Quiz — 639c66cbf3efc_enoncé mag 1.pdf

Question 1 sur 10 20:00

[{"id":84735,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 5x - 2 ?","option_a":"6x + 5","option_b":"6x² + 5","option_c":"3x + 5","option_d":"6x + 5x - 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (5x)' = 5 et (-2)' = 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\": \"6x + 5\", \"b\": \"6x² + 5\", \"c\": \"3x + 5\", \"d\": \"6x + 5x - 2\"}}","_debug_options_count":4},{"id":84736,"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},{"id":84737,"question":"Quelle est la limite de (2x + 1)\/(x - 3) lorsque x tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par x, on obtient (2 + 1\/x)\/(1 - 3\/x), qui tend vers 2\/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\": \"2\", \"b\": \"1\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":84738,"question":"L'équation x² - 4x + 4 = 0 a-t-elle deux solutions distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = (-4)² - 4*1*4 = 0, donc l'équation a une solution double (x = 2).","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":84739,"question":"Quelle est la primitive de f(x) = 4x³ ?","option_a":"x⁴ + C","option_b":"12x² + C","option_c":"x⁴\/4 + C","option_d":"4x⁴ + C","option_e":"","option_f":"","bonne_reponse":"c","explication":"La primitive de xⁿ est x^(n+1)\/(n+1) + C. Ici, n = 3, donc la primitive est x⁴\/4 + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"x⁴ + C\", \"b\": \"12x² + C\", \"c\": \"x⁴\/4 + C\", \"d\": \"4x⁴ + C\"}","_debug_options_count":4},{"id":84740,"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 1\/x n'est pas définie en x = 0 car le dénominateur devient nul.","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":84741,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"√2\/2","option_b":"1\/2","option_c":"√3\/2","option_d":"0","option_e":"","option_f":"","bonne_reponse":"b","explication":"sin(π\/6) = 1\/2, valeur à connaître par cœur dans le cercle trigonométrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"√2\/2\", \"b\": \"1\/2\", \"c\": \"√3\/2\", \"d\": \"0\"}}","_debug_options_count":4},{"id":84742,"question":"L'intégrale de 0 à 1 de x² dx est-elle égale à 1\/3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de x² de 0 à 1 est [x³\/3]₀¹ = 1\/3 - 0 = 1\/3. Donc l'affirmation est 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":84743,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"e²","option_b":"2","option_c":"1\/e²","option_d":"ln(2)","option_e":"","option_f":"","bonne_reponse":"a","explication":"ln(x) = 2 ⇒ x = e², car la fonction exponentielle est la réciproque du logarithme.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"e²\", \"b\": \"2\", \"c\": \"1\/e²\", \"d\": \"ln(2)\"}}","_debug_options_count":4},{"id":84744,"question":"La suite uₙ = n\/(n+1) converge-t-elle vers 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En calculant la limite de uₙ lorsque n tend vers l'infini, on obtient 1. Donc la suite converge vers 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}]