Matematika milliy sertifikat tushgan testlar

uzvestnik.ru MATEMATIKA MILLIY SERTIFIKAT javoblari bilan ──────────────────── VARIANT 04.12.2022 uzvestnik.ru 1 uzvestnik.ru 1. 𝑎, 𝑏, 𝑐 – turli raqamlar bo’lsa, 100𝑎 + 10𝑏 + 𝑐 ning eng katta qiymatini toping. A) 897 B) 987 C) 999 D) 988 1 2021 1 2. (2022 − 2022) : (2022 − 2023) ni hisoblang. A) 1 B) 2022 1 C) 2023 D) 2023 3. 2 va 3 ga bo’linmaydigan barcha ikki xonali natural sonlar yig’indisini toping. A) 1620 B) 1800 C) 1960 D) 3080 4. 𝐴 shahardan 𝐵 shaharga ikkita mashina yo’lga chiqdi. Birinchi mashina tezligi 𝑣1 , ikkinchi mashina tezligi 𝑣2 . (𝑣1 > 𝑣2 ). Birinchi mashina 𝐵 shaharga borib shu zahoti qaytib ikkinchi mashina bilan uchrashdi. Ikkinchi mashina bosib o’tgan masofa 𝐴 va 𝐵 shaharlar orasidagi masofaning necha foizini tashkil etadi? 2𝑣 A) 𝑣 +𝑣2 ⋅ 100% 1 2 𝑣 B) 𝑣 +𝑣 2 ⋅ 100% 1 2 2𝑣 C) 𝑣 −𝑣1 ⋅ 100% 1 2 𝑣 D) 𝑣 −𝑣 1 ⋅ 100% 1 2 5. 3 ta quvur berilgan. 1-quvur yolg’iz o’zi basseynni 5 soatda to’ldiradi, 2-quvur yolg’iz o’zi basseynni 3 soatda to’ldiradi, 3-quvur yolg’iz o’zi basseynni 2 soatda bo’shatadi. 3 ta quvur bir vaqtda necha soatda basseynni to’ldiradi? A) 20 B) 30 C) 40 2 uzvestnik.ru D) 15 12 244 6. Hisoblang. √25 ⋅ 15⋅(382 −232 ) 3 A) 0,8 B) 0,6 C) 0,2 D) 0,4 7. Ishorasi almashinuvchi geometrik progressiyada 𝑏1 = 𝑎 − 5; 𝑏2 = 𝑎 + 4; 𝑏3 = 5𝑎 + 8 bo’lsa, 𝑏4 ni toping. 1 A) 4 1 B) − 4 C) 4 D) -4 1 1 1 2 1 1 8. (𝑥+𝑦)2 ⋅ (𝑥2 + 𝑦2 ) + (𝑥+𝑦)3 ⋅ (𝑥 + 𝑦) ni soddalashtiring. 1 A) 𝑥𝑦 1 B) 𝑥 2𝑦2 C) 1 D) 𝑥 + 𝑦 9. 2𝑥 2 − 5𝑥 + 4 = 0 tenglama nechta haqiqiy ildizga ega? A) Haqiyqiy ildizga ega emas B) 1 ta C) 2 ta D) Cheksiz ko’p yechimga ega 7𝜋 7𝜋 10. 2sin 6 + cos2 4 ni hisoblang. 1 A) − 4 1 B) − 2 C) 0 1 D) 2 3 uzvestnik.ru 11. 𝑎 > 5 bo’lsa, √(3 − 𝑎)2 − √(𝑎 − 5)2 ni hisoblang. A) 1 B) −2𝑎 + 8 C) 2 D) Aniqlab bo’lmaydi 𝑎 𝑏 𝑎 2+𝑏 2+𝑐 2 𝑎 12. = 4, = 10 bo’lsa, + ni hisoblang. 𝑏 𝑐 𝑎𝑐 𝑐 21 A) 81 40 21 B) 82 40 21 C) 80 40 22 D) 81 34 2cos𝛼+cos3𝛼+cos5𝛼 13. cos3𝛼+sin𝛼sin2𝛼 ni soddalashtiring. A) cos2𝛼 B) 4cos2𝛼 C) 4sin2𝛼 D) cos𝛼 14. 3 ⋅ 4𝑥 + 2 ⋅ 25𝑥 = 5 ⋅ 10𝑥 tenglama nechta haqiqiy ildizga ega? A) Haqiyqiy ildizga ega emas B) 1 ta C) 2 ta D) Cheksiz ko’p yechimga ega 15. Toq funksiyani toping. sin𝑥+𝑥 3 A) 𝑓(𝑥) = cos𝑥−1 cos𝑥+𝑥 3 B) 𝑓(𝑥) = sin𝑥−1 tg𝑥+𝑥 3 C) 𝑓(𝑥) = ctg𝑥+𝑥 2 sin𝑥−1 D) 𝑓(𝑥) = cos𝑥−1 16. 𝑥 2 + 4𝑥 + 1 = 2√𝑥 2 + 4𝑥 + 4 tenglamaning haqiqiy ildizlar yig’indisini toping. A) -4 B) 4 4 uzvestnik.ru C) -2 D) -6 17. ||2𝑥– 1| − 7| ≤ 5 tengsizlikni qanoatlantiradigan butun yechimlari nechta? A) 20 ta B) 12 ta C) 10 ta D) 8 ta MILLIY SERTIFIKATDA TUSHGAN ORIGINAL TEST SAVOLLARI √4−𝑥 2 18. 