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
- 30 – Variant.
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29 – Variant. 1. Agar 𝑓(𝑥) = 3 𝑥+1 bo’lsa, 𝑓(𝑎 + 𝑏) quyidagilardan qaysi biriga teng? A) 𝑓(𝑎) ∙ 𝑓(𝑏) B) 𝑓(𝑎)∙𝑓(𝑏) 3
C) 𝑓(𝑎)+𝑓(𝑏) 3 D) 𝑓(𝑎) + 𝑓(𝑏) 2. Agar x haqiqiy musbat son bo’lib, 𝑥 + 3√𝑥 = 5 bo’lsa, 𝑥 + 15 √𝑥 ning qiymatini toping.
A) 9 B) 5 C) 3 D) 14
3. Agar 𝑓(𝑥) = 3 𝑥−2 bo’lsa, 𝑓(2𝑥 + 1) ni 𝑓(𝑥) orqali ifodalang. A) 27𝑓
2 (𝑥)
B) 3𝑓(𝑥) C)
9 2 𝑓(𝑥) D) 81𝑓 3 (𝑥)
4. |3𝑥 − 5| = 2𝑥 − 1 tenglamaning haqiqiy ildizlari nechta? A) 0 B) 3 C) 1 D) 2
5. ∫
cos √𝑥 √𝑥 𝑑𝑥 integralni hisoblang. A)
1 2 cos √𝑥 + 𝐶 B) −2 cos √𝑥 + 𝐶 C) − 1 2 sin √𝑥 + 𝐶 D) 2 sin √𝑥 + 𝐶 6. Agar 𝑡𝑔𝛼 + 𝑐𝑡𝑔𝛼 = 5 bo’lsa, 𝑡𝑔 2
ning qiymatini toping.
A) 5 B) 25 C) 24 D) 4
7. 𝑙𝑜𝑔 2 (𝑥 + 1) + 𝑙𝑜𝑔 2 (8 − 𝑥) ≥ 3 tengsizlikni yeching. A) (−1; 8) B) (−1; 0] ∪ [7; 8) C) (−1; 7] D) [0; 7]
8.
|𝑥−25| 𝑥 = −6 tenglamaning ildizlari yig’indisini toping. A) 25
B) − 10 7 C) – 5 D) 5
9. 𝑠𝑖𝑛 6 𝑥 + 𝑐𝑜𝑠
6 𝑥 + 3𝑠𝑖𝑛
2 𝑥𝑐𝑜𝑠
2 𝑥 − 1
ifodani soddalashtiring. A) 𝑠𝑖𝑛 2
B) 𝑐𝑜𝑠 2 𝑥 C) 1 D) 0
10.
𝑎(𝑥 + 2) 2 + 𝑏(𝑥 − 3𝑐) = −(3𝑥 2 + 8𝑥 + 48)
ayniyat bo’lsa, a+b+c ning qiymatini toping. A) 4 B) 10 C) 6 D) 3
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 11. 𝑦 = (2𝑥 − 1) 20 ∙ (sin 𝑥 − cos 𝑥) funksiyaning 𝑥 = 0 nuqtadagi hosilasini toping. A) – 39 B) 41 C) – 41 D) 39
12. ∫ 𝑥 6 ∙ ln 6𝑥 𝑑𝑥 integralni hisoblang. A)
1 49 𝑥 7 ∙ (49 ln 6𝑥 − 1) + 𝐶
B)
1 49 𝑥 7 ∙ (7 ln 6𝑥 − 1) + 𝐶
C)
1 49 𝑥 7 ∙ (7 ln 3𝑥 − 6) + 𝐶
D)
1 7 𝑥 7 ∙ (ln 3𝑥 − 1) + 𝐶
ni toping. A) 𝑓(𝑥) = 5𝑥 − 3 B) 𝑓(𝑥) = −5𝑥 + 3 C) 𝑓(𝑥) = 5𝑥 + 3 D) 𝑓(𝑥) = −5𝑥 − 3
14. Hisoblang: 0,04 ∙ 10 −9 ∙ 2,6 ∙ 10 13
A) 10,4 B) 1,04 C) 104 D) 1040 15. 130 ning 30%i bilan 45 ning 60%iga teng sonlarning ko’paytmasini toping. A) 1080 B) 1053 C) 1026 D) 999
16. Arifmetik progressiyada 𝑎 4 = 6
va 𝑎 𝑛+1 = 𝑎 𝑛 + 3 bo’lsa, progressiyaning dastlabki 12 ta hadi yig’indisini toping. A) 168 B) 158 C) 174 D) 162
17. 3 ta merganning nishonga tekkazish ehtimoli 0,8; 0;6; 0;7 ga teng bo’lsa, birinchi va uchinchi merganlarning nishonga tekkizish,ikkinchisiniki tekmasligi ehtimolini toping. A) 0,336 B) 0,664 C) 0,224 D) 0,776 18. 𝑦 = ln 𝑥 𝑥−2
funksiyaning hosilasini toping.
