Quiz — ds10809my.pdf

Question 1 sur 10 20:00

[{"id":11523,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 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 + 2\", \"b\": \"3x² + 2\", \"c\": \"6x - 5\", \"d\": \"6x + 2x - 5\"}}","_debug_options_count":4},{"id":11524,"question":"Une suite géométrique a pour premier terme u₀ = 2 et pour raison q = 3. Quel est le terme u₃ ?","option_a":"18","option_b":"54","option_c":"81","option_d":"6","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le terme général d'une suite géométrique est uₙ = u₀ × qⁿ. Donc u₃ = 2 × 3³ = 2 × 27 = 54.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"18\", \"b\": \"54\", \"c\": \"81\", \"d\": \"6\"}}","_debug_options_count":4},{"id":11525,"question":"Vrai ou Faux : La dérivée d'une fonction constante est toujours égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction constante f(x) = k a pour dérivée f'(x) = 0, car sa pente est nulle en tout point.","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":11526,"question":"Dans une classe de 30 élèves, 18 sont des filles. Quelle est la probabilité de choisir une fille au hasard ?","option_a":"0,4","option_b":"0,6","option_c":"0,3","option_d":"0,5","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité est le rapport du nombre de cas favorables sur le nombre total de cas. Ici, 18\/30 = 0,6.","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\": \"0,6\", \"c\": \"0,3\", \"d\": \"0,5\"}}","_debug_options_count":4},{"id":11527,"question":"Vrai ou Faux : Une suite arithmétique 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":11528,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"2","option_d":"3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Pour trouver la limite, on divise le numérateur et le dénominateur par n : (2 + 1\/n)\/(1 + 3\/n) → 2\/1 = 2 quand n → ∞.","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\": \"2\", \"d\": \"3\"}}","_debug_options_count":4},{"id":11529,"question":"Dans un sac contenant 5 boules rouges et 3 boules bleues, quelle est la probabilité de tirer deux boules rouges successivement sans remise ?","option_a":"10\/56","option_b":"15\/56","option_c":"25\/64","option_d":"5\/8","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité est (5\/8) × (4\/7) = 20\/56 = 15\/56 après simplification.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"10\/56\", \"b\": \"15\/56\", \"c\": \"25\/64\", \"d\": \"5\/8\"}}","_debug_options_count":4},{"id":11530,"question":"Vrai ou Faux : La fonction f(x) = x³ + 2x est toujours croissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² + 2 est toujours positive (car 3x² ≥ 0 et 2 \u003E 0), donc f est toujours croissante.","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":11531,"question":"Quelle est la somme des 5 premiers termes d'une suite arithmétique de premier terme u₀ = 4 et de raison r = 3 ?","option_a":"40","option_b":"45","option_c":"50","option_d":"55","option_e":"","option_f":"","bonne_reponse":"c","explication":"La somme des n premiers termes d'une suite arithmétique est Sₙ = n\/2 × (2u₀ + (n-1)r). Ici, S₅ = 5\/2 × (8 + 12) = 5\/2 × 20 = 50.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"40\", \"b\": \"45\", \"c\": \"50\", \"d\": \"55\"}}","_debug_options_count":4},{"id":11532,"question":"Vrai ou Faux : La probabilité de l'événement contraire est toujours égale à 1 moins la probabilité de l'événement.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, P(Ā) = 1 - P(A), où Ā est l'événement contraire de A.","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}]