Quiz — dm14.pdf

Question 1 sur 10 20:00

[{"id":50853,"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 x² - 5x + 6 = 0 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":50854,"question":"La fonction f(x) = x³ - 3x est-elle impaire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction est impaire si f(-x) = -f(x). Ici, f(-x) = (-x)³ - 3(-x) = -x³ + 3x = -(x³ - 3x) = -f(x). Donc la fonction est impaire.","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":50855,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers l'infini ?","option_a":"2","option_b":"1\/3","option_c":"0","option_d":"3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant le numérateur et le dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 + 3\/n). Quand n tend vers l'infini, 1\/n et 3\/n tendent vers 0, donc la limite est 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\/3\", \"c\": \"0\", \"d\": \"3\"}}","_debug_options_count":4},{"id":50856,"question":"Dans un triangle ABC, si cos(A) = 0,5, alors l'angle A mesure :","option_a":"30°","option_b":"45°","option_c":"60°","option_d":"90°","option_e":"","option_f":"","bonne_reponse":"c","explication":"cos(60°) = 0,5, donc si cos(A) = 0,5, alors A = 60°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"30°\", \"b\": \"45°\", \"c\": \"60°\", \"d\": \"90°\"}}","_debug_options_count":4},{"id":50857,"question":"La dérivée de la fonction f(x) = e^(2x) est f'(x) = 2e^(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","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\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":50858,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"1\/6","option_b":"1\/2","option_c":"1\/3","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un dé équilibré a 6 faces : 1, 2, 3, 4, 5, 6. Les nombres pairs sont 2, 4, 6, soit 3 faces. La probabilité est donc 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\": \"b\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/2\", \"c\": \"1\/3\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":50859,"question":"Soit une suite géométrique de premier terme u₀ = 3 et de raison q = 2. Quel est le terme u₃ ?","option_a":"12","option_b":"24","option_c":"48","option_d":"96","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le terme général d'une suite géométrique est uₙ = u₀ * qⁿ. Donc u₃ = 3 * 2³ = 3 * 8 = 24.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"12\", \"b\": \"24\", \"c\": \"48\", \"d\": \"96\"}}","_debug_options_count":4},{"id":50860,"question":"Le vecteur AB a pour coordonnées (3, -2). Le vecteur BA est égal à :","option_a":"(3, -2)","option_b":"(-3, 2)","option_c":"(2, -3)","option_d":"(-2, 3)","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le vecteur BA est l'opposé du vecteur AB, donc BA = (-3, 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"(3, -2)\", \"b\": \"(-3, 2)\", \"c\": \"(2, -3)\", \"d\": \"(-2, 3)\"}}","_debug_options_count":4},{"id":50861,"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 ln(x) 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":50862,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003C 3x + 1 ?","option_a":"x \u003E -6","option_b":"x \u003C -6","option_c":"x \u003E 6","option_d":"x \u003C 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"2x - 5 \u003C 3x + 1 ⇒ -5 - 1 \u003C 3x - 2x ⇒ -6 \u003C x ⇒ x \u003E -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\": \"x \u003E -6\", \"b\": \"x \u003C -6\", \"c\": \"x \u003E 6\", \"d\": \"x \u003C 6\"}}","_debug_options_count":4}]