Quiz — S17C.pdf

Question 1 sur 10 20:00

[{"id":86778,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x + 3x","option_d":"x + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (x²)' = 2x, (3x)' = 3 et (-5)' = 0. Ainsi, f'(x) = 2x + 3.","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 + 3x\", \"d\": \"x + 3\"}}","_debug_options_count":4},{"id":86779,"question":"La fonction f(x) = x³ est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = x³ est f'(x) = 3x², qui est toujours positive ou nulle. La fonction est donc strictement croissante sur 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":86780,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx ?","option_a":"x² + x + C","option_b":"2x² + x + C","option_c":"x² + 2x + C","option_d":"x² + x","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale d'une somme est la somme des intégrales. ∫2x dx = x² et ∫1 dx = x. On ajoute la constante d'intégration 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\": \"2x² + x + C\", \"c\": \"x² + 2x + C\", \"d\": \"x²","_debug_options_count":4},{"id":86781,"question":"La suite définie par uₙ₊₁ = 2uₙ + 1 avec u₀ = 0 est-elle arithmétique ?","option_a":"Oui","option_b":"Non","option_c":"Parfois","option_d":"On ne peut pas savoir","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite arithmétique a une différence constante entre deux termes consécutifs. Ici, uₙ₊₁ - uₙ = uₙ + 1, qui n'est pas constant.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Oui\", \"b\": \"Non\", \"c\": \"Parfois\", \"d\": \"On ne peut pas savoir\"}}","_debug_options_count":4},{"id":86782,"question":"Le nombre complexe z = 3 + 4i a pour module |z| = 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module d'un nombre complexe z = a + bi est |z| = √(a² + b²). Ici, |z| = √(3² + 4²) = √25 = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":86783,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"b","explication":"On peut simplifier f(x) = (x - 1)(x + 1)\/(x - 1) = x + 1 pour x ≠ 1. Ainsi, lim(x→1) f(x) = 1 + 1 = 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\": \"0\", \"b\": \"1\", \"c\": \"2\", \"d\": \"La limite n'existe pas\"}}","_debug_options_count":4},{"id":86784,"question":"Dans un espace vectoriel, deux vecteurs non nuls sont toujours colinéaires.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Deux vecteurs sont colinéaires s'il existe un réel λ tel que u = λv. Ce n'est pas toujours le cas, par exemple pour les vecteurs (1,0) et (0,1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":86785,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"1\/6","option_b":"1\/12","option_c":"1\/36","option_d":"1\/18","option_e":"","option_f":"","bonne_reponse":"c","explication":"Il y a 6 faces sur chaque dé, soit 6 × 6 = 36 combinaisons possibles. Seul un cas correspond à un double 6 : (6,6). La probabilité est donc 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\/18\"}}","_debug_options_count":4},{"id":86786,"question":"La fonction f(x) = eˣ 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 la fonction exponentielle f(x) = eˣ est f'(x) = eˣ. Elle est donc bien sa propre dérivée.","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":86787,"question":"Quel est le résultat de la somme des angles intérieurs d'un pentagone convexe ?","option_a":"360°","option_b":"540°","option_c":"720°","option_d":"900°","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme des angles intérieurs d'un polygone à n côtés est (n - 2) × 180°. Pour un pentagone (n=5), cela donne (5-2) × 180° = 540°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"360°\", \"b\": \"540°\", \"c\": \"720°\", \"d\": \"900°\"}}","_debug_options_count":4}]