[1; 200] sonlar to’plamida nechta natural son 4 ga (qoldiqsiz) bo’linib, 6 ga
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@ALPHRAGANUS MATEM IMTIHON2019 010819124311
JIZZAX-2019
@alphraganus – matematik kanal 30.07.2019 MATEMATIKA UU/2
natural son 4 ga (qoldiqsiz) bo’linib, 6 ga (qoldiqsiz) bo’linmaydi? 𝐴)50 𝐵)34 𝐶)42 𝐷)17 2. Koordinata o’qlarining (2;0) va (0;3) nuqtalaridan o’tadigan chiziqli funksiyani toping. 𝐴)𝑦 = 1,5𝑥 + 3 𝐵)𝑦 = −1,5𝑥 − 3 𝐶)𝑦 = −1,5𝑥 + 3 𝐷)𝑦 = 1,5𝑥 − 3
3. 𝑦 = 𝑥 2 − 5𝑥 + 3 kvadrat funksiyaning ordinatalar o’qiga nisbatan simmetrik funksiyasini aniqlang. 𝐴)𝑦 = 𝑥 2
2 + 5𝑥 + 3 𝐶)𝑦 = −𝑥 2 + 5𝑥 − 3 𝐷)𝑦 = −𝑥 2 − 5𝑥 − 3
4. 𝑎 sonining 24%i 40 ning 3 5 qismiga teng. 𝑎 ning 1 4 qismi 15 sonidan qancha ko’p? 𝐴)15 𝐵)10 𝐶)25 𝐷)20 5. Integralni hisoblang. ∫ (𝑥 2
3 (2𝑥 − 1)𝑑𝑥 2 1
𝐴)15 𝐵)10 𝐶)25 𝐷)20 6. Agar 𝑦 = 𝑙 𝑛(5𝑥 + 1) 2 − 𝑙 𝑛(2𝑥 + 1) 5 + 4 funksiyaning grafigiga (𝑥 0 ; 𝑦
0 ) nuqtada o’tkazilgan urinma 𝑂𝑥 o’qiga parallel bo’lsa, √𝑥 0 2 + 𝑦 0 2 ni toping. 𝐴)3 𝐵)4 𝐶)5 𝐷)6 7. Markazi (0; 0)
nuqtada bo’lgan
aylanadagi 𝐴(0; 2) nuqtani soat mili harakati yo’nalishida aylana bo’ylab 30 °
nuqtaning koordinatalari yig’indisini toping.
𝐴)1 𝐵)1 + √3 𝐶)2 𝐷)1 − √3 8. Kollinear bo’lmagan 𝑎⃗ va 𝑏⃗⃗ vektorlar berilgan. Agar −3𝑎⃗ + 𝑥𝑏⃗⃗ = 𝑦𝑎⃗ + 2𝑏⃗⃗ o’rinli bo’lsa, 𝑥 va 𝑦 ning qiymatini toping. 𝐴)𝑥 = −3, 𝑦 = 2 𝐵)𝑥 = 3, 𝑦 = −2 𝐶)𝑥 = 2, 𝑦 = −3 𝐷)𝑥 = −2, 𝑦 = 3
9. Agar a va b ratsional sonlar uchun 𝑎 + 𝑏 √2 2 = 5 bo’lsa, u holda 𝑎 2 + 𝑏
2
ifodaning qiymatini toping. 𝐴)15 𝐵)10 𝐶)25 𝐷)20
10. Ifodani soddalashtiring(𝑎 ∈ (−2; 2)). |𝑎 2 − 16| 4 − 𝑎 − |𝑎 2 − 9|
3 + 𝑎 − |4 − 𝑎 2 | 2 − 𝑎 𝐴)𝑎 − 6 𝐵)𝑎 − 1 𝐶) − 3(𝑎 + 1) 𝐷)2 − 𝑎
11. Tengsizliklar sistemasi nechta butun yechimga ega? { 𝑙𝑜𝑔 1 2 (𝑥 − 3) 2 > −2
(𝑥 − 2) 2 ≥ 4 𝐴)𝑐ℎ𝑒𝑘𝑠𝑖𝑧 𝑘𝑜′𝑝 𝐵)𝑏𝑢𝑡𝑢𝑛 𝑦𝑒𝑐ℎ𝑖𝑚𝑔𝑎 𝑒𝑔𝑎 𝑒𝑚𝑎𝑠 𝐶)1 ta 𝐷)3 ta
12. Hisoblang. 512 ∙ (2 6 ) 4 (2 5 ) 5 ∙ 64 ∙ (4 −2 ) −2 ∙ 8
−4
𝐴)16 𝐵)0,125 𝐶)0,25 𝐷)4 13. Tengsizlikni yeching. 3 𝑥+2
− 81 3 𝑥+1 − 9 ≥ 3
𝐴)(1; ∞) 𝐵) ( 1 3 ; ∞) 𝐶)(−∞; 1) 𝐷)(0; 1)
14. Ifodani soddalashtiring. 𝑠𝑖𝑛2𝛼 1 + 𝑐𝑜𝑠2𝛼 ∙ 𝑐𝑜𝑠𝛼
1 + 𝑐𝑜𝑠𝛼 − 1 − 𝑐𝑜𝑠𝛼 𝑠𝑖𝑛𝛼 − 1
𝐴)𝑐𝑜𝑠𝛼 − 1 𝐵) − 1 𝐶)𝑡𝑔𝛼 − 1 𝐷)𝑠𝑖𝑛𝛼 − 1
15. Tengsizlikning barcha butun
yechimlari yig’indisini toping. 𝑥 − 3
√9𝑥 + 18 − 2𝑥 2 ≤ 0 𝐴)5 𝐵)11 𝐶)9 𝐷)6 16. Merganning nishonga tekkizish ehtimoli 0,6 ga teng. U nishonga 2 marta o’q uzganda o’qlaridan biri nishonga tegishining ehtimolligini toping.
