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. ko‘phadning bir ko‘paytuvchisi x+1 bo‘lsa, m ni toping. A) 3 B) 2 C) 1 D) 4 2 / 25 2. Tengsizlikni yeching: A) (5/3;2) B) (2/3;2) C) (4/3;3) D) (1/2;∞) 3 / 25 3. 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° 4 / 25 4. ABC uchburchakning AC tomonida D nuqta olingan, bunda ∠ABC = ∠BDC. Agar AD = 10, CD = 8 bo‘lsa, BC ni toping. A) 9 B) 12 C) 15 D) 10 5 / 25 5. Soddalashtiring: (4cos² 9° −3)(4cos² 27° −3)·ctg9° A) tg9° B) 1 C) 2cos² 9° D) sin18° 6 / 25 6. Tenglamalar sistemasi nechta yechimga ega? A) 10 B) 8 C) 12 D) 6 7 / 25 7. 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) 9 D) 8 8 / 25 8. 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 9 / 25 9. ?(?) = ?5 − 7?4 + 3?3 − ? + 2 ko‘phadni ?2 + ? ga bo‘lgandagi qoldiqni aniqlang. A) 6? + 2 B) 8? + 2 C) 10? + 2 D) 4? + 2 10 / 25 10. 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? + 6 C) 6? − 24 D) −6? + 42 11 / 25 11. ?² + |? − 3| ≤ |?2 + ?| − 3 tengsizlikni yeching. A) x ≤ 3 B) x<0 C) x>3 D) 3 ≤ x 12 / 25 12. Tenglama nechta yechimga ega? A) 3 B) 4 C) 5 D) 2 13 / 25 13. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping. A) 0 B) 1 C) -1 D) 3 14 / 25 14. 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√2/5 C) 5√6/24 D) 2/5 15 / 25 15. Agar bo‘lsa, |xyz| ni toping. A) 1000 B) 800 C) 100 D) 500 16 / 25 16. Agar ? > 0, ? + ?² = 7,25; ?² − ? = 2 va ?² = √(? − 1) ∙ √(2 − ?) bo‘lsa, ?(√(? − 1) + √(2 − ?)) ning qiymatini toping. A) 6 B) 7 C) 5 D) 4 17 / 25 17. Agar ni toping. A) 0.81 B) 0.96 C) 0.9 D) 0.8 18 / 25 18. ?/? kasr (?, ? −natural sonlar)— qisqarmas kasr va (7?+6?)/(3?+2?) kasr esa qisqaradi. Ushbu kasr qanday songa qisqaradi? A) 2 B) 5 C) 3 D) 8 19 / 25 19. tenglama nechta yechimga ega, agar x ∈ (0; 50)? A) 15 B) 14 C) 16 D) 17 20 / 25 20. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi. ?³ − 24?² + 183? − 440 = 0. Uchburchakning yuzini hisoblang. A) √21 B) 35 C) 2√21 D) 4√21 21 / 25 21. Agar A) π B) π/2 C) 0 D) 3π/2 22 / 25 22. Tenglamani yeching: 3x+3 + 8·3x+2 = 33 A) 1 B) -2 C) 0 D) -1 23 / 25 23. ?(? − 1) = 2?(5? + 4) va ?(2? − 1) = 4? + 4 bo‘lsa, ?(?) ni toping A) x+25 B) 0 C) 20x+50 D) 20x+48 24 / 25 24. 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) 144 D) 36 25 / 25 25. 102022 − 22021 ayirmani 24 ga bo‘lgandagi qoldiqni toping. A) 12 B) 8 C) 0 D) 16 0% Testni qayta ishga tushiring Author: InfoMaster Matematika olimpiada