Quiz — 12.DOC

Question 1 sur 10 20:00

[{"id":59114,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x - 5","option_d":"x + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc 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 - 5\", \"d\": \"x + 3\"}}","_debug_options_count":4},{"id":59115,"question":"La suite (uₙ) définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2(n+1)+1 - (2n+1) = 2, donc c'est une suite arithmétique de raison 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":59116,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"3","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour les fonctions rationnelles, la limite en l'infini est le rapport des coefficients des termes de plus haut degré. Ici, 3x²\/x² = 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\": \"3\", \"b\": \"0\", \"c\": \"1\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":59117,"question":"Un événement A a une probabilité de 0,4. Quelle est la probabilité de son événement contraire ?","option_a":"0,6","option_b":"0,4","option_c":"0,2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité de l'événement contraire est 1 - P(A) = 1 - 0,4 = 0,6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,6\", \"b\": \"0,4\", \"c\": \"0,2\", \"d\": \"1\"}}","_debug_options_count":4},{"id":59118,"question":"La fonction exponentielle est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle eˣ est définie pour tout x réel et eˣ \u003E 0 pour tout x ∈ 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":59119,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"e²","option_b":"2","option_c":"1\/2","option_d":"ln(2)","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation ln(x) = 2 équivaut à x = e², car ln(e²) = 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\": \"e²\", \"b\": \"2\", \"c\": \"1\/2\", \"d\": \"ln(2)\"}}","_debug_options_count":4},{"id":59120,"question":"Dans un repère orthonormé, quelle est la distance entre les points A(1, 2) et B(4, 6) ?","option_a":"5","option_b":"√7","option_c":"√13","option_d":"√29","option_e":"","option_f":"","bonne_reponse":"d","explication":"La distance entre A et B est √[(4-1)² + (6-2)²] = √(9 + 16) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"5\", \"b\": \"√7\", \"c\": \"√13\", \"d\": \"√29\"}}","_debug_options_count":4},{"id":59121,"question":"Un nombre complexe z = 3 + 4i a pour module |z| = 5. Vrai ou faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module de z = a + bi est √(a² + b²). Ici, |z| = √(3² + 4²) = √(9 + 16) = √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":59122,"question":"Quelle est la valeur de la somme S = 1 + 2 + 3 + ... + n ?","option_a":"n(n+1)\/2","option_b":"n²","option_c":"2n","option_d":"n\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La somme des n premiers entiers naturels est donnée par la formule S = n(n+1)\/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\": \"n(n+1)\/2\", \"b\": \"n²\", \"c\": \"2n\", \"d\": \"n\/2\"}}","_debug_options_count":4},{"id":59123,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 6x + 2 n'est pas toujours positive (exemple : f'(0) = 2 \u003E 0, mais f'(2) = -2 \u003C 0). Donc f n'est pas croissante sur ℝ.","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}]