Quiz — img089.pdf

Question 1 sur 10 20:00

[{"id":1528,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0,5 ou x = 2","option_c":"x = -1 ou x = -2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Résolvez l'équation en utilisant la formule du discriminant Δ = b² - 4ac. Ici, Δ = 25 - 16 = 9, donc x = (5 ± 3)\/4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x = 1 ou x = 2\", \"b\": \"x = 0,5 ou x = 2\", \"c\": \"x = -1 ou x = -2\"","_debug_options_count":4},{"id":1529,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction est décroissante sur [-1, 1], donc l'affirmation est fausse.","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":1530,"question":"Quelle est la limite de (sin x)\/x quand x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"n'existe pas","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est un résultat fondamental en analyse : lim (x→0) (sin x)\/x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"∞\", \"d\": \"n'existe pas\"}}","_debug_options_count":4},{"id":1531,"question":"Soit une suite définie par uₙ₊₁ = 2uₙ + 1 avec u₀ = 0. Quelle est la valeur de u₃ ?","option_a":"7","option_b":"15","option_c":"31","option_d":"63","option_e":"","option_f":"","bonne_reponse":"c","explication":"Calculez les termes successifs : u₁ = 1, u₂ = 3, u₃ = 7. Attention à ne pas confondre avec une suite géométrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"7\", \"b\": \"15\", \"c\": \"31\", \"d\": \"63\"}}","_debug_options_count":4},{"id":1532,"question":"Le théorème des valeurs intermédiaires s'applique à toute fonction continue sur un intervalle fermé.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème nécessite que la fonction soit continue sur un intervalle fermé [a, b] et que f(a) et f(b) soient de signes opposés pour garantir l'existence d'une solution.","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":1533,"question":"Quelle est la dérivée de f(x) = ln(x² + 1) ?","option_a":"f'(x) = 2x\/(x² + 1)","option_b":"f'(x) = 1\/(x² + 1)","option_c":"f'(x) = 2x","option_d":"f'(x) = x\/(x² + 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Appliquez la dérivée d'une fonction composée : f'(x) = (2x)\/(x² + 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) = 2x\/(x² + 1)\", \"b\": \"f'(x) = 1\/(x² + 1)\", \"c\": \"f'(x) = ","_debug_options_count":4},{"id":1534,"question":"Un dé équilibré est lancé deux fois. Quelle est la probabilité d'obtenir deux fois le chiffre 6 ?","option_a":"1\/6","option_b":"1\/12","option_c":"1\/36","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"c","explication":"La probabilité d'obtenir un 6 est 1\/6. Pour deux lancers indépendants, multipliez les probabilités : (1\/6) × (1\/6) = 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/12\", \"c\": \"1\/36\", \"d\": \"1\/2\"}}","_debug_options_count":4},{"id":1535,"question":"La fonction f(x) = e^x est sa propre dérivée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^x est bien e^x, donc l'affirmation est vraie.","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":1536,"question":"Quelle est l'intégrale de f(x) = 3x² entre 0 et 2 ?","option_a":"4","option_b":"6","option_c":"8","option_d":"12","option_e":"","option_f":"","bonne_reponse":"c","explication":"Calculez l'intégrale indéfinie : ∫3x² dx = x³ + C. Évaluez entre 0 et 2 : 2³ - 0³ = 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"4\", \"b\": \"6\", \"c\": \"8\", \"d\": \"12\"}}","_debug_options_count":4},{"id":1537,"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, donc l'affirmation est vraie.","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}]