Quiz — Exercice N°3.pdf

Question 1 sur 10 20:00

[{"id":21759,"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 = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation 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":21760,"question":"La dérivée de la fonction f(x) = x³ - 3x² + 2x est f'(x) = 3x² - 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant la règle de dérivation, f'(x) = 3x² - 6x + 2 est correct.","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":21761,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"2","option_b":"1\/2","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par x², on obtient lim(x→∞) f(x) = 2\/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\": \"2\", \"b\": \"1\/2\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":21762,"question":"Dans un repère orthonormé, les vecteurs u(2;-1) et v(-4;2) sont :","option_a":"Colinéaires","option_b":"Orthogonaux","option_c":"Normaux","option_d":"Nuls","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les vecteurs sont colinéaires car v = -2u (vecteur u multiplié par -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\": \"Colinéaires\", \"b\": \"Orthogonaux\", \"c\": \"Normaux\", \"d\": \"Nuls\"}}","_debug_options_count":4},{"id":21763,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 3 nombres pairs (2,4,6) sur 6 possibles, donc P(pair) = 3\/6 = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":21764,"question":"Quelle est la somme des 5 premiers termes de la suite géométrique de premier terme 2 et de raison 3 ?","option_a":"242","option_b":"121","option_c":"62","option_d":"364","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme S = 2*(3^5 - 1)\/(3 - 1) = 2*(243-1)\/2 = 242.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"242\", \"b\": \"121\", \"c\": \"62\", \"d\": \"364\"}}","_debug_options_count":4},{"id":21765,"question":"L'équation cartésienne d'une droite passant par les points A(1;2) et B(3;4) est :","option_a":"y = x + 1","option_b":"y = 2x - 1","option_c":"y = x - 1","option_d":"y = 2x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur est (4-2)\/(3-1) = 1, donc y = x + 1 (car 2 = 1*1 + 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\": \"y = x + 1\", \"b\": \"y = 2x - 1\", \"c\": \"y = x - 1\", \"d\": \"y = 2x + 1","_debug_options_count":4},{"id":21766,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-1; 1].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 3 est négative sur [-1;1] (car 3x² ≤ 3), donc la fonction est décroissante.","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":21767,"question":"Quelle est la solution de l'inéquation 2x² - 5x + 2 \u003E 0 ?","option_a":"x ∈ ]-∞; 1\/2[ ∪ ]2; +∞[","option_b":"x ∈ ]1\/2; 2[","option_c":"x ∈ ]-∞; 2[","option_d":"x ∈ ]0; +∞[","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les racines sont x=1\/2 et x=2. Le trinôme est positif à l'extérieur des racines.","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\/2[ ∪ ]2; +∞[\", \"b\": \"x ∈ ]1\/2; 2[\", \"c\": \"x ","_debug_options_count":4},{"id":21768,"question":"L'aire d'un triangle de côtés 5, 6 et 7 est donnée par la formule :","option_a":"√(9*4*3*2)","option_b":"√(9*4*3)","option_c":"√(9*4*2)","option_d":"√(9*3*2)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la formule de Héron, p = (5+6+7)\/2 = 9, donc Aire = √(9*(9-5)*(9-6)*(9-7)) = √(9*4*3*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\": \"√(9*4*3*2)\", \"b\": \"√(9*4*3)\", \"c\": \"√(9*4*2)\", \"d\": \"√(9*","_debug_options_count":4}]