𝑥+1 ≥ 0 tengsizlikni yeching. A) [−2; 2] B) (−1; 2] C) (−1; ∞) D) {−2} ∪ (−1; 2] 19. 323 ⋅ 812 ⋅ 12517 necha xonali son? A) 52 B) 51 C) 50 D) 17 20. log cos2𝑥 (sin2𝑥) ≤ 1 tengsizlikni yeching. 𝜋 𝜋 A) [ + 𝜋𝑘; + 𝜋𝑘] , 𝑘 ∈ 𝑍 8 4 𝜋 5𝜋 B) [ 8 + 𝜋𝑘; 8 + 𝜋𝑘] , 𝑘 ∈ 𝑍 𝜋 𝜋 C) [ 8 + 𝜋𝑘; 4 + 𝜋𝑘) , 𝑘 ∈ 𝑍 𝜋 5𝜋 D) [ 4 + 2𝜋𝑘; 4 + 2𝜋𝑘) , 𝑘 ∈ 𝑍 21. 𝑓(𝑔−1 (𝑔(𝑥)) + 1) = 𝑥 2 + 5𝑥 + 6 berilgan. 𝑔−1 (𝑥) − 𝑔(𝑥) funksiyaning teskari funksiyasi. 𝑓(−1) ni toping. A) -1 B) 2 C) 1 D) 0 5 uzvestnik.ru 𝜋 22. 𝑓(𝑥) = sin2 5𝑥 − |cos2𝑥 + 𝑥| funksiya berilgan. 𝑓 ′ (− 6 ) ni toping. 7√3+2 A) 2 B) −√3 + 1 3√3+4 C) 2 3√3−2 D) 2 23. Chizmadagi ma’lumotlardan foydalanib 𝑥 ni toping. (𝐴𝐵||𝐸𝐹) A) 10 B) 15 C) 12 D) 8 24. Tekislikka ikkita 𝐴𝐵 va 𝐵𝐶 og’ma va 𝐵𝐻 perpendikulyar tushirilgan. Bunda 𝐵𝐻 = 𝐻𝐶, 𝐴𝐵 = 2𝐻𝐶, ∠𝐴𝐻𝐶 = 90∘ bo’lsa, ∠cos𝐵𝐴𝐶 ni toping. 3 A) 4 3 B) 5 2 C) 3 1 D) 2 25. Tomoni 4 ga teng bo’lgan kvadratga doira ichki chizilgan. Doiraning yuzini toping. A) 16𝜋 B) 𝜋 C) 2𝜋 D) 4𝜋 6 uzvestnik.ru 26. 𝐴𝐵𝐶 uchburchakda ∠𝐵𝐴𝐶 = 90∘ va ∠𝐵𝐶𝐴 = 30∘ bo’lib, 𝐵𝐷 bissektrisa 2√2 ga teng bo’lsa, 𝐴𝐵𝐶 uchburchak yuzini toping. A) 2√3 B) 2√2 C) 3√2 D) 3√3 27. Diagonallar soni tomonlar sonidan 6 marta ko’p bo’lgan ko’pburchakning ichki burchaklar yig’indisini toping. A) 2700 ∘ B) 1800 ∘ C) 2340 ∘ D) 2400 ∘ MILLIY SERTIFIKATDA TUSHGAN ORIGINAL TEST SAVOLLARI 28. Rombning katta diagonali 10√4 + 2√2 ga teng o’tkir burchagi 45∘ bo’lsa, diagonallari kesishish nuqtasidan tomonlarigacha bo’lgan eng qisqa masofalar yig’indisini toping. A) 10 B) 20 C) 15 D) 25 4 29. ∫−3 2 𝑥 2 |2𝑥|𝑑𝑥 ni hisoblang. A) 187 B) 175 C) 337 D) 222 30. 𝐴𝐵𝐶 uchburchakning yuzi 60 ga teng. 𝐵𝐸 ⃗⃗⃗⃗⃗ = 𝐴𝐵 ⃗⃗⃗⃗⃗ bo’lsa, 𝐴𝐸𝐶 uchburchakning yuzini toping. A) 120 B) 90 C) 60 D) 30 7 uzvestnik.ru 31. (𝐴 ∩ 𝐵) ∪ (𝐴 ∪ 𝐵)′ ning elementlar sonini toping. A) 5 B) 7 C) 6 D) 9 32. Merganning nishonga tekkizish ehtimolligi 0,8 ga teng. 5 marta o’q uzilgan. Dastlab otilgan 3 ta o’q tegib, keyingi 2 ta otilgan o’q tegmasligi ehtimolligini toping. A) 210 ⋅ 10−6 B) 211 ⋅ 10−5 C) 211 ⋅ 10−6 D) 210 ⋅ 10−5 Topshiriqlar(33-35) va javob variantlari (A-F) ni oʻzaro moslashtiring. Muntazam oltiburchakli piramidaga shar ichki chizilgan. Shar ichiga eng katta hajmli konus ichki chizilgan. Piramida asosining tomoni 6 ga, yon yogʻi asos tekisligi bilan 600 tashkil etadi. (𝜋 ≈ 3) deb oling. 33. Piramida hajmini toping. A) 162√3 B) 108 C) 32 D) 81 E) 81√3 F) 27 8 uzvestnik.ru 34. Shar hajmini toping. 35. Konus hajmini toping. 6𝑥−𝑘 2𝑥+𝑘 36. 