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 28 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. tenglama ildizlari yig‘indisini toping. A) 3 B) 0 C) 1 D) 2 2 / 25 2. Ta`lim muassasida barcha o`quvchilar kamida bitta ingliz yoki nemis tilida so`zlashа oladilar. Ayrimlari ikkala tilni ham biladilar. O`quvchilarning 85%i ingliz tilini, 75%i nemis tilini biladilar. Ikkala tilni ham biladigan o`quvchilar barcha o`quvchilarning necha % ini tashkil etadi. A) 60% B) 50% C) 65% D) 70% 3 / 25 3. ?(?) = ?5 − 7?4 + 3?3 − ? + 2 ko‘phadni ?2 + ? ga bo‘lgandagi qoldiqni aniqlang. A) 8? + 2 B) 10? + 2 C) 4? + 2 D) 6? + 2 4 / 25 4. Soddalashtiring: (4cos² 9° −3)(4cos² 27° −3)·ctg9° A) tg9° B) 1 C) 2cos² 9° D) sin18° 5 / 25 5. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping. A) -1 B) 1 C) 0 D) 3 6 / 25 6. 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) 90° B) 150° C) 135° D) 120° 7 / 25 7. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi. ?³ − 24?² + 183? − 440 = 0. Uchburchakning yuzini hisoblang. A) 4√21 B) √21 C) 35 D) 2√21 8 / 25 8. bo‘lsa ? ning qiymatini toping. A) 12 B) 40 C) 25 D) 37 9 / 25 9. Agar A) 3π/2 B) 0 C) π/2 D) π 10 / 25 10. 102022 − 22021 ayirmani 24 ga bo‘lgandagi qoldiqni toping. A) 0 B) 8 C) 12 D) 16 11 / 25 11. ?(? − 1) = 2?(5? + 4) va ?(2? − 1) = 4? + 4 bo‘lsa, ?(?) ni toping A) 0 B) 20x+50 C) x+25 D) 20x+48 12 / 25 12. ?² + |? − 3| ≤ |?2 + ?| − 3 tengsizlikni yeching. A) x>3 B) x ≤ 3 C) x<0 D) 3 ≤ x 13 / 25 13. tenglama nechta yechimga ega, agar x ∈ (0; 50)? A) 14 B) 17 C) 16 D) 15 14 / 25 14. ?/? kasr (?, ? −natural sonlar)— qisqarmas kasr va (7?+6?)/(3?+2?) kasr esa qisqaradi. Ushbu kasr qanday songa qisqaradi? A) 3 B) 2 C) 8 D) 5 15 / 25 15. ABCD to‘rtburchakda АВ = CD = 9 va bu to‘rtburchakka radiusi 4 ga teng aylana ichki chizilgan. ABCD to‘rtburchak yuzini toping. A) 81 B) 72 C) 36 D) 144 16 / 25 16. x, y sonlari (x² + 1)(y² + 1) + 2(x − y)(1 − xy) = 4(1 + xy) tenglikni qanoatlantiradi |1 + x| ∙ |1 − y| ni toping. A) 2 B) 9 C) 1 D) 3 17 / 25 17. 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) 2/5 B) 5√6/24 C) 5√2/5 D) 5√3/12 18 / 25 18. 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) 15 B) 10 C) 8 D) 9 19 / 25 19. Agar bo‘lsa, ?(0) − ?(5) ayirmani toping. A) -25 B) -26 C) -24 D) -27 20 / 25 20. Agar bo‘lsa, |xyz| ni toping. A) 500 B) 100 C) 1000 D) 800 21 / 25 21. 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) 10 C) 8 D) 9 22 / 25 22. Tenglamalar sistemasi nechta yechimga ega? A) 12 B) 6 C) 8 D) 10 23 / 25 23. Tenglamani yeching: 3x+3 + 8·3x+2 = 33 A) 0 B) -2 C) 1 D) -1 24 / 25 24. Tenglama nechta yechimga ega? A) 5 B) 3 C) 2 D) 4 25 / 25 25. ABC uchburchakning AC tomonida D nuqta olingan, bunda ∠ABC = ∠BDC. Agar AD = 10, CD = 8 bo‘lsa, BC ni toping. A) 15 B) 10 C) 12 D) 9 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