A) ln 𝑥 − 2 + 1 𝑥 B) ln 𝑥 + 1 𝑥
C) ln 𝑥 − 1 𝑥 D) ln 𝑥 + 1 − 2 𝑥
19. Agar 𝑃 = 𝑎 2 − 5𝑎𝑏
va 𝑄 = 𝑎 2 + 2𝑎𝑏 bo’lsa, 𝑃 + 𝑄 − 2𝑎 2 nitoping. A) −7𝑎𝑏 B) – 𝑎𝑏 C) 7𝑎𝑏 D) −3𝑎𝑏
20. 3𝑛 + 1 sonining 60%i 51 ga teng bo’lsa, n ning qiymatini toping. A) 26 B) 27 C) 28 D) 29 21. A(3,01;-2,03) nuqtalardan o’tuvchi va 𝑚 ⃗⃗⃗ (-10;20) vektorga perpendekulyar bo’lgan to’g’ri chiziq tenglamasini tuzing. A) 10y+5x+35,35=0 B) 10y-5x+35,35=0 C) 10y+5x-35,35=0 D) 10y-5x-35,35=0
22. ABC uchburchakning tomonlari uzunliklari AB=5, BC=4 va CA=4 bo’lsa, 𝐴𝐵 ⃗⃗⃗⃗⃗⃗∙𝐴𝐶 ⃗⃗⃗⃗⃗⃗ skalyar ko’paytmani hisoblang. A) 12,5 B) 2,5 C) 25 D) 12
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 23. A(3;0) va B(-1;2) nuqtalardan o’tuvchi hamda markazi 𝑦 = 𝑥 + 2 to’gri chiziqda yotgan aylana tenglamasini toping. A) (𝑥 − 3) 2 + (𝑦 − 5) 2 = 25
B) (𝑥 − 4) 2 + (𝑦 − 5) 2 = 25
C) (𝑥 − 3) 2 + (𝑦 − 4) 2 = 25
D) (𝑥 − 5) 2 + (𝑦 − 3) 2 = 25
24. Radiusi 10 ga teng yarim sharga asosining markazi bilan ustma-ust tushadigan konus tashqi chizilgan. Konusning balandligi qanday bo’lganda uning hajmi eng kichik bo’ladi. A) 10 2
B) 5 3
C)
10 3 D)15
25. To`g`ri to`rtburchakning ichidan olingan nuqtadan uning uchlarigacha masofalar ketma-ket 1, 5, 7 bo`lsa, to`rtinchi uchigacha bo`lgan masofani toping.
A) 4 B) 3 C) 5 D) 6
26. Teng yonli uchburchakning yon tomonlari 𝑎 va asosi 𝑏 ga teng bo’lsa, unga ichki va tashqi chizilgan aylana markazlari orasidagi masofani toping. A) 2
2 4
ab a b B) 2 2 2 4
ab a b C)
2 2 2 4 a ab a b D) 2 2 2 4
ab a b
27. Teng yonli uchburchakning asosi 8 ga va yon tomoniga tushirilgan medianasi 10 ga teng bo’lsa, yon tomonini toping. A) 4 15
B) 8 13
C)
4 17 D) 16
28. Katetlari 𝑎 va 𝑏 ga teng bo’lgan to’g’ri burchakli uchburchakning katta katetiga urinib shu katet qarshisidagi uch orqali o’tib, markazi gipotenuzada bo’lgan doiraning yuzini toping. A)
2 2 2 2 2 2 2 2 2
a b a b a a b
B) 2 2 2 2 2 2 2 2 2 a a b a b a a b
C) 2 2 2 2 2 2 2 2 2 a a b a b a a b
D) 2 2 2 2 2 2 2 2 2 a a b a b a a b
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 29. Uchburchakning uchta tomoni 𝑎 ga teng bo’lsa, unga ichki chizilgan aylana radiusini toping.
A) 3 5 a B) 3 6
C)
3 4
D) 2 3 5 a
30. Prizmaning asosi tomonlari 5 va 6 bo’lgan hamda o’tkir burchagi 45° bo’lgan parallelogrammdan iborat. Agar prizmaning yon qirrasi 4 ga teng va u asos tekisligi bilan 30° burchak tashkil qilsa, prizma hajmini toping.
