Quiz — 6569c398afe69_corrigé_Série 23 (3).pdf

Question 1 sur 10 20:00

[{"id":133642,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"3x - 5","option_c":"6x² - 5","option_d":"3x² - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 3x² est 6x, celle de -5x est -5, et la dérivée d'une constante est 0. Donc f'(x) = 6x - 5.","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\": \"3x - 5\", \"c\": \"6x² - 5\", \"d\": \"3x² - 5\"}}","_debug_options_count":4},{"id":133643,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 a pour terme général uₙ = 3 × 2ⁿ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Ici, uₙ = 3 × 2ⁿ, 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":133644,"question":"Soit une fonction f définie par f(x) = x³ - 3x² + 4. Quel est le coefficient directeur de la tangente à la courbe en x = 1 ?","option_a":"0","option_b":"-3","option_c":"3","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur de la tangente est égal à f'(1). f'(x) = 3x² - 6x, donc f'(1) = 3(1)² - 6(1) = -3.","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\", \"b\": \"-3\", \"c\": \"3\", \"d\": \"-1\"}}","_debug_options_count":4},{"id":133645,"question":"La limite d'une suite géométrique de raison q = 0.5 et de premier terme u₀ = 10 est égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si |q| \u003C 1, alors la limite de la suite est 0. Ici, q = 0.5, donc la limite est bien 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},{"id":133646,"question":"Quelle est la dérivée de la fonction g(x) = e^(2x) ?","option_a":"e^(2x)","option_b":"2e^(2x)","option_c":"2e^x","option_d":"e^x","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de e^(u(x)) est u'(x) × e^(u(x)). Ici, u(x) = 2x, donc u'(x) = 2. Ainsi, g'(x) = 2e^(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"e^(2x)\", \"b\": \"2e^(2x)\", \"c\": \"2e^x\", \"d\": \"e^x\"}}","_debug_options_count":4},{"id":133647,"question":"Une suite arithmétique de premier terme u₀ = 5 et de raison r = -2 est décroissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite arithmétique est décroissante si sa raison r est négative. Ici, r = -2 \u003C 0, donc la suite 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":133648,"question":"Soit f(x) = ln(x). Quelle est la valeur de f'(2) ?","option_a":"1\/2","option_b":"2","option_c":"1","option_d":"-1\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est 1\/x. Donc f'(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\": \"1\/2\", \"b\": \"2\", \"c\": \"1\", \"d\": \"-1\/2\"}}","_debug_options_count":4},{"id":133649,"question":"La limite d'une suite géométrique de raison q = 2 et de premier terme u₀ = 1 est égale à +∞.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si |q| \u003E 1, alors la suite diverge vers +∞. Ici, q = 2 \u003E 1, donc la limite est bien +∞.","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":133650,"question":"Quelle est la dérivée de la fonction h(x) = sin(3x) ?","option_a":"cos(3x)","option_b":"3cos(3x)","option_c":"-3cos(3x)","option_d":"cos(x)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de sin(u(x)) est u'(x) × cos(u(x)). Ici, u(x) = 3x, donc u'(x) = 3. Ainsi, h'(x) = 3cos(3x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"cos(3x)\", \"b\": \"3cos(3x)\", \"c\": \"-3cos(3x)\", \"d\": \"cos(x)\"}}","_debug_options_count":4},{"id":133651,"question":"Une suite arithmétique de premier terme u₀ = 10 et de raison r = 0 est constante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si r = 0, alors tous les termes de la suite sont égaux à u₀. Donc la suite est constante.","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}]