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 123 Ko'rishlar 1 izoh SaqlashSaqlanganOlib tashlandi 0 0 Savollar 12345678910111213141516171819202122232425 Vaqtingiz tugadi! Tomonidan yaratilgan InfoMaster 10-sinf Matematika olimpiada №3 2021-2022 o'quv yili viloyat bosqichida tushgan savollar. 1 / 25 1. ABC uchburchakda AB=BC,AM -mediana. Agar AB+MB=9 va MC+AC=7 bo‘lsa, uning asosini toping. A) 4 B) 5 C) 6 D) 7 2 / 25 2. f(x)=x²-4x va f(x)=-2x²+8x-p funksiyalar umumiy uchga ega bo`lsa, p ning qiymatini toping. A) 24 B) 18 C) 12 D) 6 3 / 25 3. 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) 8 B) 9 C) 11 D) 10 4 / 25 4. (?² − 2? + 3)(?² + 6? + 12) = 6 bo‘lsa, ? + ? ni toping. A) 2 B) -3 C) 3 D) -2 5 / 25 5. x, y sonlari (x² + 1)(y² + 1) + 2(x − y)(1 − xy) = 4(1 + xy) tenglikni qanoatlantiradi |1 + x| ∙ |1 − y| ni toping. A) 3 B) 9 C) 1 D) 2 6 / 25 6. ABC uchburchakning AC tomonida D nuqta olingan, bunda ∠ABC = ∠BDC. Agar AD = 10, CD = 8 bo‘lsa, BC ni toping. A) 10 B) 15 C) 12 D) 9 7 / 25 7. ?(?) = ?5 − 7?4 + 3?3 − ? + 2 ko‘phadni ?2 + ? ga bo‘lgandagi qoldiqni aniqlang. A) 6? + 2 B) 8? + 2 C) 4? + 2 D) 10? + 2 8 / 25 8. Agar A) π B) 0 C) π/2 D) 3π/2 9 / 25 9. 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√6/24 B) 5√3/12 C) 5√2/5 D) 2/5 10 / 25 10. ABC – gipotenuzasi AB bo‘lgan to‘g‘ri burchakli uchburchak. Gipotenuzaning ikki tomon davomida AB to‘g‘ri chiziqda AK = AC va BM = BC shartlar bilan kesmalar ajratilgan. KCM burchakni toping. A) 135° B) 90° C) 150° D) 120° 11 / 25 11. Tenglamalar sistemasi nechta yechimga ega? A) 6 B) 8 C) 10 D) 12 12 / 25 12. Tenglama nechta yechimga ega? A) 4 B) 3 C) 5 D) 2 13 / 25 13. 102022 − 22021 ayirmani 24 ga bo‘lgandagi qoldiqni toping. A) 8 B) 0 C) 12 D) 16 14 / 25 14. Agar bo‘lsa, |xyz| ni toping. A) 1000 B) 100 C) 800 D) 500 15 / 25 15. 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) 10 C) 9 D) 15 16 / 25 16. Soddalashtiring: (4cos² 9° −3)(4cos² 27° −3)·ctg9° A) 1 B) sin18° C) 2cos² 9° D) tg9° 17 / 25 17. ?² + |? − 3| ≤ |?2 + ?| − 3 tengsizlikni yeching. A) x<0 B) x ≤ 3 C) x>3 D) 3 ≤ x 18 / 25 18. a,b,c−ABC uchburchakning tomonlari. Agar a4 + b4 + c4 + 32 = 2(a²b² + b²c² + a²c²) bo‘lsa, ABC uchburchak yuzini toping. A) 1 B) 2√2 C) √2 D) √3 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. ABCD to‘rtburchakda АВ = CD = 9 va bu to‘rtburchakka radiusi 4 ga teng aylana ichki chizilgan. ABCD to‘rtburchak yuzini toping. A) 72 B) 144 C) 81 D) 36 21 / 25 21. Agar ni toping. A) 0.96 B) 0.8 C) 0.9 D) 0.81 22 / 25 22. tenglama nechta yechimga ega, agar x ∈ (0; 50)? A) 17 B) 16 C) 15 D) 14 23 / 25 23. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping. A) -1 B) 0 C) 3 D) 1 24 / 25 24. 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) 6 B) 8 C) 7 D) 5 25 / 25 25. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi. ?³ − 24?² + 183? − 440 = 0. Uchburchakning yuzini hisoblang. A) 2√21 B) 4√21 C) 35 D) √21 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
