) 6 + 4√3 D) 6√3 29. To’g’ri burchakli uchburchakning to’g’ri burchagidan chiqqan medianasi bu burchakni 1:2 kabi nisbatda bo’lsa va 3 sm ga teng bo’lsa, uchburchakning yuzini toping. A) 9√3
2 B) 9√3 4
30. Teng yonli trapetsiyaning pastki asosi 30 sm ga, ustki asosi 18 sm ga teng.Bu trapetsiyaning diogonallari o’zaro perpendekulyar.Uning yuzini toping. A) 529 B)574 C) 576 D) 625
26 – Variant. 1. Agar 𝑓 (𝑥 + 1 𝑥
3𝑥 2 +3 4𝑥 + 3
bo’lsa, 𝑓(8) ning qiymatini toping. A) 15 B) 9 C) 14 3 D) 7 3
2. Agar 𝑎√𝑎 − 10√𝑎 = 3 bo’lsa, √𝑎 + 1 √𝑎 ning qiymatini toping. A) 3 B) 9 C) √13 D) √11
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 3. Hisoblang. 𝑠𝑖𝑛 2
2 10° + 𝑠𝑖𝑛 2 15° + ⋯ + 𝑠𝑖𝑛 2 180°
A) 19 B) 18 C) 17 D) 16
4. Agar √5−5 √10−3
= 𝑥 bo’lsa, 3+√10 √5+1
ni x orqali ifodalang. A) 𝑥
B) 𝑥 √5 C) − 4𝑥 √5 D) − 𝑥 4√5
5. Agar ∫ 𝑥 ∙ 𝑓(𝑥)𝑑𝑥 = 𝑥+1 𝑥 tenglik o’rinli bo’lsa, 𝑓(𝑥) funksiya javoblardan qaysi biriga teng? A) − 1
3 B) − 1 𝑥
C) −
1 𝑥 D) – 𝑥 6. 5𝑥
2 − (7𝑚 − 1)𝑥 − 11 = 0
tenglamaning ildizlari 𝑥 1 𝑣𝑎 𝑥
2 . Agar
𝑥 1 = −𝑥 2 bo’lsa, 𝑚 ning qiymatini toping. A) −
1 7 B) − 7 5 C) 1 7 D) 0 7. {
𝑥 − 2𝑦 + 𝑧 = −1 2𝑥 + 3𝑦 − 𝑧 = 6 3𝑥 + 𝑦 + 𝑧 = 7 tenglamalar sistemasining ildizlari yig’indisini toping.
A) 2 B) 3 C) 4 D) 5
mumkin. Agar sayyoh borgan yo’li orqali qaytmasa, sayyoh necha xil usulda tog’ga chiqib tushishi mumkin? A) 9 B) 81 C) 72 D) 64
9. – 5; 11; x; - 2 sonlarining o’rta arifmetigi y ning 1 5 qismiga teng va 3𝑥 − 4𝑦 = −44 bo’lsa, 𝑦 ning qiymatini toping.
A) 30 B) 20 C) 40 D) 12.
10. Tenglamani yeching: 3 2+𝑥
− 3 2−𝑥
= 80
A) – 2 B) 2 C) 0 D) 2; - 2 11. Hisoblang: 𝑡𝑔5° ∙ 𝑡𝑔10° ∙ 𝑡𝑔15° ∙ … ∙ 𝑡𝑔80° ∙ 𝑡𝑔85°
A) – 1 B) 1 C) 0 D) 0,5 12. 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
funksiya grafigi I, II, IV choraklardan o’tishi ma’lum bo’lsa, 𝑎, 𝑏 𝑣𝑎 𝑐 larni nol bilan taqqoslang. A) 𝑎 > 0; 𝑏 > 0; 𝑐 > 0 B) 𝑎 < 0; 𝑏 > 0; 𝑐 < 0 C) 𝑎 > 0; 𝑏 < 0; 𝑐 > 0 D) 𝑎 > 0; 𝑏 < 0; 𝑐 < 0
13. |5𝑥 − 2| = 4 − 3𝑥 tenglamaning haqiqiy ildizlari nechta? A) 0 B) 1 C) 2 D) 3 GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 14. 𝑦 = 𝑘𝑥 + 𝑙 funksiya l ning qanday qiymatida toq funksiya bo’ladi? A) -1 B) 0 C) 1 D) 2
