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 47 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. Tengsizlikning butun yechimlarining o‘rta arifmetik qiymatini toping: A) -10/3 B) -4/3 C) -5/2 D) -3 2 / 25 2. tengsizlik yechimi bo`la oladigan tub sonlar nechta? A) 4 B) 5 C) 2 D) 3 3 / 25 3. x, y sonlari (x² + 1)(y² + 1) + 2(x − y)(1 − xy) = 4(1 + xy) tenglikni qanoatlantiradi |1 + x| ∙ |1 − y| ni toping. A) 1 B) 2 C) 3 D) 9 4 / 25 4. Agar ?1 = 6? − 6 va у2//?1 hamda у2 to‘g‘ri chiziq ?(6; 6) nuqtadan o‘tsa, ?2 ni toping. A) −6? + 6 B) 6? − 24 C) 6? − 30 D) −6? + 42 5 / 25 5. Agar bo‘lsa, ?(0) − ?(5) ayirmani toping. A) -25 B) -27 C) -24 D) -26 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) 120° B) 135° C) 90° D) 150° 7 / 25 7. ?(?) = ?5 − 7?4 + 3?3 − ? + 2 ko‘phadni ?2 + ? ga bo‘lgandagi qoldiqni aniqlang. A) 10? + 2 B) 4? + 2 C) 6? + 2 D) 8? + 2 8 / 25 8. (?² − 2? + 3)(?² + 6? + 12) = 6 bo‘lsa, ? + ? ni toping. A) 3 B) -3 C) -2 D) 2 9 / 25 9. 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) 9 B) 8 C) 15 D) 10 10 / 25 10. 102022 − 22021 ayirmani 24 ga bo‘lgandagi qoldiqni toping. A) 8 B) 12 C) 0 D) 16 11 / 25 11. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping. A) -1 B) 1 C) 0 D) 3 12 / 25 12. Agar bo‘lsa, |xyz| ni toping. A) 100 B) 500 C) 800 D) 1000 13 / 25 13. Tenglama nechta yechimga ega? A) 4 B) 5 C) 2 D) 3 14 / 25 14. a,b,c−ABC uchburchakning tomonlari. Agar a4 + b4 + c4 + 32 = 2(a²b² + b²c² + a²c²) bo‘lsa, ABC uchburchak yuzini toping. A) √2 B) √3 C) 2√2 D) 1 15 / 25 15. ?² + |? − 3| ≤ |?2 + ?| − 3 tengsizlikni yeching. A) x<0 B) 3 ≤ x C) x ≤ 3 D) x>3 16 / 25 16. Soddalashtiring: (4cos² 9° −3)(4cos² 27° −3)·ctg9° A) 2cos² 9° B) 1 C) tg9° D) sin18° 17 / 25 17. Tenglamalar sistemasi nechta yechimga ega? A) 10 B) 12 C) 6 D) 8 18 / 25 18. Agar ? > 0, ? + ?² = 7,25; ?² − ? = 2 va ?² = √(? − 1) ∙ √(2 − ?) bo‘lsa, ?(√(? − 1) + √(2 − ?)) ning qiymatini toping. A) 4 B) 7 C) 5 D) 6 19 / 25 19. ?(? − 1) = 2?(5? + 4) va ?(2? − 1) = 4? + 4 bo‘lsa, ?(?) ni toping A) 20x+50 B) 20x+48 C) x+25 D) 0 20 / 25 20. 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) 5 D) 8 21 / 25 21. Tenglamani yeching: 3x+3 + 8·3x+2 = 33 A) -1 B) -2 C) 1 D) 0 22 / 25 22. Agar ni toping. A) 0.81 B) 0.9 C) 0.8 D) 0.96 23 / 25 23. bo‘lsa ? ning qiymatini toping. A) 12 B) 40 C) 37 D) 25 24 / 25 24. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi. ?³ − 24?² + 183? − 440 = 0. Uchburchakning yuzini hisoblang. A) √21 B) 2√21 C) 35 D) 4√21 25 / 25 25. tenglama nechta yechimga ega, agar x ∈ (0; 50)? A) 17 B) 15 C) 16 D) 14 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
