Quiz — 1576612548_62572_exercice-2.pdf

Question 1 sur 10 20:00

[{"id":40170,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0,5 ou x = 2","option_c":"x = -1 ou x = -2","option_d":"x = 1 ou x = 0,5","option_e":"","option_f":"","bonne_reponse":"b","explication":"La résolution de l'équation du second degré donne deux solutions : x = 2 et x = 0,5 (en utilisant la formule des racines ou la factorisation).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x = 1 ou x = 2\", \"b\": \"x = 0,5 ou x = 2\", \"c\": \"x = -1 ou x = -2\"","_debug_options_count":4},{"id":40171,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2 ; 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = -1 et x = 1. La fonction est décroissante sur [-1 ; 1] et croissante ailleurs.","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":40172,"question":"Quel est le terme général d'une suite géométrique de premier terme u₀ = 3 et de raison q = 2 ?","option_a":"uₙ = 3 × 2ⁿ","option_b":"uₙ = 3 + 2n","option_c":"uₙ = 3 × n²","option_d":"uₙ = 2 × 3ⁿ","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le terme général d'une suite géométrique est uₙ = u₀ × qⁿ. Ici, u₀ = 3 et q = 2, donc uₙ = 3 × 2ⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"uₙ = 3 × 2ⁿ\", \"b\": \"uₙ = 3 + 2n\", \"c\": \"uₙ = 3 × n²\", ","_debug_options_count":4},{"id":40173,"question":"Le triangle ABC est rectangle en A avec AB = 3 cm et AC = 4 cm. Quelle est la longueur de BC ?","option_a":"5 cm","option_b":"7 cm","option_c":"√7 cm","option_d":"√13 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, BC² = AB² + AC² = 9 + 16 = 25, donc BC = 5 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"5 cm\", \"b\": \"7 cm\", \"c\": \"√7 cm\", \"d\": \"√13 cm\"}}","_debug_options_count":4},{"id":40174,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction logarithme népérien est définie uniquement pour x \u003E 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":40175,"question":"Quelle est la valeur de la dérivée de f(x) = x² + 2x + 1 en x = 1 ?","option_a":"2","option_b":"3","option_c":"4","option_d":"5","option_e":"","option_f":"","bonne_reponse":"d","explication":"La dérivée f'(x) = 2x + 2. En x = 1, f'(1) = 2(1) + 2 = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"2\", \"b\": \"3\", \"c\": \"4\", \"d\": \"5\"}}","_debug_options_count":4},{"id":40176,"question":"Un dé équilibré est lancé deux fois. Quelle est la probabilité d'obtenir deux fois le chiffre 6 ?","option_a":"1\/6","option_b":"1\/12","option_c":"1\/36","option_d":"1\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"La probabilité d'obtenir un 6 est 1\/6. Pour deux lancers indépendants, la probabilité est (1\/6) × (1\/6) = 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/12\", \"c\": \"1\/36\", \"d\": \"1\/3\"}}","_debug_options_count":4},{"id":40177,"question":"La droite d'équation y = 2x + 3 passe par le point A(1 ; 5).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant x = 1 dans l'équation, on obtient y = 2(1) + 3 = 5, donc le point A appartient à la droite.","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":40178,"question":"Quel est le développement limité de la fonction f(x) = eˣ au voisinage de 0 à l'ordre 2 ?","option_a":"1 + x + x²\/2","option_b":"1 + x","option_c":"1 + x²","option_d":"1 + 2x + x²","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le développement limité de eˣ à l'ordre 2 est 1 + x + x²\/2 + o(x²).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"1 + x + x²\/2\", \"b\": \"1 + x\", \"c\": \"1 + x²\", \"d\": \"1 + 2x + x²\"","_debug_options_count":4},{"id":40179,"question":"La somme des angles d'un triangle est égale à 180 degrés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale de la géométrie euclidienne : la somme des angles d'un triangle est toujours égale à 180 degrés.","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}]