Quiz — dl170809c.pdf

Question 1 sur 10 20:00

[{"id":16119,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = -1 ou x = -6","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0, donc les solutions sont x = 2 et x = 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\": \"x = 2 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4},{"id":16120,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle dérivable en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction est un polynôme, donc elle est dérivable en tout point de son domaine de définition, y compris x = 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":16121,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par x², on obtient (2 + 3\/x - 5\/x²)\/(1 - 4\/x²), donc la limite est 2\/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\": \"2\", \"b\": \"1\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":16122,"question":"L'intégrale ∫(3x² + 2x + 1)dx est égale à :","option_a":"x³ + x² + x + C","option_b":"x³ + x² + C","option_c":"3x³ + 2x² + x + C","option_d":"x³ + x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 3x² est x³, celle de 2x est x², celle de 1 est x, donc le résultat est x³ + 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\": \"x³ + x² + x + C\", \"b\": \"x³ + x² + C\", \"c\": \"3x³ + 2x² + x +","_debug_options_count":4},{"id":16123,"question":"Une urne contient 5 boules rouges et 3 boules bleues. On tire une boule au hasard. La probabilité de tirer une boule bleue est :","option_a":"3\/8","option_b":"5\/8","option_c":"3\/5","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 8 boules au total, dont 3 bleues. La probabilité est donc 3\/8.","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\/8\", \"b\": \"5\/8\", \"c\": \"3\/5\", \"d\": \"1\/2\"}}","_debug_options_count":4},{"id":16124,"question":"La dérivée de la fonction f(x) = sin(2x) est f'(x) = 2cos(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la règle de dérivation des fonctions composées, f'(x) = cos(2x) * 2 = 2cos(2x).","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":16125,"question":"Quelle est la solution de l'inéquation x² - 4x + 3 \u003C 0 ?","option_a":"x ∈ ]1, 3[","option_b":"x ∈ ]-∞, 1[ ∪ ]3, +∞[","option_c":"x ∈ ]-∞, 1[","option_d":"x ∈ ]3, +∞[","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'inéquation x² - 4x + 3 \u003C 0 est vérifiée entre les racines x = 1 et x = 3, donc x ∈ ]1, 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\": \"x ∈ ]1, 3[\", \"b\": \"x ∈ ]-∞, 1[ ∪ ]3, +∞[\", \"c\": \"x ∈ ","_debug_options_count":4},{"id":16126,"question":"L'aire sous la courbe de f(x) = x² entre x = 0 et x = 2 est égale à :","option_a":"8\/3","option_b":"4\/3","option_c":"2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'aire est donnée par l'intégrale ∫(x²)dx de 0 à 2, soit [x³\/3] de 0 à 2 = 8\/3 - 0 = 8\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"8\/3\", \"b\": \"4\/3\", \"c\": \"2\", \"d\": \"1\"}}","_debug_options_count":4},{"id":16127,"question":"La probabilité conditionnelle P(A|B) est définie par :","option_a":"P(A ∩ B)\/P(B)","option_b":"P(A) * P(B)","option_c":"P(A) + P(B)","option_d":"P(A)\/P(B)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité conditionnelle P(A|B) est définie comme le rapport P(A ∩ B)\/P(B).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"P(A ∩ B)\/P(B)\", \"b\": \"P(A) * P(B)\", \"c\": \"P(A) + P(B)\", \"d\": \"P","_debug_options_count":4},{"id":16128,"question":"La fonction f(x) = e^(2x) est-elle 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) = e^(2x) est f'(x) = 2e^(2x), qui est toujours positive. Donc la fonction est 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}]