15. ∫ cos √𝑥 3 √𝑥 2 3 𝑑𝑥 integralni hisoblang. A) 3cos √𝑥 3 + 𝐶
B) − 1 3 cos √𝑥 3 + 𝐶 C) 3sin √𝑥 3 + 𝐶
D) − 1 3 sin √𝑥 3 + 𝐶
16. Agar 𝑡𝑔𝛼 + 𝑐𝑡𝑔𝛼 = 3 bo’lsa, 𝑐𝑡𝑔 2 𝛼 − 2𝑐𝑡𝑔𝛼 + 𝑡𝑔𝛼 ning qiymatini toping.
A) 3 B) 2 C) 1 D) 0
17. Alida 36000 so’m, Valida 24000 so’m pul bor. Vali Aliga pulining necha foizini bersa, Alining puli Valining pulidan ikki marta ko’p bo’ladi? A) 25 B) 16 2 3
C) 33 1 3 D) 50
18. (𝑥 2 −𝑥+1)∙(4−𝑥) 3 (𝑥−5)
2 ∙(𝑥+1)
≥ 0 tengsizlikning butun yechimlari nechta? A) 6 B) 7 C) 4 D) 5
19. 𝑦 = √4𝑥 + 3 grafikka absissa o’qini (− 15 4 ; 0)
nuqtadan kesib o’tuvchi urinma o’tkazilgan bo’lsa, urinmaning urinish nuqtasini toping. A) (
11 4 ; √14) B) ( 7 4 ; √10)
C) ( 13 4 ; 4) D) ( 9 4 ; 2√3)
20. Hisoblang: 3 − √14 + 9√70 14√5−5√14 − √5
A) 2 B) 3 C) 4 D) 5 21. Ikkita qo’shni burchaklar ayirmasi 30° ga teng bo’lsa, burchaklardan kattasini toping.
A) 84 ° B) 105° C) 96° D) 75°
22. Bir burchagi 60 o bo’lgan to’g’ri burchakli uchburchakka tomoni 6 sm ga teng bo’lgan romb shunday ichki chizilganki, 60 o
barcha uchlari uchburchakning tomonlarida yotadi.Uchburchakning yuzini toping. A) 27√3
2 B) 81√3 2
C) 243 3
4 D)
81 3
4
23. Uchburchak uchlarining koordinatalari A(-4;2), B(6;5),C(1;-4). A uchidan tushirilgan balandligi orqali o’tuvchi to’g’ri chiziq tenglamasini tuzing. A) 5
5 0
y B) 5 9 2 0
y C)
5 9 2 0 x y D) 5 9 5 0
y GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 24. Teng yonli uchburchakning yon tomoni 10 ga teng, asosi 16 ga teng. Uchburchakka tashqi va ichki chizilgan aylanalar markazlari orasidagi masofani toping. A) 5 B) 2 C) 7 D) 6
25. Og’ma prizma asosi parallelogrammdan iborat. Tomonlari a=3, b=5, asosdagi burchak
45° ,yon qirrasi c=4. Yon qirra va asos tekisligi orasidagi burchak 𝛽 = 30° bo’lsa, prizma hajmini hisoblang. A) 14 2
B) 15 2
C) 20 2
D) 18 2
26. ABC uchburchakning tomonlari uzunliklari AB=5 va BC=4 va AC=4 bo’lsa, 𝐶𝐴 ⃗⃗⃗⃗⃗⃗ ∙ 𝐶𝐵 ⃗⃗⃗⃗⃗⃗ skalyar ko’paytmani hisoblang. A) 3.5 B) 4 C) 4.5 D) 5
27. Radiusi 3 ga teng bo’lgan aylanaga ikkita AB va AC urinmalar o’tkazilgan bo’lib, bunda A nuqta aylana markazidan 4 ga teng masofada joylashgan. Berilgan aylanaga, AB va AC urinmalarga urinuvchi aylana(hosil bo’lgan yangi aylananing radiusi berilgan aylananing radiusidan katta)ning radiusini toping. A) 19 B) 20 C) 21 D) 22
28. To’g’ri burchakli trapetsiyaning diogonali kata yon tomoniga teng, balandligi 6, kata yon tomoni 12 ga teng bo’lsa, uning o’rta chizg’ini toping. A)
7 3 B)
6 3 C)
8 3 D)
9 3
