Quiz — img309.pdf

Question 1 sur 10 20:00

[{"id":93738,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x² + 2x","option_d":"6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 0. Donc 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\": \"3x² + 2\", \"c\": \"6x² + 2x\", \"d\": \"6x + 2x - 5\"}}","_debug_options_count":4},{"id":93739,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 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 uniquement si |q| \u003C 1. Ici, q = 2, donc la suite 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":93740,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers l'infini ?","option_a":"0","option_b":"2","option_c":"1\/3","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"En divisant numérateur et dénominateur par n, on obtient (2 + 1\/n)\/(1 + 3\/n). Quand n → ∞, cela tend vers 2\/1 = 2. Mais ici, la limite est 2\/1 = 2, donc la bonne réponse est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"2\", \"c\": \"1\/3\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":93741,"question":"Dans une urne contenant 4 boules rouges et 6 boules bleues, quelle est la probabilité de tirer une boule rouge ?","option_a":"0,4","option_b":"0,6","option_c":"0,5","option_d":"0,25","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 4 boules rouges sur un total de 10 boules. La probabilité est donc 4\/10 = 0,4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,4\", \"b\": \"0,6\", \"c\": \"0,5\", \"d\": \"0,25\"}}","_debug_options_count":4},{"id":93742,"question":"La dérivée d'une fonction constante est toujours égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée d'une fonction constante est toujours égale à 0, car sa pente est nulle.","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":93743,"question":"Quelle est la formule de la dérivée de la fonction f(x) = e^(2x) ?","option_a":"e^(2x)","option_b":"2e^(2x)","option_c":"e^(x)","option_d":"2e^(x)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de e^(u(x)) est u'(x) * e^(u(x)). Ici, u(x) = 2x, donc u'(x) = 2. Ainsi, f'(x) = 2e^(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"e^(2x)\", \"b\": \"2e^(2x)\", \"c\": \"e^(x)\", \"d\": \"2e^(x)\"}}","_debug_options_count":4},{"id":93744,"question":"Une suite arithmétique de raison r = -3 et de premier terme u₀ = 10 est-elle décroissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite arithmétique est décroissante si sa raison est négative. Ici, r = -3 \u003C 0, donc la suite est bien décroissante.","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":93745,"question":"Quelle est la probabilité de tirer deux boules rouges successivement sans remise dans une urne contenant 5 boules rouges et 5 boules bleues ?","option_a":"0,2","option_b":"0,25","option_c":"0,5","option_d":"0,1","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité de tirer une boule rouge en premier est 5\/10 = 0,5. Ensuite, il reste 4 boules rouges sur 9. La probabilité totale est 0,5 * (4\/9) ≈ 0,222, soit environ 0,25.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0,2\", \"b\": \"0,25\", \"c\": \"0,5\", \"d\": \"0,1\"}}","_debug_options_count":4},{"id":93746,"question":"La dérivée de la fonction f(x) = ln(x) est f'(x) = 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est bien 1\/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":93747,"question":"Quelle est la limite de la suite uₙ = (n² + 1)\/(n + 1) quand n tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"n","option_e":"","option_f":"","bonne_reponse":"c","explication":"En divisant numérateur et dénominateur par n, on obtient (n + 1\/n)\/(1 + 1\/n). Quand n → ∞, cela tend vers n\/1 = ∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"∞\", \"d\": \"n\"}}","_debug_options_count":4}]