Quiz — synthèse 3 (2014).pdf

Question 1 sur 10 20:00

[{"id":38650,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A. 6x + 2","option_b":"B. 3x + 2","option_c":"C. 6x² + 2","option_d":"D. 3x² + 2x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : f'(x) = 6x + 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\": \"A. 6x + 2\", \"b\": \"B. 3x + 2\", \"c\": \"C. 6x² + 2\", \"d\": \"D. 3x² +","_debug_options_count":4},{"id":38651,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle ]-∞, -1[.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² - 3 est positive sur ]-∞, -1[ car 3x² \u003E 3 pour x \u003C -1.","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":38652,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"A. x = 1 et x = 2","option_b":"B. x = -1 et x = -2","option_c":"C. x = 0.5 et x = 2","option_d":"D. x = -0.5 et x = 2","option_e":"","option_f":"","bonne_reponse":"c","explication":"Les solutions sont x = [5 ± √(25 - 16)] \/ 4 = [5 ± 3]\/4 → x = 2 ou x = 0.5.","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. x = 1 et x = 2\", \"b\": \"B. x = -1 et x = -2\", \"c\": \"C. x = 0.5 ","_debug_options_count":4},{"id":38653,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux vecteurs orthogonaux ont un produit scalaire nul.","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":38654,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x) \/ (x² - 1) quand x tend vers +∞ ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par x², on obtient lim (2 + 3\/x) \/ (1 - 1\/x²) = 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. 0\", \"b\": \"B. 2\", \"c\": \"C. +∞\", \"d\": \"D. -∞\"}}","_debug_options_count":4},{"id":38655,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","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.","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":38656,"question":"Quelle est l'équation de la tangente à la courbe y = x² + 1 au point d'abscisse x = 1 ?","option_a":"A. y = 2x + 1","option_b":"B. y = 2x - 1","option_c":"C. y = x + 1","option_d":"D. y = 3x - 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"La tangente a pour équation y = f'(1)(x - 1) + f(1) = 2(x - 1) + 2 = 2x.","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. y = 2x + 1\", \"b\": \"B. y = 2x - 1\", \"c\": \"C. y = x + 1\", \"d\": \"","_debug_options_count":4},{"id":38657,"question":"La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'un événement impossible est égale 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":38658,"question":"Quelle est la solution de l'inéquation 3x - 7 \u003C 2x + 5 ?","option_a":"A. x \u003C 12","option_b":"B. x \u003E 12","option_c":"C. x \u003C -12","option_d":"D. x \u003E -12","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 2x \u003C 5 + 7 → x \u003C 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\": \"A. x \u003C 12\", \"b\": \"B. x \u003E 12\", \"c\": \"C. x \u003C -12\", \"d\": \"D. x \u003E -12","_debug_options_count":4},{"id":38659,"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":"Par définition, le centre de gravité est le point d'intersection des médianes d'un triangle.","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}]