29. ABDCA 1 B 1 C 1 D 1 to’g’ri burchakli parallelepiped berilgan. AB=8, BC=2, BB 1 =6 bo’lsa, ABCDB 1 C 1 ko’pyoqli figuraning to’la sirtiyuzini toping. A) 76 B) 96 C) 76 + 4√10 D) 76 + 9√10 30. Teng yonli uchburchakning asosidagi burchagi 30 o ga, yuzi 4√3 ga teng bo’lsa, uning uchidan tushirilgan balandligini toping. A) 4 B) 3 C) 2 D) 2,5
27 – Variant. 1. 𝑦 = 𝑥
2 + 4𝑥 − 7
funksiyaning eng kichik qiymati 𝑎 ga teng bo’lsa, 𝑓(𝑎) ning qiymatini toping. A) – 2 B) 60 C) 70 D) – 11
2. 𝑦 = |𝑥 − 1| ∙ 6 𝑥 funksiya hosilasining noldagi qiymatini toping. A) −1 + ln 6 B) 1 + ln 6 C) −1 − ln 6 D) 1 − ln 6
3. 𝐴 = {𝑥| 𝑥 2 < 64; 𝑥 ∈ 𝑅}
𝐵 = {𝑥| 𝑥 2 > 9; 𝑥 ∈ 𝑁} bo’lsa, 𝑛(𝐴 ∩ 𝐵)
ni toping. A) 5 B) 4 C) 8 D) 10
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 4. 2𝑐𝑜𝑠
2 𝑥 =
2+√3 2 tenglamaning eng kichik musbat yechimini toping. A)
𝜋 12 B) 𝜋 8 C) 𝜋 6 D) 𝜋 15
5. 1 kg mis 12000 so’m. 1 kg qo’rg’oshin 18000 so’m. Mis va qo’rg’oshindan mos ravishda 4:1 kabi nisbatda olinib, 1 kg aralashma hosil qilindi. Hosil bo’lgan aralashma narxini toping. A) 14200 B) 13500 C) 15300 D) 13200
6. (𝑥
2 + 8𝑥 + 15) ∙ √4𝑥 − 9 ≤ 0
tengsizlikni yeching. A) [−5; −2] ∪ [ 9 4 ; ∞) B) [−5; −2] C) [ 9
; ∞) D) { 9 4
7. 𝑥
2 ∙ |𝑥 − 1| + 𝑥 2 − 2𝑥 + 1 ≤ 0 tengsizlik nechta butun yechimga ega? A) 0 B) 1 C) 2 D) 3
8. 𝑦 = −𝑥 va 𝑦 = 𝑥 2 − 3𝑥 + 2
funksiyalar orasidagi eng kichik masofani toping. A) √2
B) √2 2 C) 3√2
5 D) 2
9. 𝑦 = 27 𝑙𝑜𝑔 3 𝑥 − 3 funksiyaning qiymatlar sohasini toping. A) (0; ∞) B) (−3; 0) C) (−3; ∞) D) (0; 3)
10. 𝑦 = (𝑥 − 1) 20 ∙ (sin 𝑥 + cos 𝑥)
funksiyaning 𝑥 = 0 nuqtadagi hosilasini toping. A) 21 B) – 19 C) – 21 D) 19
11. ∫ 𝑥 3 ∙ ln 3𝑥 𝑑𝑥 integralni hisoblang. A)
1 16 𝑥 4 ∙ (4 ln 3𝑥 − 1) + 𝐶
B)
1 16 𝑥 4 ∙ (ln 3𝑥 − 1) + 𝐶
C)
1 4 𝑥 4 ∙ (4 ln 3𝑥 − 1) + 𝐶
D)
1 16 𝑥 4 ∙ (2 ln 3𝑥 − 1) + 𝐶
qolganini Samarqandga jo’natishni necha xil usulda amalda oshirish mumkin? A) 300 B) 336 C) 330 D) 320
13. Aniq integralni hisoblang: ∫ [𝑥] [𝑥]
𝑑𝑥 4 1 A) 32 B) 5 C) 27 D) 36
14. Agar lg(𝑎 − 𝑏) = lg 𝑎 + lg 𝑏 bo’lsa, a ni b orqali ifodalang. A)
1−𝑏 𝑏 B) 1−𝑏 1+𝑏
C) 𝑏 1−𝑏 D) 𝑏 1+𝑏 15. Agar 𝑎 + 𝑏 + 𝑐 + 𝑑 = 0 bo’lsa, 𝑎+𝑑 𝑏+𝑐
+ 𝑑+𝑐
𝑎+𝑏 − 𝑎+𝑏 𝑐+𝑑 ning qiymatini toping. A) – 3 B) – 1 C) 3 D) 0
16. Agar (𝑥 2 − 𝑦
3 ) 𝑛 ifoda yoyilganda, birhadlaridan biri 𝐴𝑥 8 𝑦
ga teng bo’lsa, A ning qiymatini toping. A) 35 B) – 28 C) 28 D) – 35
17. Agar 𝑥 + 𝑦 + 𝑧 = 3𝜋 bo’lsa, 𝑡𝑔𝑥+𝑡𝑔𝑦+𝑡𝑔𝑧 𝑡𝑔𝑥∙𝑡𝑔𝑦∙𝑡𝑔𝑧 ning qiymatini toping. A) 2,5 B) 1 C) 2 D) 0,5
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 18. Taqqoslang: 𝑥 = √9!−8!
