Quiz — Devoir-de-contrôle-n2_-_-4-Maths-mars-2017-_.pdf

Question 1 sur 10 20:00

[{"id":21729,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 2","option_c":"x = 12","option_d":"x = -4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 7, on ajoute 5 des deux côtés : 3x = 12, puis on divise par 3 : x = 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 = 4\", \"b\": \"x = 2\", \"c\": \"x = 12\", \"d\": \"x = -4\"}}","_debug_options_count":4},{"id":21730,"question":"La fonction f(x) = x² est-elle une fonction paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction est paire si f(-x) = f(x). Ici, f(-x) = (-x)² = x² = f(x), donc la fonction est paire.","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":21731,"question":"Quelle est la dérivée de la fonction f(x) = 2x³ - 3x² + 5 ?","option_a":"f'(x) = 6x² - 6x","option_b":"f'(x) = 6x² - 3x","option_c":"f'(x) = 2x² - 3x","option_d":"f'(x) = 6x - 6x²","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 2x³ est 6x², celle de -3x² est -6x, et celle de 5 est 0. Donc f'(x) = 6x² - 6x.","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) = 6x² - 6x\", \"b\": \"f'(x) = 6x² - 3x\", \"c\": \"f'(x) = 2x² ","_debug_options_count":4},{"id":21732,"question":"Dans une classe de 30 élèves, 12 sont des filles. Quelle est la probabilité de choisir une fille au hasard ?","option_a":"0.4","option_b":"0.3","option_c":"0.5","option_d":"0.6","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité est le nombre de cas favorables divisé par le nombre total de cas : 12\/30 = 0.4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0.4\", \"b\": \"0.3\", \"c\": \"0.5\", \"d\": \"0.6\"}}","_debug_options_count":4},{"id":21733,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc la suite est arithmétique.","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":21734,"question":"Quelle est la solution de l'inéquation 2x + 3 \u003E 7 ?","option_a":"x \u003E 2","option_b":"x \u003E -2","option_c":"x \u003C 2","option_d":"x \u003C -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 2x + 3 \u003E 7, on soustrait 3 des deux côtés : 2x \u003E 4, puis on divise par 2 : x \u003E 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\": \"x \u003E 2\", \"b\": \"x \u003E -2\", \"c\": \"x \u003C 2\", \"d\": \"x \u003C -2\"}}","_debug_options_count":4},{"id":21735,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"Δ = b² - 4ac","option_b":"Δ = b² + 4ac","option_c":"Δ = 4ac - b²","option_d":"Δ = b - 4ac","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant d'une équation du second degré est donné par 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\": \"Δ = b² - 4ac\", \"b\": \"Δ = b² + 4ac\", \"c\": \"Δ = 4ac - b²\", \"d","_debug_options_count":4},{"id":21736,"question":"La fonction f(x) = 1\/x est-elle définie en 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},{"id":21737,"question":"Quelle est la somme des 5 premiers termes de la suite arithmétique de premier terme 3 et de raison 2 ?","option_a":"35","option_b":"40","option_c":"25","option_d":"50","option_e":"","option_f":"","bonne_reponse":"a","explication":"La somme des n premiers termes d'une suite arithmétique est donnée par Sₙ = n\/2 * (2u₁ + (n-1)r). Ici, S₅ = 5\/2 * (6 + 8) = 5\/2 * 14 = 35.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"35\", \"b\": \"40\", \"c\": \"25\", \"d\": \"50\"}}","_debug_options_count":4},{"id":21738,"question":"La fonction f(x) = x³ est-elle croissante sur ℝ ?","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 f'(x) = 3x², qui est toujours positive ou nulle. Donc la fonction est croissante sur ℝ.","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}]