Uy » Online olimpiada » Matematika olimpiada » 10-sinf Matematika olimpiada №3 Matematika olimpiadaViloyat 2021-2022 o'quv yili 10-sinf Matematika olimpiada №3 InfoMaster Avgust 19, 2024 38 Ko'rishlar 1 izoh SaqlashSaqlanganOlib tashlandi 0 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! 10-sinf Matematika olimpiada №3 2021-2022 o'quv yili viloyat bosqichida tushgan savollar. 1 / 25 1. Teng yonli uchburchakning asosi 12 sm, yon tomoni 18 sm. Yon tomonlariga bissektrisalar tushirilgan. Bissektrisalarning tomonlari bilan kesishgan nuqtalari orasidagoi masofani toping. A) 8,1 sm B) 6,4 sm C) 5,6 sm D) 7,2 sm 2 / 25 2. 7(kx−2)=7k+2(x−8) tenglama k ning qanday qiymatlarida ildizga ega bo`lmaydi? A) (2/7; ∞) B) k=2/7 C) ∅ D) (−∞; 2/7) 3 / 25 3. Soddalashtiring: (4cos² 9° −3)(4cos² 27° −3)·ctg9° A) 1 B) sin18° C) 2cos² 9° D) tg9° 4 / 25 4. Agar ? > 0, ? + ?² = 7,25; ?² − ? = 2 va ?² = √(? − 1) ∙ √(2 − ?) bo‘lsa, ?(√(? − 1) + √(2 − ?)) ning qiymatini toping. A) 6 B) 5 C) 4 D) 7 5 / 25 5. ABCD to‘rtburchakda АВ = CD = 9 va bu to‘rtburchakka radiusi 4 ga teng aylana ichki chizilgan. ABCD to‘rtburchak yuzini toping. A) 36 B) 144 C) 72 D) 81 6 / 25 6. Tenglama nechta yechimga ega? A) 2 B) 4 C) 5 D) 3 7 / 25 7. Agar A) π B) π/2 C) 0 D) 3π/2 8 / 25 8. ?² + |? − 3| ≤ |?2 + ?| − 3 tengsizlikni yeching. A) x<0 B) x>3 C) x ≤ 3 D) 3 ≤ x 9 / 25 9. 102022 − 22021 ayirmani 24 ga bo‘lgandagi qoldiqni toping. A) 8 B) 16 C) 0 D) 12 10 / 25 10. Ayirmasi noldan farqli bo‘lgan arifmetik progressiyaning 4-hadidan boshlab 14- hadigacha bo‘lgan hadlar yig‘indisi 77 ga teng. Progressiyaning 7 ga teng bo‘lgan had nomerini toping. A) 11 B) 8 C) 9 D) 10 11 / 25 11. Agar cos ∠A = 1/5 va sin∠B = 1/2 bo‘lsa, АВС uchburchakning mos ravishda А va В uchlaridan tushirilgan balandliklar nisbatini toping. A) 5√2/5 B) 5√6/24 C) 2/5 D) 5√3/12 12 / 25 12. Qavariq to‘rtburchakning diagonallari 3 va 4 ga teng. Agar qarama qarshi tomonlarining o‘rtalarini tutashtirishdan hosil bo‘lgan kesmalar uzunliklari o‘zaro teng bo‘lsa, qavariq to‘rtburchakning yuzini toping. A) 7 B) 6 C) 8 D) 5 13 / 25 13. ABCD to‘rtburchakda А va В burchaklar- to‘g‘ri, tg∠D = 3/4 va ВС = AD/2 = АВ + 2 bo‘lsa, АС ni toping. A) 8 B) 9 C) 10 D) 15 14 / 25 14. (?² − 2? + 3)(?² + 6? + 12) = 6 bo‘lsa, ? + ? ni toping. A) 3 B) -3 C) 2 D) -2 15 / 25 15. tenglama nechta yechimga ega, agar x ∈ (0; 50)? A) 16 B) 14 C) 15 D) 17 16 / 25 16. ?/? kasr (?, ? −natural sonlar)— qisqarmas kasr va (7?+6?)/(3?+2?) kasr esa qisqaradi. Ushbu kasr qanday songa qisqaradi? A) 2 B) 3 C) 5 D) 8 17 / 25 17. Agar ni toping. A) 0.8 B) 0.81 C) 0.96 D) 0.9 18 / 25 18. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping. A) 0 B) -1 C) 3 D) 1 19 / 25 19. ?(? − 1) = 2?(5? + 4) va ?(2? − 1) = 4? + 4 bo‘lsa, ?(?) ni toping A) 0 B) 20x+48 C) 20x+50 D) x+25 20 / 25 20. Tenglamalar sistemasi nechta yechimga ega? A) 6 B) 10 C) 12 D) 8 21 / 25 21. Agar bo‘lsa, |xyz| ni toping. A) 500 B) 1000 C) 100 D) 800 22 / 25 22. x, y sonlari (x² + 1)(y² + 1) + 2(x − y)(1 − xy) = 4(1 + xy) tenglikni qanoatlantiradi |1 + x| ∙ |1 − y| ni toping. A) 9 B) 1 C) 2 D) 3 23 / 25 23. Agar bo‘lsa, ?(0) − ?(5) ayirmani toping. A) -27 B) -25 C) -26 D) -24 24 / 25 24. Tenglamani yeching: 3x+3 + 8·3x+2 = 33 A) 1 B) -2 C) -1 D) 0 25 / 25 25. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi. ?³ − 24?² + 183? − 440 = 0. Uchburchakning yuzini hisoblang. A) √21 B) 4√21 C) 35 D) 2√21 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
