Quiz — correction devoir contrôle 2 math 3M 20-21.pdf

Question 1 sur 5 10:00

[{"id":1307,"question":"Quelle est la solution de l'équation \u003Cem\u003Ex² - 5x + 6 = 0\u003C\/em\u003E ?","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":"Pour résoudre l'équation du second degré \u003Cem\u003Ex² - 5x + 6 = 0\u003C\/em\u003E, on utilise la méthode du discriminant : Δ = b² - 4ac = 25 - 24 = 1. Les solutions sont donc x = (5 ± √1)\/2, soit x = 2 ou 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":1308,"question":"Quelle est la dérivée de la fonction \u003Cem\u003Ef(x) = 3x² - 2x + 1\u003C\/em\u003E ?","option_a":"f'(x) = 6x - 2","option_b":"f'(x) = 3x - 2","option_c":"f'(x) = 6x² - 2x","option_d":"f'(x) = 3x² - 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : la dérivée de \u003Cem\u003E3x²\u003C\/em\u003E est \u003Cem\u003E6x\u003C\/em\u003E, celle de \u003Cem\u003E-2x\u003C\/em\u003E est \u003Cem\u003E-2\u003C\/em\u003E, et celle de \u003Cem\u003E1\u003C\/em\u003E est \u003Cem\u003E0\u003C\/em\u003E. Ainsi, \u003Cem\u003Ef'(x) = 6x - 2\u003C\/em\u003E.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f'(x) = 6x - 2\", \"b\": \"f'(x) = 3x - 2\", \"c\": \"f'(x) = 6x² - 2x\",","_debug_options_count":4},{"id":1309,"question":"Dans un repère orthonormé, quel est le produit scalaire des vecteurs \u003Cem\u003Eu(2; -3)\u003C\/em\u003E et \u003Cem\u003Ev(-1; 4)\u003C\/em\u003E ?","option_a":"-14","option_b":"14","option_c":"-6","option_d":"6","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le produit scalaire de deux vecteurs \u003Cem\u003Eu(x; y)\u003C\/em\u003E et \u003Cem\u003Ev(x'; y')\u003C\/em\u003E est donné par \u003Cem\u003Exx' + yy'\u003C\/em\u003E. Ici, \u003Cem\u003E2 × (-1) + (-3) × 4 = -2 - 12 = -14\u003C\/em\u003E.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"-14\", \"b\": \"14\", \"c\": \"-6\", \"d\": \"6\"}}","_debug_options_count":4},{"id":1310,"question":"Quelle est l'équation réduite de la droite passant par les points A(1; 2) et B(3; 6) ?","option_a":"y = 2x","option_b":"y = x + 1","option_c":"y = 3x - 1","option_d":"y = -2x + 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur de la droite est \u003Cem\u003E(6-2)\/(3-1) = 2\u003C\/em\u003E. En utilisant le point A(1; 2), l'équation est \u003Cem\u003Ey - 2 = 2(x - 1)\u003C\/em\u003E, soit \u003Cem\u003Ey = 2x\u003C\/em\u003E.","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 = 2x\", \"b\": \"y = x + 1\", \"c\": \"y = 3x - 1\", \"d\": \"y = -2x + 4\"}","_debug_options_count":4},{"id":1311,"question":"Quel est le volume d'un cube d'arête 4 cm ?","option_a":"64 cm³","option_b":"16 cm³","option_c":"32 cm³","option_d":"12 cm³","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le volume d'un cube se calcule par la formule \u003Cem\u003EV = arête³\u003C\/em\u003E. Ici, \u003Cem\u003EV = 4³ = 64 cm³\u003C\/em\u003E.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"64 cm³\", \"b\": \"16 cm³\", \"c\": \"32 cm³\", \"d\": \"12 cm³\"}}","_debug_options_count":4}]