Quiz — 56.DOC

Question 1 sur 10 20:00

[{"id":15029,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x + 5","option_d":"x + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme à terme. La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2x + 3\", \"b\": \"x² + 3\", \"c\": \"2x + 5\", \"d\": \"x + 3\"}}","_debug_options_count":4},{"id":15030,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc elle est arithmétique.","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":15031,"question":"Quel est le discriminant d'une équation du second degré ax² + bx + c = 0 ?","option_a":"b² - 4ac","option_b":"a² - 4bc","option_c":"4ac - b²","option_d":"b² + 4ac","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant Δ = b² - 4ac détermine la nature des racines de l'équation du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"b² - 4ac\", \"b\": \"a² - 4bc\", \"c\": \"4ac - b²\", \"d\": \"b² + 4ac\"}","_debug_options_count":4},{"id":15032,"question":"La fonction exponentielle est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle, définie pour tout réel x, prend des valeurs strictement positives (eˣ \u003E 0 pour tout x ∈ ℝ).","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":15033,"question":"Quelle est la limite de (3n² + 2n - 1)\/(2n² + 5) quand n tend vers l'infini ?","option_a":"3\/2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour les limites de polynômes à l'infini, on compare les termes de plus haut degré. Ici, 3n²\/2n² = 3\/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\": \"3\/2\", \"b\": \"0\", \"c\": \"1\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":15034,"question":"Un événement impossible a une probabilité de :","option_a":"0","option_b":"1","option_c":"0,5","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En probabilités, un événement impossible a une probabilité de 0, tandis qu'un événement certain a une probabilité de 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\": \"0\", \"b\": \"1\", \"c\": \"0,5\", \"d\": \"1\/2\"}}","_debug_options_count":4},{"id":15035,"question":"La dérivée de sin(x) est cos(x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de la fonction sinus est bien la fonction cosinus : d\/dx [sin(x)] = cos(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":15036,"question":"Quelle est l'intégrale de f(x) = 2x entre 0 et 3 ?","option_a":"9","option_b":"6","option_c":"3","option_d":"12","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 2x est x². Évaluée entre 0 et 3 : 3² - 0² = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"9\", \"b\": \"6\", \"c\": \"3\", \"d\": \"12\"}}","_debug_options_count":4},{"id":15037,"question":"Une suite géométrique a pour raison q = -2. Est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite géométrique converge si et seulement si |q| \u003C 1. Ici, |q| = 2 \u003E 1, donc elle diverge.","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":15038,"question":"Quel est le résultat de (a + b)² ?","option_a":"a² + 2ab + b²","option_b":"a² + b²","option_c":"2a + 2b","option_d":"a² - b²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'identité remarquable (a + b)² = a² + 2ab + b² est fondamentale en algèbre.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"a² + 2ab + b²\", \"b\": \"a² + b²\", \"c\": \"2a + 2b\", \"d\": \"a² - b","_debug_options_count":4}]