𝑥−1 = 3 − 𝑥+1 tenglama berilgan. a) Tenglama bitta ildizga ega bo’ladigan 𝑘 ning eng katta qiymatini toping. Javob a)___________________________________ b) Tenglama bitta ildizga ega bo’ladigan 𝑘 ning barcha qiymatlari yig’indisini toping. Javob b)___________________________________ 37. 3(log 2 sin𝑥)2 + log 2 (1 − cos2𝑥) = 2 tenglamani yeching. a) Tenglamaning eng kichik musbat ildizini toping. Javob a)___________________________________ 𝜋 5𝜋 b) Tenglamaning (− 2 ; 2 ) kesmada nechta ildizga ega? Javob b)___________________________________ 38. 𝑔(𝑥) = 𝑘𝑥 + 𝑏 va 𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 funksiya grafiklari berilgan. Grafikdan foydalanib, quyidagilarni hisoblang. a) 𝑓 ′ (2) ni hisoblang. Javob a) 1 1 1 b) 𝑓 ′ (𝑎) − 5𝑓 ′ (𝑏) + 2𝑓 ′ (𝑐 ) ni hisoblang. Javob b) 9 uzvestnik.ru 39. 𝑓(𝑥) = 𝑥 4 − 2𝑥 3 + 2𝑥 2 − 2𝑥 + 1 bo’lsa, a) 𝑓(1 + √2) + 𝑓(1 − √2) ni hisoblang. Javob a) b) 𝑓(𝑥) = 0 nechta turli haqiqiy ildizga ega? Javob b) 40. Rasmda 𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 parabola va 𝑔(𝑥) = 𝑘𝑥 + 𝑙 to’g’ri chiziq grafiklari tasvirlangan. (−2; 0) va (𝑥0 ; 𝑦0 ) nuqtalar parabola va to’g’ri chiziq kesishgan nuqtalar bo’lsa, a) 𝑥0 + 𝑦0 ni hisoblang. Javob a)_________________________________________ b) Bo’yalgan sohaning yuzini toping. Javob b)_________________________________________ 41. 𝐴𝐵𝐶 uchburchakda 𝐴𝐵 = 7, 𝐵𝐶 = 10, 𝐴𝐶 = 15 ga teng. Uchburchakka ikkita aylana shunday ichki chizilganki, 𝑅 radiusli aylana uchburchak tomonlariga, 𝑟 - radiusli aylana esa 𝐴𝐶, 𝐵𝐶 va 𝑅 radiusli aylanaga urinadi. (Rasmga qarang) a) 𝑅 =? Javob a)_________________________________________ b) 𝑟 =? Javob b)_________________________________________ 10 uzvestnik.ru 42. Quyidagi chizmada yuzi 42 ga teng bo’lgan 𝐴𝐵𝐶𝐷 trapetsiya tasvirlangan. Trapetsiyaning 𝐵𝐶 yon 𝐶𝐿 3 𝐾𝐵 𝐷𝐶 5 tomonidan 𝐾 va 𝐿 nuqtalar olingan. 𝐿𝐾 = 2, 𝐿𝐾 = 2 va 𝐴𝐵 = 9 bo’lsa, a) 𝐴𝐾𝐵 uchburchakning yuzini toping. Javob a)________________________________________ b) 𝐴𝐾𝐿𝐷 yuzini toping. Javob b)________________________________________ 1 43. Rasmda aylananing 4 qismi tasvirlangan. 𝐴𝐶 = 𝐴𝐵 = 𝑅 -aylana radiusi, 𝐶𝐷 = 1, 𝐵𝐷 = 3√2 bo’lsa, a) sin∠𝐶𝐴𝐷 ning ichki burchagini toping. Javob a)________________________________________ b) 𝐶𝐴𝐷 uchburchakning yuzini toping. Javob b)________________________________________ 44. Silindrga oktaedr ichki chizilgan. Oktaedrning hajmi 36 ga teng. a) Oktaedrning qirrasini toping. Javob a) b) Silindr hajmini toping. Javob b) 11 uzvestnik.ru 45. Tomonlari 2 va 10 ga teng bo’lgan to’g’ri to’rtburchakli metaldan asoslari ikkita doira va yon sirti qirqib olinib silindr hosil qilindi. (𝜋 ≈ 3) deb oling. a) Eng kam chiqindi chiqarib silindr yasalsa, uning hajmini toping. Javob a) b) Silindr yasashdan hosil bo’lgan chiqindi metalning necha foizini tashkil etadi? Javob b) 12 uzvestnik.ru uzvestnik.ru MATEMATIKA Milliy Sertifikat — Tayyorgarlik testlari VARIANT 2 19.02.2023 javoblari bilan uzvestnik.ru 1. Natural 𝑎 va 𝑏 sonlar uchun 𝑎 + 𝑏 = 111 tenglik bajarilsa, 𝑎𝑏 − 1 ayirmaning eng katta qiymatini toping. A) 2555 B) 3079 C) 110 D) 1 1−3+5−7+9−11+...