A) 30 2
B) 32 2
C)
36 2 D) 25 2
30 – Variant.
1. Hisoblang: √98 ∙ 0,02 ∙ 2,25 A) 2,15 B) 2,25 C) 2,3 D) 2.1
2. ∫ (𝑥 − 6) 5 ∙ 𝑥𝑑𝑥
7 6
aniq integralni hisoblang. A) 0 B) 1 C) 1
1 6 D) 1 1 7
3. Arifmetik progressiyada 𝑎 2 ∙ 𝑎
3 = 60
va 𝑎
1 + 𝑎
5 = 24
o’rinli bo’lsa, progressiyaning ayirmasi va birinchi hadi ayirmasining modulini toping. A) 5 B) 7 C) 9 D) 11
tenglik o’rinli bo’lsa, n ning eng katta qiymatini toping. A) 32 B) 30 C) 28 D) 26
5. 𝑓(𝑥) 6 – darajali funksiya bo’lsa, (𝑥 − 4) 2 ∙ 𝑓(𝑥) + 4𝑥 ni 𝑥 0 = 4 nuqtadagi hosilasini toping. A) 6 B) 4 C) 8 D) 16
6. Agar 𝑓(𝑥) = 𝑘𝑥 + 3 funksiya uchun 𝑓(1) = 1 o’rinli bo’lsa, 𝑓(−1) ni toping. A) 1 B) 3 C) 5 D) 7
2 − 27)(𝑥 + 5) = (𝑥 − 3)(6𝑥 + 30)
Tenglamaning barcha ildizlarining yig’indisini toping. A) – 6 B) 2 C) – 2 D) – 3
8. Agar 𝑠𝑖𝑛𝛽 + cos 𝛽 = −1,35 ga teng bo’lsa, 𝛽 qaysi chorakda yotadi? A) I B) II C) III D) IV
9. Agar 6 𝑎 + 6
−𝑎 = 6
bo’lsa, 6 2𝑎 − 5 ∙ 6 𝑎 + 6 −𝑎 ning qiymatini toping. A) 5 B) 6 C) 4 D) 7
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 10. Chizmada 𝑓(𝑥) funksiyaning grafigi tasvirlangan. Chizmaga ko’ra qaysi biri o’rinli?
A) 𝑓
′ (5) + 𝑓(0) = 0
B) 𝑓
′ (3) + 𝑓(−2) = 0
C) 𝑓
′ (3) + 𝑓(−1) = 0
D) 𝑓
′ (4) + 𝑓(0) = 0
4 𝑥 − 𝑠𝑖𝑛
4 𝑥 tenglamani yeching. A)
𝜋 10 + 2𝜋𝑛 5 ; 𝜋 2 + 𝜋𝑛 𝑛 ∈ 𝑍 B)
𝜋 5 + 2𝜋𝑛 5 ; 𝜋 2 + 2𝜋𝑛 𝑛 ∈ 𝑍 C)
𝜋 10 + 2𝜋𝑛 5 ; 𝜋 2 + 2𝜋𝑛 𝑛 ∈ 𝑍 D)
𝜋 10 + 𝜋𝑛 5 ; 𝜋 2 + 𝜋𝑛 𝑛 ∈ 𝑍
12. | 6 4−𝑥
| ≥ 1 5 7 tengsizlikning butun yechimlari yig’indisini toping. A) 12 B) 28 C) 24 D) 21
13. ∫ sin 𝑥 ∙ 𝑐𝑜𝑠 3 𝑥 𝑑𝑥
integralni hisoblang. A)
𝑠𝑖𝑛 4 𝑥 4 + 𝐶
B) −
𝑐𝑜𝑠 4 𝑥 4 + 𝐶
C) −
𝑠𝑖𝑛 4 𝑥 4 + 𝐶
D)
𝑐𝑜𝑠 4 𝑥 4 + 𝐶
14. 0,125 ∙ 4 2𝑥−3 = (
0,25 √2 ) −𝑥 tenglamani yeching. A) 2 B) – 15 C) – 16 D) 6
15. Markazi (0;0) nuqtada bo’lgan aylanadagi 𝐴 ( √3 2 ; 1 2 ) nuqtani soat strelkasi harakati yo’nalishida aylana bo’ylab 120° ga burish natijasida hosil bo’lgan nuqtaning koordinatalarini toping.
