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 111 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. Ninachi va chivin to‘g‘ri chiziq bo‘ylab harakatlanmoqda. Ninachi chivinni quvib yetmoqchi. Ninachining tezligi 1,2 m/s va chivinniki 30 sm/s. Necha sekunddan so‘ng ular orasidagi masofa 6,5 m dan 20 sm gacha qisqaradi? A) 5 s B) 8 s C) 7 s D) 6 s 2 / 25 2. Berilgan funksiyaga teskari funksiyani aniqlang. f(x)=x2f2(x)+f(x) A) II B) I C) III D) IV 3 / 25 3. Agar bo‘lsa, ?(0) − ?(5) ayirmani toping. A) -25 B) -24 C) -26 D) -27 4 / 25 4. Tenglamalar sistemasi nechta yechimga ega? A) 8 B) 6 C) 10 D) 12 5 / 25 5. Agar ?1 = 6? − 6 va у2//?1 hamda у2 to‘g‘ri chiziq ?(6; 6) nuqtadan o‘tsa, ?2 ni toping. A) 6? − 30 B) −6? + 42 C) −6? + 6 D) 6? − 24 6 / 25 6. Agar ni toping. A) 0.9 B) 0.8 C) 0.96 D) 0.81 7 / 25 7. Agar bo‘lsa, |xyz| ni toping. A) 500 B) 800 C) 100 D) 1000 8 / 25 8. 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√3/12 B) 5√6/24 C) 2/5 D) 5√2/5 9 / 25 9. (?² − 2? + 3)(?² + 6? + 12) = 6 bo‘lsa, ? + ? ni toping. A) -2 B) 3 C) -3 D) 2 10 / 25 10. Agar A) π/2 B) 3π/2 C) 0 D) π 11 / 25 11. Agar ? > 0, ? + ?² = 7,25; ?² − ? = 2 va ?² = √(? − 1) ∙ √(2 − ?) bo‘lsa, ?(√(? − 1) + √(2 − ?)) ning qiymatini toping. A) 7 B) 4 C) 6 D) 5 12 / 25 12. tenglama nechta yechimga ega, agar x ∈ (0; 50)? A) 15 B) 16 C) 14 D) 17 13 / 25 13. ABCD to‘rtburchakda АВ = CD = 9 va bu to‘rtburchakka radiusi 4 ga teng aylana ichki chizilgan. ABCD to‘rtburchak yuzini toping. A) 144 B) 36 C) 81 D) 72 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) √3 B) 1 C) 2√2 D) √2 15 / 25 15. 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) 5 B) 6 C) 7 D) 8 16 / 25 16. 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 17 / 25 17. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping. A) -1 B) 0 C) 3 D) 1 18 / 25 18. Tenglamani yeching: 3x+3 + 8·3x+2 = 33 A) -1 B) -2 C) 1 D) 0 19 / 25 19. bo‘lsa ? ning qiymatini toping. A) 25 B) 12 C) 40 D) 37 20 / 25 20. 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) 150° B) 135° C) 120° D) 90° 21 / 25 21. 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) 2 C) 3 D) 1 22 / 25 22. ?(?) = ?5 − 7?4 + 3?3 − ? + 2 ko‘phadni ?2 + ? ga bo‘lgandagi qoldiqni aniqlang. A) 8? + 2 B) 10? + 2 C) 6? + 2 D) 4? + 2 23 / 25 23. ?² + |? − 3| ≤ |?2 + ?| − 3 tengsizlikni yeching. A) x>3 B) x ≤ 3 C) x<0 D) 3 ≤ x 24 / 25 24. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi. ?³ − 24?² + 183? − 440 = 0. Uchburchakning yuzini hisoblang. A) 2√21 B) √21 C) 35 D) 4√21 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) 12 C) 9 D) 10 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
