Quiz — M-EA-SRE-JMF-1.pdf

Question 1 sur 10 20:00

[{"id":29120,"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 = 1\/2","option_c":"x = -1 ou x = -2","option_d":"x = 0 ou x = 5\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"La solution s'obtient en utilisant la formule du discriminant Δ = b² - 4ac, puis x = (-b ± √Δ) \/ (2a). Ici, Δ = 9, donc 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 = 1\/2\", \"c\": \"x = -1 ou x = -2\"","_debug_options_count":4},{"id":29121,"question":"La fonction f(x) = x³ - 3x est décroissante sur l'intervalle [-1, 1].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² - 3 est négative sur [-1, 1] car 3x² ≤ 3, donc f est décroissante sur cet intervalle.","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":29122,"question":"Quelle est la limite de (3x² + 2x - 1)\/(x² + 1) lorsque x tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"3","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"En divisant numérateur et dénominateur par x², on obtient (3 + 2\/x - 1\/x²)\/(1 + 1\/x²). Lorsque x → ∞, les termes en 1\/x tendent vers 0, donc la limite est 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"3\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":29123,"question":"Le vecteur u(2, -3) et le vecteur v(-4, 6) sont colinéaires.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux vecteurs sont colinéaires s'il existe un réel k tel que u = k·v. Ici, u = -0.5·v, donc ils sont colinéaires.","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":29124,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x + 1) ?","option_a":"f'(x) = 1\/(2x + 1)","option_b":"f'(x) = 2\/(2x + 1)","option_c":"f'(x) = 1\/(x + 1)","option_d":"f'(x) = 2x\/(2x + 1)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 2x + 1, donc u' = 2. Ainsi, f'(x) = 2\/(2x + 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\": \"f'(x) = 1\/(2x + 1)\", \"b\": \"f'(x) = 2\/(2x + 1)\", \"c\": \"f'(x) = 1\/(","_debug_options_count":4},{"id":29125,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un dé a 6 faces : 1, 2, 3, 4, 5, 6. Les nombres pairs sont 2, 4, 6, soit 3 faces. La probabilité est donc 3\/6 = 1\/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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":29126,"question":"Quelle est l'intégrale de f(x) = 3x² entre 0 et 2 ?","option_a":"4","option_b":"8","option_c":"12","option_d":"16","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'intégrale de 3x² est x³. En évaluant entre 0 et 2, on obtient 2³ - 0³ = 8. L'intégrale est donc 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"4\", \"b\": \"8\", \"c\": \"12\", \"d\": \"16\"}}","_debug_options_count":4},{"id":29127,"question":"La fonction f(x) = e^x est sa propre dérivée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^x est e^x, donc la fonction est bien sa propre dérivée.","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":29128,"question":"Quelle est la solution de l'inéquation x² - 4x + 3 \u003E 0 ?","option_a":"x ∈ ]-∞, 1[ ∪ ]3, +∞[","option_b":"x ∈ ]1, 3[","option_c":"x ∈ ]-∞, 3[","option_d":"x ∈ ]0, 4[","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les racines de x² - 4x + 3 = 0 sont x = 1 et x = 3. Le polynôme est positif à l'extérieur des racines.","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 ∈ ]-∞, 1[ ∪ ]3, +∞[\", \"b\": \"x ∈ ]1, 3[\", \"c\": \"x ∈ ","_debug_options_count":4},{"id":29129,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours nul.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux vecteurs orthogonaux ont un produit scalaire 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}]