√8! ; 𝑦 = √8!+7! √7!
; 𝑧 = √7!+6! √6!
A) 𝑥 > 𝑦 > 𝑧 B) 𝑧 > 𝑦 > 𝑥 C) 𝑥 = 𝑧 < 𝑦 D) 𝑥 = 𝑧 > 𝑦
19. Agar 𝑙𝑜𝑔 18 48 = 𝐴
bo’lsa, 𝑙𝑜𝑔 3 2 ni a orqali ifodalang. A) 𝐴−1
𝐴+4 B) 2𝐴+1 4−𝐴
C)
2𝐴−1 4−𝐴
D) 4𝐴−1
𝐴+1
20. 3, 9, 9, 27, 27, 27, 81, 81, 81, 81, … ketma – ketlikning 40 – hadi A, 15 – hadi B ga teng bo’lsa, 𝐴 𝐵 ni toping. A) 81 B) 9 C) 27 D) 243
21. Agar 𝑎⃗(−1; 5; 𝑥) 𝑣𝑎 𝑎⃗(1; 5; −7) vektorlar perpendikulyar bo’lsa, x ning qiymatini toping. A) 24
B)
3 3 7 C)
7 24 D) 7 24 22. Teng yonli trapetsiyaning pastki asosi 36 𝑠𝑚 ga, ustki asosi esa 50 𝑠𝑚 ga teng. Bu trapetsiyaning diagonallari o’zaro perpendikulyar. Uning yuzini toping. A) 1850 B) 1849 C) 1847 D)1851
23. Bir burchagi 60° bo’lgan to’g’ri bur- chakli uchburchakka tomoni 6 sm ga teng bo’lgan romb shunday ichki chizilganki, 60° li burchak ular uchun umumiy, rombning barcha uchlari uchburchakning tomonlarida yotadi. Uchburchakning yuzini toping. A) 27√3
2 B) 81√3 2
C) 81√3
4 D) 81√3 8
24. Uchburchak uchlarining koordinatalari (−4; 2);(6;5);𝐶(1;−4).𝐴 uchidan tushirilgan balandligi orqali o’tuvchi to’g’ri chiziq tenglamasini tuzing
. A) 5x-9y+2=0 B) 5x+9y+2=0 C) 9y-5x-2=0 D) 5x+9y-2=0
25. Og’ma prizmaning asosi parallelogramlardan iborat bo’lib, uning asosi tomonlari 5 va 4 ga va ular orasidagi burchak 45° ga teng. Yon qirrasi uzunligi 4 ga va asos tekisligi bilan 30° li burchak tashkil qiladi. Prizmaning hajmini toping. A) 18 2
B) 24 C)
20 2 D) 25
26. Teng yonli uchburchakning yon tomoni 20 ga, asosidagi burchak kosinusi 2√6 5
tushirilgan balandligini toping. A) 4 B) 5 C) 6 D) 5.5
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 27. Perimetri 36 sm bo’lgan parallelogramda diagonallar o’tkazilgan. Ikkita qo’shni uchburchaklar perimetrlari orasidagi ayirma 10 sm ga teng. Parallelogramning tomonlari uzunliklarini toping. A) 14,6 B) 14;4 C)12;6 D) 8;10
28. 𝑎⃗(−1;5;𝑥) va 𝑏⃗(−1; −2; −5) vektorlar uchun 𝑎⃗⊥𝑏⃗ bo’lsa, 𝑥 ni toping. A)
9 5 B) 4 5
C) 5 9 D)
5 4
