Quiz — img144.pdf

Question 1 sur 10 20:00

[{"id":1548,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = -2","option_c":"x = 2","option_d":"x = -12","option_e":"","option_f":"","bonne_reponse":"a","explication":"En isolant x : 3x - 2x = 5 + 7 → x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x = 12\", \"b\": \"x = -2\", \"c\": \"x = 2\", \"d\": \"x = -12\"}}","_debug_options_count":4},{"id":1549,"question":"La fonction f(x) = x² - 4x + 3 est croissante sur l'intervalle [2 ; +∞[.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 2x - 4 est positive pour x \u003E 2, donc la fonction est croissante sur [2 ; +∞[.","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":1550,"question":"Quel est le produit scalaire de deux vecteurs orthogonaux ?","option_a":"Leur norme","option_b":"0","option_c":"1","option_d":"Leur somme","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Leur norme\", \"b\": \"0\", \"c\": \"1\", \"d\": \"Leur somme\"}}","_debug_options_count":4},{"id":1551,"question":"La limite de (3x² - 2x + 1)\/(x² + 1) quand x tend vers +∞ est :","option_a":"3","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par x², on obtient (3 - 2\/x + 1\/x²)\/(1 + 1\/x²) → 3\/1 = 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\": \"3\", \"b\": \"0\", \"c\": \"1\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":1552,"question":"Une série statistique est toujours représentée par un diagramme en bâtons.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une série statistique peut être représentée par différents types de diagrammes (circulaire, en bâtons, histogramme) selon la nature des données.","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":1553,"question":"Quelle est la solution de l'inéquation -2x + 5 ≤ 3x - 7 ?","option_a":"x ≥ 12\/5","option_b":"x ≤ 12\/5","option_c":"x ≥ -12\/5","option_d":"x ≤ -12\/5","option_e":"","option_f":"","bonne_reponse":"a","explication":"En isolant x : -2x - 3x ≤ -7 - 5 → -5x ≤ -12 → x ≥ 12\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x ≥ 12\/5\", \"b\": \"x ≤ 12\/5\", \"c\": \"x ≥ -12\/5\", \"d\": \"x ≤ -","_debug_options_count":4},{"id":1554,"question":"Le centre de gravité d'un triangle est l'intersection de ses médianes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le centre de gravité d'un triangle est bien le point d'intersection de ses médianes.","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":1555,"question":"La dérivée de la fonction f(x) = ln(x) est :","option_a":"1\/x","option_b":"x","option_c":"e^x","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de la fonction logarithme népérien est 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"1\/x\", \"b\": \"x\", \"c\": \"e^x\", \"d\": \"1\"}}","_debug_options_count":4},{"id":1556,"question":"Un événement certain a une probabilité égale à :","option_a":"0","option_b":"0,5","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un événement certain a une probabilité de 1 (100%).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"0,5\", \"c\": \"1\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":1557,"question":"La fonction f(x) = (2x + 1)\/(x - 3) admet une asymptote verticale en x = 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction a une asymptote verticale en x = 3 car le dénominateur s'annule en ce point et le numérateur ne s'annule pas.","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}]