+2021−2023 2. Hisoblang. 1−2+3−4+5−6+...+2021−2022 A) 1 B) −1 1012 C) − 1011 1012 D) 1011 1055 +1054 +1050 3. Hisoblang. 1049 +1053 +1054 A) 100 B) 1 C) 10 D) 1000 2 4. Ikki ishchi bir ishning 3 qismini 4 kunda bajara oladi. Agar ular alohida ishlasa, birinchi ishchi ishni ikkinchisidan 5 kun oldinroq bajarib tugatadi. Yolg’iz ishlaganda birinchi ishchi ishni necha kunda tugata oladi? A) 10 B) 12 C) 15 D) 20 5. 500 kg ruda, tarkibida 12,5 % temir bo’lgan 200 kg ruda ajratib olindi. Qolgan rudada temir ulushi dastlabkidan 20% ortiq bo’ldi. Dastlab ruda tarkibida qancha(kg) temir bo’lgan? A) 212,5 B) 202,5 C) 45 D) 205 6. Hisoblang. uzvestnik.ru 2022 ⋅ 2024 + 1 2026 ⋅ 2028 + 1 √ ⋅ − 1 + √25 2024 ⋅ 2030 + 9 2020 ⋅ 2026 + 9 A) 2021 B) 2022 C) 6 D) 5 7. Arifmetik progressiyada 𝑎5 + 𝑎𝑛−4 = 24 va 𝑆𝑛 = 96 bo’lsa, 𝑛 ni toping. A) 7 B) 9 C) 4 D) 8 8. Birinchi hadi 5 dan katta bo’lgan geometrik progressiyada 𝑏1 + 𝑏2 + 𝑏3 = 21 va 𝑏3 + 𝑏4 + 𝑏5 = 84 bo’lsa, uning dastlabki oltita hadining yig’indisini toping. A) 25 B) -174 C) 20 D) -147 9. Ifodani soddalashtiring. 𝑎2 + 𝑏2 𝑎2 + 𝑏2 𝑏2 𝑎2 :( + 2 − ) 𝑎+𝑏 𝑎𝑏 𝑎 − 𝑎𝑏 𝑎𝑏 + 𝑏2 A) 1 B) 𝑎2 + 𝑏2 C) 𝑎 + 𝑏 D) 𝑎 − 𝑏 10. Tenglamani yeching. 𝑥 𝑥 𝑥 𝑥+ + +⋯+ =7 1+2 1+2+3 1 +2 +3 + ⋯+7 A) 5 B) 4 C) 3 D) 2 𝑎𝑏|𝑏−𝑐−1| 𝑏𝑐|𝑎+𝑐+1| 𝑎𝑐|𝑎+1+𝑏| 11. Agar 𝑎 < 𝑎3 < 𝑎2 , 𝑏3 < 𝑏 < 𝑏2 , 𝑐 3 < 𝑐 2 < 𝑐 bo’lsa, + + ifodani |𝑎𝑏| |𝑏𝑐| |𝑎𝑐| soddalashtiring. A) 1 B) -1 C) −2𝑎 − 2𝑏 − 2𝑐 − 3 uzvestnik.ru D) 𝑎 + 𝑏 1 1 12. Soddalashtiring. 2tg53∘ (sin106∘ + tg106∘ ) A) tg 2 53∘ B) 1 C) 2 D) tg53∘ 𝑎 2 −𝑏2 +3𝑎−3𝑏 13. Agar 𝑎 − 𝑏 = 4 bo’lsa, 𝑎2 −𝑏2 +6𝑎+9 ni hisoblang. 1 A) 4 7 B) 4 C) 1 4 D) 7 14. Tengsizlikning [2; 2023] oraliqda nechta natural yechimi bor? 2𝑥 + 3𝑥 + 4𝑥 + 5𝑥 > 54 A) 2021 B) 2023 C) 0 D) 2022 15. Quyidagi funksiyalardan nechtasi toq? 1) 𝑦 = 2𝑥 + 2−𝑥 2) 𝑦 = 𝑥√1 + 𝑥 2 3) 𝑦 = 1 + sin2𝑥 4) 𝑦 = log 2 (𝑥 + √1 + 𝑥 2 ) A) 1 tasi B) 2 tasi C) 3 tasi D) 4 tasi 4𝑥 2 9 16. Tenglamaning haqiqiy ildizlari sonini toping. 𝑥 2 + (5𝑥+2)2 = 5 A) 4 B) 3 C) 2 D) 1 17. Tenglama ildizlari 𝑥 va 𝑦 bo’lsa, 𝑥 ⋅ 𝑦 ni hisoblang. |𝑥 + 𝑦 − 12| + (𝑥 − 𝑦 − 2)2 = 0 A) 25 uzvestnik.ru B) 28 C) 30 D) 35 18. Tengsizlikning [1; 2023] kesmada nechta natural yechimga ega? 