10-sinf Matematika olimpiada №3 Oktabr 3, 2022Oktabr 3, 2022 da chop etilgan InfoMaster tomonidan 10-sinf Matematika olimpiada №3 ga fikr bildirilmagan. 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! 10-sinf Matematika olimpiada №3 2021-2022 o'quv yili viloyat bosqichida tushgan savollar. 1 / 25 1. a ning qanday qiymatlarida kvadrat tenglamaning ildizlari yig‘indisi manfiy bo‘ladi? A) 0<a<2 B) a<1 C) 0<a<1 D) a<0 2 / 25 2. Hisoblang: A) -1/4 B) -1/8 C) 1/4 D) 1/8 3 / 25 3. 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? − 24 C) −6? + 42 D) −6? + 6 4 / 25 4. ?(? − 1) = 2?(5? + 4) va ?(2? − 1) = 4? + 4 bo‘lsa, ?(?) ni toping A) 20x+48 B) 0 C) x+25 D) 20x+50 5 / 25 5. 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) 7 C) 8 D) 5 6 / 25 6. Agar bo‘lsa, |xyz| ni toping. A) 800 B) 1000 C) 100 D) 500 7 / 25 7. 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) 72 C) 144 D) 81 8 / 25 8. ?(?) = ?5 − 7?4 + 3?3 − ? + 2 ko‘phadni ?2 + ? ga bo‘lgandagi qoldiqni aniqlang. A) 6? + 2 B) 10? + 2 C) 8? + 2 D) 4? + 2 9 / 25 9. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi. ?³ − 24?² + 183? − 440 = 0. Uchburchakning yuzini hisoblang. A) 35 B) √21 C) 2√21 D) 4√21 10 / 25 10. Tenglamani yeching: 3x+3 + 8·3x+2 = 33 A) 0 B) -1 C) -2 D) 1 11 / 25 11. 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) 9 D) 12 12 / 25 12. Agar bo‘lsa, ?(0) − ?(5) ayirmani toping. A) -25 B) -24 C) -26 D) -27 13 / 25 13. Agar A) π B) π/2 C) 3π/2 D) 0 14 / 25 14. tenglama nechta yechimga ega, agar x ∈ (0; 50)? A) 15 B) 17 C) 16 D) 14 15 / 25 15. ?² + |? − 3| ≤ |?2 + ?| − 3 tengsizlikni yeching. A) x<0 B) x>3 C) x ≤ 3 D) 3 ≤ x 16 / 25 16. 102022 − 22021 ayirmani 24 ga bo‘lgandagi qoldiqni toping. A) 12 B) 8 C) 0 D) 16 17 / 25 17. Soddalashtiring: (4cos² 9° −3)(4cos² 27° −3)·ctg9° A) 2cos² 9° B) tg9° C) sin18° D) 1 18 / 25 18. 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) 2/5 C) 5√3/12 D) 5√6/24 19 / 25 19. 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 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) 90° B) 135° C) 120° D) 150° 21 / 25 21. a,b,c−ABC uchburchakning tomonlari. Agar a4 + b4 + c4 + 32 = 2(a²b² + b²c² + a²c²) bo‘lsa, ABC uchburchak yuzini toping. A) 1 B) √3 C) √2 D) 2√2 22 / 25 22. Tenglama nechta yechimga ega? A) 4 B) 2 C) 3 D) 5 23 / 25 23. 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) 3 C) 9 D) 1 24 / 25 24. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping. A) -1 B) 0 C) 1 D) 3 25 / 25 25. Agar ni toping. A) 0.96 B) 0.8 C) 0.9 D) 0.81 0% Testni qayta ishga tushiring Author: InfoMaster Matematika olimpiada