Quiz — corrsynt34M010.pdf

Question 1 sur 10 20:00

[{"id":32130,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 2","option_c":"x = 12","option_d":"x = -4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 7, on ajoute 5 aux deux côtés : 3x = 12, puis on divise par 3 : x = 4.","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 = 4\", \"b\": \"x = 2\", \"c\": \"x = 12\", \"d\": \"x = -4\"}}","_debug_options_count":4},{"id":32131,"question":"La fonction f(x) = x² - 4x + 3 admet un minimum en x = 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 s'annule en x = 2. Comme le coefficient devant x² est positif, la fonction admet bien un minimum en x = 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":32132,"question":"Quel est le résultat de √(16) + √(9) ?","option_a":"7","option_b":"5","option_c":"10","option_d":"13","option_e":"","option_f":"","bonne_reponse":"a","explication":"√(16) = 4 et √(9) = 3. Donc √(16) + √(9) = 4 + 3 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"7\", \"b\": \"5\", \"c\": \"10\", \"d\": \"13\"}}","_debug_options_count":4},{"id":32133,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est l'énoncé du théorème de Pythagore, valable uniquement pour les triangles rectangles.","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":32134,"question":"Quelle est la dérivée de la fonction f(x) = 5x³ - 2x² + x - 1 ?","option_a":"f'(x) = 15x² - 4x + 1","option_b":"f'(x) = 5x² - 2x + 1","option_c":"f'(x) = 15x² - 4x","option_d":"f'(x) = 15x² - 2x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 5x³ est 15x², celle de -2x² est -4x, celle de x est 1, et celle de -1 est 0. Donc f'(x) = 15x² - 4x + 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\": \"f'(x) = 15x² - 4x + 1\", \"b\": \"f'(x) = 5x² - 2x + 1\", \"c\": \"f'(x","_debug_options_count":4},{"id":32135,"question":"La médiane d'un triangle est toujours plus courte que la moitié de la longueur du côté opposé.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La médiane d'un triangle peut être plus longue ou plus courte que la moitié du côté opposé, selon la position du point.","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":32136,"question":"Résolvez l'inéquation : 2x + 3 \u003E 7.","option_a":"x \u003E 2","option_b":"x \u003E 5","option_c":"x \u003C 2","option_d":"x \u003C 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Soustraire 3 des deux côtés : 2x \u003E 4. Diviser par 2 : x \u003E 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\": \"x \u003E 2\", \"b\": \"x \u003E 5\", \"c\": \"x \u003C 2\", \"d\": \"x \u003C 5\"}}","_debug_options_count":4},{"id":32137,"question":"Le cosinus d'un angle aigu dans un triangle rectangle est toujours inférieur à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le cosinus d'un angle aigu est défini comme le rapport de la longueur du côté adjacent à l'hypoténuse. Comme l'hypoténuse est toujours plus longue que le côté adjacent, cos(θ) \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":32138,"question":"Quelle est la solution du système d'équations ? { 2x + y = 5 ; x - y = 1 }","option_a":"x = 2, y = 1","option_b":"x = 1, y = 3","option_c":"x = 3, y = -1","option_d":"x = 0, y = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"En additionnant les deux équations : 3x = 6 → x = 2. En remplaçant dans la deuxième équation : 2 - y = 1 → y = 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\": \"x = 2, y = 1\", \"b\": \"x = 1, y = 3\", \"c\": \"x = 3, y = -1\", \"d\": \"x","_debug_options_count":4},{"id":32139,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0, car la division par zéro est impossible.","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}]