𝜋𝑥 − √10 3log3 (𝑥−4) A) 3 B) 2 C) 4 D) 0 21. Tengsizlikning [−4; 5] oraliqdagi butun yechimlari yig’indisini toping. 16(2𝑥 + 3) (2𝑥 + 3)(𝑥 2 + 3𝑥) − ≥0 𝑥 2 + 3𝑥 A) 15 B) 9 C) 8 D) 10 22. 𝑦 = cos 𝑛 𝑥 ⋅ cos𝑛𝑥 bo’lsa, 𝑦 ′ (𝑥) ni toping. A) 𝑛 ⋅ cos 𝑛−1 𝑥 ⋅ sin(𝑛𝑥 − 𝑥) B) −𝑛 ⋅ cos 𝑛−1 𝑥 ⋅ cos(𝑛𝑥 + 𝑥) C) −𝑛 ⋅ cos 𝑛−1 𝑥 ⋅ sin(𝑛𝑥 + 𝑥) D) 𝑛 ⋅ cos 𝑛−1 𝑥 ⋅ sin(𝑛𝑥 + 𝑥) 23. Soddalashtiring. 1 1 1 1 + + + ⋯+ cos𝑥cos2𝑥 cos2𝑥cos3𝑥 cos3𝑥cos4𝑥 cos2022𝑥cos2023𝑥 sin2022𝑥 A) sin2𝑥⋅cos2023𝑥 uzvestnik.ru sin2023𝑥 B) cos𝑥cos2022𝑥 2sin2022𝑥 C) sin2𝑥⋅cos2023𝑥 2sin2022𝑥 D) cos𝑥cos2023𝑥 24. Aylanada 𝐴, 𝐵, 𝐶, 𝐷 nuqtalar olingan. 𝑂 - aylana markazi, 𝐴 va 𝐷 nuqtalar bilan bir to’g’ri chiziqda yotadi. Agar ∠𝐴𝐵𝐶 = 30∘ va 𝑂𝐷 = 3 bo’lsa, 𝐶𝐷 ni toping. A) 3 B) 4 C) √3 D) 3√3 25. 𝐴𝐵𝐶 uchburchakda 𝐴𝐷, 𝐵𝑁, 𝐶𝑀 medianalar keshishgan nuqta 𝐺 nuqta bo’lsin. Agar 𝐴𝐵𝐶 uchburchak yuzasi 48 ga teng bo’lsa, 𝐺𝐷𝑁 uchburchak yuzasini toping. A) 5 B) 4 C) 3 D) 12 26. 𝐴(−10; −3), 𝐵(−4; 5), 𝐶(5; 5) va 𝐷(11; −3) nuqtalardan o’tuvchi aylana radiusini toping. 5 A) 10 8 5 B) 11 8 6 C) 8 7 6 D) 7 7 uzvestnik.ru 27. Tomoni 4 bo’lgan muntazam oltiburchak uchta tomonlarining o’rtalarini tutashtirib muntazam uchburchak yasalgan. Bo’yalgan soha yuzini toping. A) 1 B) 6√3 C) 2√3 D) √3 28. Tekis burchagi 60∘ bo’lgan ikki yoqli burchakning qirrasida 𝐴 va 𝐵 nuqtalar olingan. Ulardan ikki yoqli burchakning turli yoqlarida 𝐴1 , 𝐵1 nuqtalardan burchakning qirrasiga perpendikulyar qilib 𝐴𝐴1 = 16 va 𝐵𝐵1 = 13. Agar 𝐴1 𝐵1 = 17 bo’lsa, 𝐴𝐵 ni toping. A) √202 B) √53 C) 6√2 D) √506 1 2 29. 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 funksiya uchun 𝑓 ′ (1) = 0, 𝑓(2) − 𝑓 ′ (2) = 1 va ∫0 𝑓 (𝑥)𝑑𝑥 = 3 bo’lsa, 𝑏 − 𝑎 − 𝑐 toping. 1 A) 4 3 B) 4 C) 1 D) 0 uzvestnik.ru 30. 𝐴𝐵𝐶𝐷𝐴1 𝐵1 𝐶1 𝐷1 kubda ⃗⃗⃗⃗⃗ 𝐵𝐶 + ⃗⃗⃗⃗⃗ 𝐶𝐷 va ⃗⃗⃗⃗⃗⃗⃗⃗⃗ 𝐷1 𝐴1 + 𝐴 ⃗⃗⃗⃗⃗⃗⃗ 1 𝐵 vektorlar orasidagi burchak kosinusini toping. √6 A) 3 √3 B) 2 √3 C) 4 √6 D) − 3 31. A to’plamning elementlar soni 9 ta, B to’plamning elementlar soni 7 ta, U universal elementlar soni 16. 𝑛((𝐴 ∪ 𝐵)′ ) eng ko’pi bilan nechaga teng? (𝐴′ – 𝐴 to’plamning universal to’plamgacha to’ldiruvchisi) A) 7 B) 13 C) 17 D) 11 32. 10 kishidan 1 ta boshliq, 2 ta yordamchi 2 ta mutaxasisni necha xil usulda tanlanadi. A) 7850 B) 7560 C) 3780 D) 3840 Gipotenuzasi 4√2 bo’lgan to’g’ri burchakli uchburchakning to’g’ri burchagi uchidagi bissektrisasi uni ikkita teng yonli uchburchakka ajratadi. Berilgan uchburchak gipotenuza atrofida 3600 ga aylantirildi. (𝜋 ≈ 3) 33. Hosil bo’lgan jismning to’la sirtini toping. 