29. Trapetsiyaning o’rta chizig’i 36 ga, asoslari ayirmasining moduli 10 ga teng teng bo’lsa, uning asoslarini toping. A) 40; 32 B) 41; 31 C) 42; 30 D) 44; 28
30. Aylana to’g’ri burchakli uchburchakning katta katetiga urinib, shu katet qarshisidagi burchak uchidan o’tadi, markazi esa gipotenuzada yotadi. Agar katetlarining uzunliklari 6 va 8 bo’lsa, aylana uzunligini toping. A)
7, 5 B) 10
C) 12, 5
D)
5
1. Agar 𝑀 = 1 − 2 + 2 2 − 2 3 + ⋯ + 2
8 − 2 9 bo’lsa, 1 − 2 + 2 2 − 2
3 + ⋯ + 2
6 − 2
7
ni M orqali ifodalang. A) 𝑀+1
4 B) 𝑀−1 4
𝑀+3 4 D) 𝑀 4
2. Agar 3 𝑥 = 5
𝑦 bo’lsa, 9 𝑥 𝑦
𝑦 𝑥 ni toping. (x va y haqiqiy sonlar ). A) 1 B) 2 C) – 4 D) – 2
3. a, b va c musbat butun sonlardir. Agar 𝑎 + 𝑏 = 10 va 𝑏 + 𝑐 = 14 bo’lsa, 𝑎 ∙ 𝑏 ∙ 𝑐 ko’paytmaning eng katta qiymatini toping.
A) 225 B) 240 C) 162 D) 96
4. Ifodaning birlar xonasidagi raqamini aniqlang. 0! + 2! + 4! + 6! + ⋯ + 34! A) 1 B) 5 C) 7 D) 6
5. (𝑛 + 2)! = 20 ∙ 𝑛! bo’lsa, n ni toping A) 6 B) 10 C) 3 D) 4
6. Quyida keltirilgan tasdiqlangan nechtasi to’g’ri ? 1) 2
13 − 3
10 toq son 2) 3 8
7 toq son 3) 4 −2
juft son 4) 8
0 + 1
toq son A) 0 B) 2 C) 1 D) 3
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 7.
𝑙𝑜𝑔 2 (7𝑥+1)−1 𝑙𝑜𝑔 2 (𝑥−2)+𝑙𝑜𝑔 2 4 = 1 tenglamani yeching. A) 17 B) 43 18 C)
25 12 D) 1 6
8. Agar 4 cos 𝑥 − 6 sin 𝑥 = 0 bo’lsa, |sin 2𝑥| ning qiymatini toping. A) 1
B) 12 13 C) 9 13 D) 3 4
9. Agar 𝑙𝑜𝑔 5 25! = 𝑥
bo’lsa, 𝑙𝑜𝑔 5 24! ni x orqali ifodalang. A) x – 4 B) x+2 C) x – 2 D) x
10. Agar sin 85° = 𝑎 bo’lsa, sin 80° ni a orqali ifodalang. A) 1 − 2𝑎 2 B) 2𝑎 2 − 1
C) √
𝑎−1 2 D) 𝑎−1 2
11. Agar 𝑙𝑜𝑔 (𝑥+6) ((𝑛 − 2)𝑥 + 𝑚 + 3) bo’lsa, m+n ni toping. A) 0 B) 8 C) 3 D) 6
12. 124! – 13!+13 sonining mezonini toping. A) 3 B) 5 C) 4 D) 8
13. Soddalashtiring: sin 7°∙cos 17°∙𝑡𝑔27°∙𝑐𝑡𝑔37° sin 73°∙cos 83°∙𝑡𝑔53°∙𝑐𝑡𝑔63°
A) 2 B) 1 C) 0,5 D) 0,25 14. Aniqmas integralni hisoblang: ∫ 𝑐𝑜𝑠
3 𝑥𝑑𝑥
A) sin 𝑥 + 1 3
3 𝑥 + 𝐶
B) sin 𝑥 + 𝑠𝑖𝑛 3 𝑥 + 𝐶
C) 𝑠𝑖𝑛𝑥 − 1 3
3 𝑥 + 𝐶
D) sin 𝑥 − 𝑠𝑖𝑛 3 𝑥 + 𝐶
15. Tengsizliklar sistemasini yeching: { 3𝑥 2 − 5𝑥 − 2 ≥ 0 3𝑥−1
𝑥 < 0
A) ( 1 3 ; 2] B) [2; ∞) C) (0; 1
) D) ∅
16.