A) (− √3 2 ; 1 2 ) B) ( √3 2
1 2 ) C) ( 0;-1) D) (-1;0)
16. Qutida T,A,O,N harflari bor. Taakkaliga olingan 3 harfni ketma – ket qo’yilganda “ONA” so’zi hosil bo’lishi ehtimolini toping. A)
1 3 B) 1 6 C) 1 24 D) 1 120
17. Tengsizlikni yeching: 𝑙𝑜𝑔 2
𝑥 − 3 < 2𝑙𝑜𝑔 2 𝑥 A) (0; 2) B) ( 1 2
C) (0; ∞) D) (0; 1 2
18. −√69 3 − √67
3 − √65
3 sonining butun qismini toping. A) -12 B) -11 C) -13 D)-25
19. ( 2 10 ∙ 2 100
∙ … ∙ 2 10 10 ) : 128
ifodani hisoblang va standart ko’sinishga keltiring. A) 80 ∙ 10 −55 B) 0,8 ∙ 10 −54
C) 8 ∙ 10 −53
D) 0,008 ∙ 10 −52
20. Tengsizlikni yeching: (√5 − 1) 𝑥2−5𝑥+4
𝑥−4 ≥ 1
A) (−∞; 1] ∪ (4; ∞) B) [1; 4) C) [1; 4) ∪ (4; ∞) D) 1; ∞)
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 21. Arifmetik progressiyaning dastlabki 4 ta hadining yig’indisi 244 ga teng. Agar 𝑎 7 − 𝑎 8 = −32 va 𝑎 𝑛 = 333 bo’lsa, n ni toping.
A) 8 B) 9 C) 10 D) 11
22. Teng yonli uchburchakning asosi 𝑎 ga va yon tomoni 𝑏 ga teng bo’lsa, uchidagi burchakning kotangensini toping. A)
2 2 4 2 b a b B) 2 a b
C) 2 2 2 2 2 4 b a a b a D) 2
a
23. Prizmaning asosi tomonlari 5 va 6 bo’lgan hamda o’tkir burchagi 45° bo’lgan parallelogrammdan iborat. Agar prizmaning yon qirrasi 12 ga teng va u asos tekisligi bilan 30° burchak tashkil qilsa, prizmaning hajmini toping. A)
81 2 B)
90 2
C) 96 2
D) 97 2
24. Bir burchagi 60° bo’lgan to’g’ri burchakli uchburchakka tomoni 𝑎 ga teng bo’lgan romb shunday ichki chizilganki, 60° li burchak ular uchun umumiy, rombning barcha uchlari rombning tomonlarida yotadi. Uchburchakning tomonlarini toping. A) 3
3 ; ;
2 2
a a B) 3 3
; 2 2 a a a
C) 3 3
3 ; ;
2 2
a a D) 3 ;
; 2 2 a a a
25. ABC uchburchakda ∠𝐶=90°, cos𝐵=5/13, AB=39 bo’lsa, 𝐴𝐶=? A) 30 B) 24 C) 36 D) 40
26. 𝑅 radiusli aylanaga trapetsiya ichki chizilgan. Trapetsiyaning pastki asosi qolgan tomonlaridan ikki marta 2 marta katta. Trapetsiyaning yuzini toping. A) 2
2 R B) 2 3 3
4 R
C) 2 3 2 R D) 2 6 3
5 R
27. 3 ta tengdosh prizmaning balandliklari nismati mos ravishda 4:9:12 kabi nisbatda bo’lsa, prizmalar asos yuzalari nisbatini aniqlang. A) 12:9:4 B) 9:4:3 C) 16:81:144 D) 8:18:24
28. To’g’ri konusning balandligi 10 ga, asosining radiusi 6 ga teng va asosining markazidan yasovchisiga eng qisqa masofadagi nuqtalardan asosga parallel tekislik o’tkazildi. Hosil bo’lgan kesik konusning kichik asosi radiusini toping. A)
75 34 B) 75 17
C) 150
17 D) 97 34
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 29. Parallelogrammning o’tmas burchagi 150° ga, tomonlari 12 va 18 ga va burchaklari bisektrissalari kesishishidan hosil bo’lgan to’g’ri to’rtburchakning yuzini toping. A) 12 B) 9 C) 8 D) 10 30. To’g’ri silindrning asosi radiusi 4 cm, balandligi 5 cm. Yon sirtidan A va B nuqtalar olingan. A va B nuqtalardan asos tekisligigacha bo’lgan masofalar mos ravishda 2 cm va 3 cm. Agar AB kesma uzunligi 5 cm bo’lsa, silindr o’qidan AB kesmagacha bo’lgan masofani toping. A) 2√6 B) 2√3 C) √10 D) √8
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly
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