34. Hosil bo’lgan jismning hajmini toping. uzvestnik.ru 35. Hosil bo’lgan jismga ichki chizilgan shar hajmini toping. A) 16√2 B) 32 C) 32√2 D) 48√2 E) 30√2 F) 15√2 36. Tenglamani yeching. (𝑥 2 − 𝑥 − 1)3 + (𝑥 2 − 3𝑥 + 2)3 = (2𝑥 2 − 4𝑥 + 1)3 a) Tenglamaning nechta haqiqiy ildizi bor? Javob a)_________________________ b) Tenglamaning nechta musbat ildizi bor? Javob b)_________________________ sin2𝑥 37. Tenglamani yeching. sin2𝑥−2 ⋅cos2𝑥−2 = 2√3 a) Tenglamaning (0; 5) oraliqda nechta ildizi bor? Javob a)_________________________ b) Tenglamaning (0; 5) oraliqdagi ildizlaridan eng kattasi va eng kichigining ildizlarining musbat ayirmasini toping. Javob b)_________________________ 38. 𝑦 = 𝑔′ (𝑥) funksiya grafigi parabola bo’lib, (2; 7), (4; 3) va (6; −9) nuqtalardan o’tishi ma’lum. 𝑦 = 𝑔(𝑥) funksiyaning grafigining a) 𝑥0 = −2 nuqtasiga o’tkazilgan urinmaning burchak koeffitsientini toping. Javob a)_________________________ b) Funksiyaning statsionar nuqtalar yig’indisini toping. Javob b)_________________________ 39. 𝐴𝐵𝐶𝐷 kvadrat 𝐵𝐷 diagonalining 𝐷 uchi davomida 𝐸 nuqta olingan va 𝐷𝐸 = 3. a) Kvadratning diagonali 18 bo’lsa, 𝐶𝐸 ni toping. Javob a)_________________________ b) Agar 𝐶𝐸 = √29 bo’lsa, kvadratning yuzini toping. Javob b)_________________________ uzvestnik.ru 3 40. Grafigi 𝑂𝑌 o’qiga nisbatan simmetrik bo’lgan 𝑦 = 𝑛√𝑥 2 + 𝑚 + 𝑑 funksiya grafigi (0; 4) va (1; 3) nuqtalardan o’tadi. a) 𝑛 + 𝑚 + 𝑑 ni toping. Javob a)________________ b) Funksiya grafigi va abssisalar o’qi chegaralangan soha yuzini toping. Javob b)________________ 41. O’tkir burchakli 𝐴𝐵𝐶 uchburchakning 𝐵𝐻 va 𝐴𝐷 balandliklari mos ravishda 𝐹 va 𝐸 nuqtalarni ∠𝐸𝐹𝐶 = ∠𝐵𝐸𝐶 = 90∘ bo’ladigan qilib olingan. Bunda 𝐴𝐻 = 5 𝐻𝐶 = 3 va 𝐵𝐷 = 2 a) 𝐶𝐸 kesma uzunligini toping. Javob a)____________________________________ b) Agar 𝐸𝐹 = √12 − 6√3 bo’lsa, 𝐶𝐸𝐹 uchburchakning yuzini toping. Javob b)____________________________________ 42. Qirrasi 6√2 bo’lgan muntazam tetraedrga shar ichki chizilgan. a) Muntazam tetraedrning hajmini toping. Javob a)_____________________________________ b) Sharning to’la sirtini toping. Javob b)______________________________________ 43. Burchaklari teng bo’lgan 𝐴𝐵𝐶𝐷𝐸𝐹 oltiburchakda 𝐴𝐵 = 1, 𝐵𝐶 = 4, 𝐴𝐹 = 2, 𝐸𝐹 = 3 bo’lsa, a) 𝐶𝐷 tomoni toping. Javob a)______________________________________ b) 𝐴𝐵𝐶𝐷𝐸𝐹 oltiburchakning yuzasini toping. Javob b)______________________________________ 𝑥 44. Koordinatalar tekisligida 𝑦1 = √3𝑥 va 𝑦 = funksiyalarning grafiklari yasalgan. Birinchi √3 chorakda bu to’g’ri chiziqlar orasida 𝐴(𝑎; 𝑏) nuqta olingan va 𝑎2 + 𝑏2 = 144. 𝐴𝐿 va 𝐴𝐾 kesmalar mos ravishda 𝐴 nuqtadan 𝑦1 va 𝑦2 to’g’ri chiziqlargacha bo’lgan eng yaqin uzvestnik.ru masofalar. 