Quiz — S 03 09 4M LPA.pdf

Question 1 sur 10 20:00

[{"id":9218,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2x","option_d":"3x² + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'un terme ax^n est nax^(n-1). Appliquez cette règle à chaque terme de la fonction.","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\": \"3x + 2\", \"c\": \"6x² + 2x\", \"d\": \"3x² + 2\"}}","_debug_options_count":4},{"id":9219,"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 de raison |q| \u003E 1 diverge vers l'infini. Ici, q = 2 \u003E 1, 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":9220,"question":"Soit f(x) = x³ - 3x + 1. Quel est le coefficient directeur de la tangente à la courbe en x = 1 ?","option_a":"0","option_b":"1","option_c":"-2","option_d":"3","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur de la tangente est égal à f'(1). Calculez f'(x) = 3x² - 3, puis f'(1) = 0.","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\": \"3\"}}","_debug_options_count":4},{"id":9221,"question":"Dans une classe de 30 élèves, 18 sont des filles. Quelle est la probabilité de choisir une fille au hasard ?","option_a":"0,4","option_b":"0,6","option_c":"0,18","option_d":"0,3","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité est le rapport du nombre de cas favorables sur le nombre total de cas : 18\/30 = 0,6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0,4\", \"b\": \"0,6\", \"c\": \"0,18\", \"d\": \"0,3\"}}","_debug_options_count":4},{"id":9222,"question":"La dérivée d'une fonction constante est toujours nulle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction constante f(x) = k est f'(x) = 0 pour tout 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":9223,"question":"Soit une suite définie par u0 = 1 et un+1 = 2un + 1. Que vaut u2 ?","option_a":"3","option_b":"5","option_c":"7","option_d":"9","option_e":"","option_f":"","bonne_reponse":"c","explication":"Calculez u1 = 2×1 + 1 = 3, puis u2 = 2×3 + 1 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"3\", \"b\": \"5\", \"c\": \"7\", \"d\": \"9\"}}","_debug_options_count":4},{"id":9224,"question":"Deux événements A et B ont P(A) = 0,5 et P(B) = 0,4. Si P(A ∩ B) = 0,2, sont-ils indépendants ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vérifiez si P(A ∩ B) = P(A) × P(B). Ici, 0,2 = 0,5 × 0,4, donc les événements sont indépendants.","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":9225,"question":"Quelle est la limite de la suite un = (2n + 1)\/n quand n tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"Divisez le numérateur et le dénominateur par n : un = (2 + 1\/n) → 2 quand n → ∞.","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\": \"∞\"}}","_debug_options_count":4},{"id":9226,"question":"La fonction f(x) = x² - 4x + 3 admet-elle un minimum en x = 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Calculez f'(x) = 2x - 4. f'(2) = 0 et f''(x) = 2 \u003E 0, donc f admet un minimum en x = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":9227,"question":"Soit une urne avec 5 boules rouges et 3 boules bleues. Quelle est la probabilité de tirer deux boules rouges sans remise ?","option_a":"25\/64","option_b":"15\/28","option_c":"10\/28","option_d":"5\/8","option_e":"","option_f":"","bonne_reponse":"b","explication":"Probabilité = (5\/8) × (4\/7) = 20\/56 = 15\/28.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"25\/64\", \"b\": \"15\/28\", \"c\": \"10\/28\", \"d\": \"5\/8\"}}","_debug_options_count":4}]