Quiz — 6458d11ab21c6_Devoir de synthèse n°3 Enoncé.pdf

Question 1 sur 10 20:00

[{"id":25999,"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. Les solutions sont donc 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":26000,"question":"La fonction f(x) = x² - 4x + 3 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = x² - 4x + 3 est une parabole ouverte vers le haut avec un minimum en x = 2. Elle prend des valeurs négatives entre ses racines (x = 1 et x = 3).","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":26001,"question":"Quel est le coefficient directeur de la droite d'équation y = 3x - 2 ?","option_a":"3","option_b":"-2","option_c":"1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans l'équation réduite y = mx + p, m représente le coefficient directeur. Ici, m = 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\": \"-2\", \"c\": \"1\", \"d\": \"0\"}}","_debug_options_count":4},{"id":26002,"question":"Si A et B sont deux événements incompatibles, alors P(A ∪ B) = P(A) + P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour deux événements incompatibles, la probabilité de leur union est bien la somme de leurs probabilités individuelles.","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":26003,"question":"Quelle est la forme factorisée de l'expression 4x² - 9 ?","option_a":"(2x - 3)(2x + 3)","option_b":"(4x - 9)(x + 1)","option_c":"(2x + 3)²","option_d":"(2x - 3)²","option_e":"","option_f":"","bonne_reponse":"a","explication":"4x² - 9 est une différence de carrés : (2x)² - 3² = (2x - 3)(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)(2x + 3)\", \"b\": \"(4x - 9)(x + 1)\", \"c\": \"(2x + 3)²\", \"d\"","_debug_options_count":4},{"id":26004,"question":"La dérivée de la fonction f(x) = x³ est f'(x) = 3x².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x³ est bien 3x², selon la règle de dérivation des fonctions puissances.","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":26005,"question":"Résoudre l'inéquation 2x - 5 \u003E 3.","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"2x - 5 \u003E 3 ⇒ 2x \u003E 8 ⇒ x \u003E 4.","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 4\", \"b\": \"x \u003C 4\", \"c\": \"x \u003E 1\", \"d\": \"x \u003C 1\"}}","_debug_options_count":4},{"id":26006,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par Δ = b² - 4ac.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule du discriminant est bien Δ = b² - 4ac.","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":26007,"question":"Quelle est la valeur de x dans l'équation 3(x + 2) = 2x + 9 ?","option_a":"x = 3","option_b":"x = 1","option_c":"x = -3","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"3(x + 2) = 2x + 9 ⇒ 3x + 6 = 2x + 9 ⇒ 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 = 3\", \"b\": \"x = 1\", \"c\": \"x = -3\", \"d\": \"x = 0\"}}","_debug_options_count":4},{"id":26008,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","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}]