𝑀 va 𝑁 nuqtalar 𝐴 nuqtaga mos ravishda 𝐾 va 𝐿 nuqtalarga simmetrik bo’lgan nuqtalar. a) 𝐾𝐿 ni toping. Javob a)________________________________ b) 𝑁𝑀 ni toping. Javob b)________________________________ 45. Binoning hajmi 96m3 . Balandligi va eni bir xil 𝑎, uzunligi 𝑏 bo’lgan binoning bir devori uy devoriga yopishgan. Binoning uy devori bilan umumiy bo’lmagan qirralari armaturadan, uchta yon devorini shisha oynadan va tomini tunukadan tiklagan. a) Agar bino uchun armaturani eng kam miqdorda sarflagan bo’lsa, jami qancha armatura sarflagan (m)? Javob a)_______________________________________ b) Agar 1m armatura 1$, 1m2 shisha oyna 10$ va 1m2 tunuka 5$ tursa, binoni tiklash uchun jami qancha ($) sarflagan? Javob b)___________________________________ uzvestnik.ru MILLIY SERTIFIKAT MATEMATIKA Original test savollari VARIANT 3 24.12.2023 Manba: uzvestnik.ru 1 uzvestnik.ru EKUK(12;6)+EKUB(6;12) 1. Hisoblang. √EKUK(12;3)⋅EKUB(3;12) A) 3 B) 9 C) 6 D) 1 18 41 17 7 4 5 99 2. Hisoblang. 65 ⋅ (18 − 36) + 6 + (7 + 49) : 49 16 A) 3 B) 6 C) 2 5 D) 6 3. Oltin va kumush qotishmasining massasi 1,06 kg. Qotishmani suvga solinganda 70 gr 1 1 massasini yo’qotadi. Oltin suvda massasining 19 qismini, kumush esa 10 qismini yo’qotadi. Oltin va kumushning dastlabki massalarini toping. A) Oltin 760 gramm, kumush 300 gramm B) Oltin 490 gramm, kumush 570 gramm C) Oltin 630 gramm, kumush 430 gramm D) Oltin 570 gramm, kumush 490 gramm 4. O’qishga qabul qilish uchun 5000 nafar talabaga kvota ajratilgan. Talabalar sonini oshirish maqsadida ketma-ket uch yil bir xil foizga qabul kvotasi oshirildi va kvota soni 6655 taga yetdi. Qabul kvotasi har yili necha foizga oshirilgan. A) 11 B) 10 C) 12 D) 15 5. Hisoblang: √√47 − √31 ⋅ √√47 + √31 A) 7 B) 5 C) 6 D) 4 6. 𝑚, 𝑛 ∈ 𝑁 uchun 38 ⋅ 210 ⋅ 3−4 ⋅ 2−4 = 2𝑚 ⋅ 3𝑛 bo’lsa, 𝑚 + 𝑛 ni toping. A) 11 B) 9 C) 10 2 uzvestnik.ru D) 8 7. Arifmetik progressiyaning birinchi hadi 8, oxirgi hadi esa 74 ga teng. Agar arifmetik progressiyaning ayirmasi butun son bo’lib u 3 va 9 sonlari orasida bo’lsa, progressiyaning yig’indisini toping. A) 462 B) 492 C) 512 D) 382 2𝑛 8. 𝑏𝑛 = 3𝑛−1 ketma-ketlikning barcha hadlari yig’indisini toping. A) 6 B) 1 C) 2 D) 3 √9+6𝑥+𝑥 2 −√9−6𝑥+𝑥 2 9. Agar 𝑥 > 3 da √9+6𝑥+𝑥 2 ni hisoblang. +√9−6𝑥+𝑥 2 3 A) − 𝑥 𝑥 B) 3 3 C) 𝑥 D) 1 1 1 10. arccos(− 2) + arcsin(− 2) ni hisoblang. 𝜋 A) 4 𝜋 B) 2 2𝜋 C) 3 D) 1 2cos2 2𝛼+cos6𝛼−1 11. Ifodani soddalashtiring. 0,5sin6𝛼+sin2𝛼⋅cos2𝛼 A) 2ctg5𝛼 B) 2tg5𝛼 C) ctg5𝛼 D) tg5𝛼 𝑟 2 +5𝑟 2𝑟−9 12. Soddalashtiring. 𝑟 3 −27 − 𝑟 3 −27 1 A) 3−𝑟 1 B) 𝑟 3 uzvestnik.ru 𝑟+3 C) 𝑟−3 1 D) 𝑟−3 25 𝑐 13. Agar 2𝑎 = 5, 2𝑏 = 3 bo’lsa, ( 3 ) = 405 tenglikdan foydalanib c ni a va b orqali ifodalang. 