Quiz — Devoir de Synthèse N°1 Lycée pilote - Math - 3ème Mathématiques (2014-2015) Mr ammar.pdf

Question 1 sur 10 20:00

[{"id":16459,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"A : x = 2 ou x = 3","option_b":"B : x = -2 ou x = -3","option_c":"C : x = 1 ou x = 6","option_d":"D : x = 0","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\": \"A : x = 2 ou x = 3\", \"b\": \"B : x = -2 ou x = -3\", \"c\": \"C : x = 1","_debug_options_count":4},{"id":16460,"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 f(x) = x³ est bien f'(x) = 3x², car la dérivée de x^n est n*x^(n-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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":16461,"question":"Quelle est l'intégrale de la fonction f(x) = 2x entre 0 et 1 ?","option_a":"A : 0","option_b":"B : 1","option_c":"C : 2","option_d":"D : 4","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale de 2x entre 0 et 1 est [x²] de 0 à 1 = 1² - 0² = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A : 0\", \"b\": \"B : 1\", \"c\": \"C : 2\", \"d\": \"D : 4\"}}","_debug_options_count":4},{"id":16462,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est le théorème de Pythagore : dans un triangle rectangle, a² + b² = c² où c est l'hypoténuse.","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":16463,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"A : 0","option_b":"B : 1","option_c":"C : 2","option_d":"D : Indéterminée","option_e":"","option_f":"","bonne_reponse":"c","explication":"La fonction se simplifie en f(x) = (x+1) pour x ≠ 1. Donc la limite lorsque x tend vers 1 est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A : 0\", \"b\": \"B : 1\", \"c\": \"C : 2\", \"d\": \"D : Indéterminée\"}}","_debug_options_count":4},{"id":16464,"question":"Le volume d'une sphère de rayon r est donné par V = (4\/3)πr³.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule du volume d'une sphère est bien V = (4\/3)πr³.","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":16465,"question":"Quelle est la solution de l'inéquation 3x - 2 \u003E 7 ?","option_a":"A : x \u003E 3","option_b":"B : x \u003C 3","option_c":"C : x \u003E 5","option_d":"D : x \u003C 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 2 \u003E 7 ⇒ 3x \u003E 9 ⇒ x \u003E 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\": \"A : x \u003E 3\", \"b\": \"B : x \u003C 3\", \"c\": \"C : x \u003E 5\", \"d\": \"D : x \u003C 5\"}","_debug_options_count":4},{"id":16466,"question":"La fonction f(x) = 1\/x est continue sur ℝ.","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, donc elle n'est pas continue sur ℝ.","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":16467,"question":"Quelle est la dérivée de la fonction f(x) = sin(x) ?","option_a":"A : cos(x)","option_b":"B : -cos(x)","option_c":"C : tan(x)","option_d":"D : 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de sin(x) est cos(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A : cos(x)\", \"b\": \"B : -cos(x)\", \"c\": \"C : tan(x)\", \"d\": \"D : 1\"}","_debug_options_count":4},{"id":16468,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, le produit scalaire de deux vecteurs orthogonaux est égal à 0.","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}]