3 𝑥 ∙|𝑥−2|∙(𝑥 2 −7𝑥+10)
25−𝑥 2 ≥ 0 tengsizlikni qanoatlantiruvchi yechimlar to’plamini toping. A) [−5; 2] B) (−5; 2] C) (0; 5) D) [0; 2]
17. Tenglamani yeching: 4 1+𝑥
− 4 1−𝑥
= 15
A) 4 B) – 1 C) 1 D) 1; - 1 18. Agar 𝑓(2𝑥 + 1) = 4 ∙ 𝑓(7) − 9 va 𝑔(𝑥) = 𝑥 2 − 2𝑥 + 5 bo’lsa, 𝑔(𝑓(13)) ni toping.
A) 8 B) 13 C) 29 D) 50
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 19. 𝑦 = 𝑥 2 − 6𝑥 + 4
funksiyaning eng kichik qiymati 𝑎 ga teng bo’lsa, 𝑓(𝑎) ning qiymatini toping. A) 60 B) 49 C) 58 D) 59
20. Hisoblang: sin 2°+sin 4°+sin 6°+⋯+sin 88° cos 2°+cos 4°+cos 6°+⋯+cos 88°
A) 0 B) 1 C) – 1 D) – 2 21. Aylana to’g’ri burchakli uchburchakning katta katetiga urinib, shu katet qarshisidagi burchak uchidan o’tadi, markazi esa gipotenuzada yotadi. Agar katetlarining uzunliklari 6 va 8 bo’lsa, aylana diametrini toping. A) 12,5 B) 7,5 C) 5 D) 10
22. Soatning soat mili 15 ° ga burilsa minut mili necha gradusga buriladi? A) 180 B) 30 C) 150 D) 120
23.
O‘lchamlari 80x40x10 𝑠𝑚 bo’lgan to’g’ri burchakli parallelepiped shaklidagi mis g’o’lasidan qalinligi 1 𝑚𝑚 bo’lgan tunuka taxtasi tayyorlandi. Bu tunuka taxtaning yuzini toping. A)
2 32 m
B) 2 32000 dm C)
2 0, 032 km D) 2
24 . ABC uchburchakning tomonlarining uzunliklari AB=5, BC=4, AC=6 bo‘lsa, 𝐵𝐴 ⃗⃗⃗⃗⃗⃗ ∙ 𝐵𝐶 ⃗⃗⃗⃗⃗⃗ skalyar ko‘paytmani hisoblang. A)-2,5 B) 0,5 C) 2,5 D) 1,25
25. Teng yonli ABCD trapetsiyada AC dioganal CD tomonga perpendikulyar. Agar AD = 4, |AB| 2 +|BC|
2 = 11 bo‘lsa, |AB| ni toping. A) 3 B) √2 C) 2 D) 1,5
26. Uchburchakli piramidaning asosining tomonlari 6, 6 va 8 ga teng. Asosidagi barcha ikki yoqli burchaklari 45° ga teng bo’lsa, piramidaning balandligini toping. A) 2 5
5 B) 3 6 5
C) 4 5
5 D) 2 10 5
27. Muntazam uchburchakka tomoni uzunligi 1 ga teng bo’lgan kvadrat ichki chizilgan. Uchburchakning peremetrini toping. A) 7 3
1 5 B) 7 3
1 6 C)
7 3 1 12 D) 3 2 3
28. (2; −3) nuqtani Ox o’qiga nisbatan simmetrik bo’lgan nuqtasini toping. A) (-2;-3) B) (2;3) C) (3;2) D) (-3;2)
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 29. To’g’ri burchakli uchburcha katetlari a va b ga teng, hamda a tomon qarshisidagi o’tkir burchak x ga teng bo’lsa, sinx ni toping. A)
a b B)
b a C)
2 2
a b D) 2 2
a b
30. ABC uchburchakning tomonlari uzunliklari AB=5, BC=4 va CA=4 bo’lsa, 𝐶𝐴 ⃗⃗⃗⃗⃗⃗ ∙𝐶𝐵
⃗⃗⃗⃗⃗⃗ skalyar ko’paytmani hisoblang. A) 2,5 B) 3 C) 3,5 D) 4
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