𝑏+4𝑎 A) 2𝑎−𝑏 4𝑏+𝑎 B) 2𝑎+𝑏 2𝑎+𝑏 C) 4𝑏+𝑎 2𝑎−𝑏 D) 4𝑏−𝑎 14. Tengsizlikni qanoatlantiradigan butun sonlar nechta? 𝑥 2 − 6|𝑥| + 5 ≤ 0 A) 8 B) 9 C) 10 D) 11 𝑥 3 15. 5𝑥−3 − 5 ⋅ 5𝑥−3 = 0 tenglamaning nechta haqiqiy ildizi bor? A) 0 B) 1 C) 2 D) Cheksiz ko’p 16. 2𝑥 2 − 4𝑥 − 6 = 0 tenglama ildizlari yig’indisini toping. A) -4 B) 2 C) 4 D) -2 17. Tenglama ildizlari ko’paytmasini toping. 𝑥 𝑥 1 1 ( ) +( ) =6 √3 + 2√2 √3 − 2√2 A) -4 B) 4 C) -2 D) 2 18. Tengsizlikning natural yechimlari nechta? 25 − 4𝑥 3 ≥0 √10 − 2 4 uzvestnik.ru A) 10 B) 4 C) 8 D) 6 19. √log 3 (36 − 12𝑥 + 𝑥 2 )8 + 6log 9 √18 − 3𝑥 = 7 tenglamaning ildizlar yig’indisini toping. A) -3 B) 3 C) 17 D) -7 20. Quyidagi funksiyalardan nechtasi toq emas, juft ham emas? 𝑥 4 +𝑥 2 +1 a) (𝑥+1)2 +1 𝑥sin𝑥 b) 𝑥 2 +1 cos𝑥 c) 𝑥+tg𝑥 (𝑥+1)3 +1 d) sin𝑥+𝑥 A) 1 B) 2 C) 3 D) 4 21. Funksiyaning eng kichik musbat davrini toping. 𝑥 𝑥 𝑓(𝑥) = 2cos 2 𝑥 + sin + tg 2 3 A) 12𝜋 B) 6𝜋 C) 4𝜋 D) 9𝜋 1 22. 𝑓(𝑥) = 𝑥 2 +3 funksiyaning (1; 0) nuqtadan o’tuvchi boshlang’ich funksiyasini toping. 1 𝑥 𝜋 A) 𝐹(𝑥) = 3√3 (arctg − 6) √3 1 𝑥 𝜋 B) 𝐹(𝑥) = 3√3 (arctg + 6) √3 1 𝑥 𝜋 C) 𝐹(𝑥) = (arctg − 6) √3 √3 √3 𝑥 𝜋 D) 𝐹(𝑥) = 3 (arctg + 6 ) √3 𝜋 23. 𝑓(𝑥) = |𝑥 − sin2 𝑥 − cos𝑥| funksiyaning 𝑥0 = 3 nuqtadagi hosilasini toping. A) −1 5 uzvestnik.ru B) 1 C) 0 D) Mavjud emas 24. Aylana uzunligi 12 cm, uzunligi 3 cm bo’lgan yoyning burchak o’lchovini toping. 𝜋 A) 3 𝜋 B) 2 𝜋 C) 4 𝜋 D) 6 25. Rasnda 𝐴𝐵 ∥ 𝐸𝐷 bo’lsa, 𝑥 burchak qiymatini toping. A) 50∘ B) 30∘ C) 35∘ D) 20∘ 26. Quyidagi chizmada muntazam beshburchak berilgan. Bunga ko’ra 𝛼 burchak qiymatini toping. 6 uzvestnik.ru A) 45∘ B) 55∘ C) 35∘ D) 40∘ 1 ⃗⃗⃗⃗⃗ boʻlsa, BEC uchburchak yuzini toping. ⃗⃗⃗⃗⃗ = − 𝐵𝐴 27. ABC uchburchakning yuzi 60 ga, 𝐵𝐸 2 A) 60 B) 120 C) 30 D) 90 28. ABC teng yonli 𝐴𝐵 = 𝐴𝐶 uchburchakka aylana ichki chizilgan va yon tomonini urinish nuqtasidan 2 va 5 ga teng kesmalarga ajratgan bo’lib, 𝐴𝐵 < 𝐵𝐶 bo’lsa, uchburchak yuzini toping. A) 10√3 B) 5√6 C) 5√3 D) 10√6 29. ABCD to’g’ri burchakli trapetsiyaning asoslari 𝐵𝐶 = 8 va 𝐴𝐷 = 24 ga teng bo’lsa, diagonallar kesishgan nuqtadan kichik yon tomonigacha bo’lgan eng qisqa masofani toping. A) 3 B) 6 C) 4,5 D) 5,8 30. Tekislikda yotmagan O nuqtadan tekislikka ikkita OA va OB og’malar tushirilgan. OA og’maning uzunligi OB og’maning uzunligidan 14 ga ortiq. Ularning proyeksiyalari mos ravishda 36 va 20 bo’lsa, O nuqtadan tekislikkacha bo’lgan eng qisqa masofani toping. 7 uzvestnik.ru A) 25 B) 20 C) 15 D) 12 31. A = {−3 ≤ 𝑥 ≤ 2, 𝑥 ∈ 𝑍}, B = {−1 < 𝑥 < 3

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