Quiz — Devoir de Contrôle N°2 - Math - 3ème Math (2017-2018) Mr Ksaier Mohamed Salah.pdf

Question 1 sur 10 20:00

[{"id":4296,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"A) x = 2 ou x = 3","option_b":"B) x = -2 ou x = -3","option_c":"C) x = 1 ou x = 6","option_d":"D) x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0, donc les solutions sont x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) x = 2 ou x = 3\", \"b\": \"B) x = -2 ou x = -3\", \"c\": \"C) x = 1 ou","_debug_options_count":4},{"id":4297,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle croissante sur l'intervalle [0, 2] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² - 6x + 2 est positive sur [0, 2], donc la fonction est croissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":4298,"question":"Quelle est la probabilité de tirer un as dans un jeu de 32 cartes ?","option_a":"A) 1\/8","option_b":"B) 1\/32","option_c":"C) 4\/32","option_d":"D) 1\/4","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un jeu de 32 cartes contient 4 as, donc la probabilité est 4\/32 = 1\/8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A) 1\/8\", \"b\": \"B) 1\/32\", \"c\": \"C) 4\/32\", \"d\": \"D) 1\/4\"}}","_debug_options_count":4},{"id":4299,"question":"L'équation sin(x) = 0,5 admet-elle une solution dans l'intervalle [0, π] ?","option_a":"A) Oui, x = π\/6","option_b":"B) Non","option_c":"C) Oui, x = π\/3","option_d":"D) Oui, x = π\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"sin(π\/6) = 0,5, donc x = π\/6 est une solution dans [0, π].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) Oui, x = π\/6\", \"b\": \"B) Non\", \"c\": \"C) Oui, x = π\/3\", \"d\": \"","_debug_options_count":4},{"id":4300,"question":"La dérivée de la fonction f(x) = e^(2x) est-elle f'(x) = 2e^(2x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^(2x) est 2e^(2x) par la règle de dérivation des fonctions exponentielles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":4301,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"A) 0","option_b":"B) 1","option_c":"C) 2","option_d":"D) La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"c","explication":"En simplifiant, f(x) = x + 1 pour x ≠ 1, donc la limite est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A) 0\", \"b\": \"B) 1\", \"c\": \"C) 2\", \"d\": \"D) La limite n'existe pas\"","_debug_options_count":4},{"id":4302,"question":"Un dé équilibré à 6 faces est lancé. Quelle est la probabilité d'obtenir un nombre pair ?","option_a":"A) 1\/6","option_b":"B) 1\/2","option_c":"C) 1\/3","option_d":"D) 2\/3","option_e":"","option_f":"","bonne_reponse":"b","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A) 1\/6\", \"b\": \"B) 1\/2\", \"c\": \"C) 1\/3\", \"d\": \"D) 2\/3\"}}","_debug_options_count":4},{"id":4303,"question":"La fonction f(x) = ln(x) est-elle définie pour x = -1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction ln(x) n'est définie que pour x \u003E 0, donc elle n'est pas définie pour x = -1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":4304,"question":"Quelle est l'aire d'un triangle rectangle dont les côtés de l'angle droit mesurent 3 cm et 4 cm ?","option_a":"A) 6 cm²","option_b":"B) 12 cm²","option_c":"C) 5 cm²","option_d":"D) 7 cm²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'aire d'un triangle rectangle est (base × hauteur)\/2 = (3 × 4)\/2 = 6 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) 6 cm²\", \"b\": \"B) 12 cm²\", \"c\": \"C) 5 cm²\", \"d\": \"D) 7 cm²\"","_debug_options_count":4},{"id":4305,"question":"La suite u_n = n² est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite u_n = n² tend vers l'infini lorsque n tend vers l'infini, donc elle n'est pas convergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]