𝐴)0,6 𝐵)0,24 𝐶)0,48 𝐷)0,5 17. To’g’ri konusning balandligi 5 cm va asos radiusi 3cm. Uning yon sirtida joylashgan asosining markaziga eng JIZZAX-2019
@alphraganus – matematik kanal yaqin bo’lgan nuqtalar orqali tekislik o’tkazilgan. Hosil
bo’lgan kesik
konusning kichik asosi yuzini katta asosi yuziga nisbatini toping. 𝐴) 15
𝐵) 25 34 𝐶) 625
1156 𝐷) 112 289
18. Ifodani soddalashtiring(𝑥 > 0). √ 9 − 4√5
5𝑥 4 ∙ (5√𝑥 + √20𝑥) 0,5 ∙ 2
−1
𝐴)√ 5 17 𝐵)1 𝐶) 3 √17
𝐷)0,5 19. Ko’phadlarni ko’paytiring. (3𝑎 + 5)(4𝑎 − 3) 𝐴)12𝑎
2 + 29𝑎 − 15 𝐵)12𝑎 2 + 11𝑎 − 15 𝐶)12𝑎 2 − 11𝑎 − 15 𝐷)12𝑎 2 − 29𝑎 − 15
20. Rasmda 𝐴𝐵𝐶 uchburchak va uning 𝐵𝐷 bissektrisasi tasvirlangan. Agar 𝐴𝐵 = 8 va 𝐵𝐶 = 10 bo’lsa, 𝐷𝐶: 𝐴𝐶 nisbatini toping.
𝐴) 4 9 𝐵) 5 9
4 5 𝐷) 9 5
21. 𝑎 soni quyidagilardan qaysi biriga teng bo’lganda 𝑎; 𝑎 + 4 va 𝑎 + 6 sonlar tub sonlar bo’ladi? 𝐴)13 𝐵)19 𝐶)11 𝐷)17 22. 𝑛 natural
sonning qanday
qiymatlarida 2 +
1 𝑛+ 2 3 = 13 5
tenglik o’rinli bo’ladi? 𝐴)3 𝐵)4 𝐶)2 𝐷)1 23. 𝑓(𝑥) = 15 4𝑥 2 + 12𝑥 2 5 funksiyaning eng kichik qiymatini toping. 𝐴)7 𝐵)8 𝐶)6 𝐷)5 24. Arifmetik progressiyani tashkil etuvchi
𝑛 + 3; 𝑛 + 9; 𝑛 + 15; … ; 𝑛 + 123 ketma-ketlikning o’n birinchi hadi 67 ga teng bo’lsa, bu ketma- ketlikning to’rtinchi hadini toping. 𝐴)25 𝐵)19 𝐶)24 𝐷)22
25. Hisoblang. (𝑡𝑔 7𝜋 24 + 𝑡𝑔 5𝜋 24 ) ∙ 𝑐𝑜𝑠 𝜋 12 + 2 𝐴)1 𝐵)3 𝐶)4 𝐷)2 26. 𝛼 tekislik va uni kesib o’tadigan 𝐴𝐵 kesma
berilgan. Kesmaning uchlaridan 𝛼 tekislikkacha bo’lgan masofalar 𝐴𝐴 1 = 19 𝑐𝑚, 𝐵𝐵 1 = 9𝑐𝑚
bo’lsa, 𝐴𝐵 kesmani 𝐴 uchidan boshlab hisoblaganda 3: 4 nisbatda bo’luvchi 𝐶 nuqtadan 𝛼 tekislikkacha bo’lgan masofani toping. 𝐴)6 𝐵)7,2 𝐶)7 𝐷)6,8 27. 𝐴𝐵𝐶𝐷 parallelogrammning 𝐵𝐶 va 𝐶𝐷 tomonlaridan mos ravishda 𝑀 va 𝑁 nuqtalar shunday tanlab olinganki, 𝐶 uchidan boshlab hisoblaganda (𝐵𝐶 va 𝐶𝐷 tomonlarini)2: 1 nisbatda bo’ladi. Agar parallelogrammning yuzi 45 ga teng bo’lsa, 𝐴𝑀𝑁 uchburchak yuzini toping. 𝐴)15 𝐵)25 𝐶)20 𝐷)10 28. Agar charxpalak 5 minutda 36 2 3 marta aylansa, u 12 minutda necha marta aylanadi? 𝐴)86
1 3 𝐵)91 𝐶)86 𝐷)88 29. Tenglamani yeching. 𝑥 + 4
6 − 3
2 3 + 4
− 𝑥 − 3
3 + 2
2 + 1 3 = 𝑥 8 + 2 3 4 ( 4 7) −1 𝐴) − 14 𝐵)30 𝐶)14 𝐷) − 30 30. ( |𝑥|+𝑥
𝑥−1 ) 2 − 14𝑥
𝑥−1 + 12 = 0 tenglamaning barcha haqiqiy ildizlari yig’indisini toping.
𝐴)3 𝐵)5 𝐶) − 1 𝐷)2
A D C B JIZZAX-2019
@alphraganus – matematik kanal 1 B 2 C 3 B 4 B 5 D 6 B 7 B 8 C 9 C 10 B
11 A 12 C
13 C 14 B
15 A 16 C
17 C 18 D
19 B 20 B
21 A 22 D
23 C 24 A
25 C 26 C
27 C 28 D
29 A 30 C
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