Quiz — cor S11 math mr arbii ex 1+3+4.pdf

Question 1 sur 10 20:00

[{"id":136408,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 2 ou x = 0.5","option_c":"x = -1 ou x = -2","option_d":"x = 1 ou x = -0.5","option_e":"","option_f":"","bonne_reponse":"b","explication":"Résolvez l'équation en utilisant le discriminant Δ = b² - 4ac. Ici, Δ = 25 - 16 = 9, donc les solutions sont x = (5 ± 3)\/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\": \"x = 1 ou x = 2\", \"b\": \"x = 2 ou x = 0.5\", \"c\": \"x = -1 ou x = -2\"","_debug_options_count":4},{"id":136409,"question":"La fonction f(x) = x³ - 3x² + 4 est croissante sur l'intervalle [0, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Calculez la dérivée f'(x) = 3x² - 6x. Sur [0, 2], f'(x) ≤ 0, donc la fonction est décroissante.","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":136410,"question":"Quelle est l'équation de l'asymptote oblique de la fonction f(x) = (2x² + 3x - 1)\/(x + 1) ?","option_a":"y = 2x + 1","option_b":"y = 2x - 1","option_c":"y = x + 2","option_d":"y = x - 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Effectuez la division polynomiale : (2x² + 3x - 1) ÷ (x + 1) = 2x + 1 avec un reste. L'asymptote oblique est donc y = 2x + 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\": \"y = 2x + 1\", \"b\": \"y = 2x - 1\", \"c\": \"y = x + 2\", \"d\": \"y = x - 2","_debug_options_count":4},{"id":136411,"question":"Le volume d'un cube de côté a est égal à :","option_a":"a³","option_b":"3a","option_c":"a²","option_d":"6a²","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le volume d'un cube est donné par la formule V = côté³, soit V = a³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"a³\", \"b\": \"3a\", \"c\": \"a²\", \"d\": \"6a²\"}}","_debug_options_count":4},{"id":136412,"question":"La section d'un cube par un plan parallèle à une face est toujours un carré.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si le plan est parallèle à une face, la section est bien un carré. La propriété est donc vraie.","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":136413,"question":"Quelle est la limite de la fonction f(x) = (x² - 4)\/(x - 2) lorsque x tend vers 2 ?","option_a":"0","option_b":"2","option_c":"4","option_d":"La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"d","explication":"Simplifiez l'expression : (x² - 4)\/(x - 2) = (x - 2)(x + 2)\/(x - 2) = x + 2 pour x ≠ 2. La limite est donc 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"0\", \"b\": \"2\", \"c\": \"4\", \"d\": \"La limite n'existe pas\"}}","_debug_options_count":4},{"id":136414,"question":"Un tétraèdre régulier a toutes ses arêtes de même longueur.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, un tétraèdre régulier a toutes ses arêtes de même longueur et toutes ses faces sont des triangles équilatéraux.","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":136415,"question":"Quelle est la dérivée de la fonction f(x) = sin(2x) ?","option_a":"2cos(2x)","option_b":"cos(2x)","option_c":"-2cos(2x)","option_d":"sin(2x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Appliquez la règle de dérivation des fonctions composées : f'(x) = 2cos(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\": \"2cos(2x)\", \"b\": \"cos(2x)\", \"c\": \"-2cos(2x)\", \"d\": \"sin(2x)\"}}","_debug_options_count":4},{"id":136416,"question":"L'équation x² + y² + z² = 9 représente :","option_a":"Une sphère de centre O et de rayon 3","option_b":"Un plan","option_c":"Un cylindre","option_d":"Un cône","option_e":"","option_f":"","bonne_reponse":"a","explication":"Cette équation est celle d'une sphère centrée à l'origine (0,0,0) avec un rayon de 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\": \"Une sphère de centre O et de rayon 3\", \"b\": \"Un plan\", \"c\": \"Un ","_debug_options_count":4},{"id":136417,"question":"La fonction f(x) = e^x est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle e^x est strictement positive pour tout x réel, car e^x \u003E 0 pour tout x ∈ 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}]