Quiz — 6428230e9e1e0_énoncé_magazine 31 (Révision).pdf

Question 1 sur 10 20:00

[{"id":62123,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"6x² + 2x","option_c":"3x + 2","option_d":"6x + 2x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d’une fonction polynôme s’obtient en appliquant la règle de dérivation : 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\": \"6x + 2\", \"b\": \"6x² + 2x\", \"c\": \"3x + 2\", \"d\": \"6x + 2x\"}}","_debug_options_count":4},{"id":62124,"question":"La limite de 1\/x quand x tend vers 0+ est égale à +∞.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En effet, lorsque x tend vers 0 par valeurs positives, 1\/x tend vers +∞.","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":62125,"question":"Quel est le résultat de l’intégrale ∫(2x + 1) dx ?","option_a":"x² + x + C","option_b":"x² + C","option_c":"2x² + x + C","option_d":"x² + 2x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L’intégrale de 2x est x² et celle de 1 est x, donc le résultat est x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x² + x + C\", \"b\": \"x² + C\", \"c\": \"2x² + x + C\", \"d\": \"x² + 2x","_debug_options_count":4},{"id":62126,"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, le produit scalaire de deux vecteurs orthogonaux est 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":62127,"question":"Quelle est la solution de l’équation 2x - 3 = 7 ?","option_a":"x = 5","option_b":"x = 2","option_c":"x = 10","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En ajoutant 3 aux deux côtés, on obtient 2x = 10, puis x = 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 = 5\", \"b\": \"x = 2\", \"c\": \"x = 10\", \"d\": \"x = -2\"}}","_debug_options_count":4},{"id":62128,"question":"La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle e^x est strictement positive pour tout x réel.","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":62129,"question":"Quel est le résultat de (x + 2)² ?","option_a":"x² + 4x + 4","option_b":"x² + 2x + 4","option_c":"x² + 4","option_d":"x² + 4x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En développant (x + 2)², on obtient x² + 4x + 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\": \"x² + 4x + 4\", \"b\": \"x² + 2x + 4\", \"c\": \"x² + 4\", \"d\": \"x² + 4","_debug_options_count":4},{"id":62130,"question":"La dérivée de ln(x) est 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de la fonction logarithme népérien ln(x) est bien 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":62131,"question":"Quelle est la probabilité d’obtenir un 6 en lançant un dé équilibré ?","option_a":"1\/6","option_b":"1\/2","option_c":"1\/3","option_d":"1\/4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un dé équilibré a 6 faces, donc la probabilité d’obtenir un 6 est de 1\/6.","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\/6\", \"b\": \"1\/2\", \"c\": \"1\/3\", \"d\": \"1\/4\"}}","_debug_options_count":4},{"id":62132,"question":"La fonction f(x) = x³ est paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = -x³ ≠ f(x), donc elle est impaire.","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}]