Quiz — serie 14( énoncé)Revision.pdf

Question 1 sur 10 20:00

[{"id":85400,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2x","option_c":"6x + 2x","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynomiale se calcule terme par terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0. Donc f'(x) = 6x + 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\": \"6x + 2\", \"b\": \"3x² + 2x\", \"c\": \"6x + 2x\", \"d\": \"3x + 2\"}}","_debug_options_count":4},{"id":85401,"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 générale 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":85402,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"1\/6","option_b":"1\/3","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un dé équilibré a 6 faces. Les nombres pairs sont 2, 4 et 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\": \"c\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/3\", \"c\": \"1\/2\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":85403,"question":"Dans un repère orthonormé, la distance entre les points A(2; 3) et B(5; 7) est :","option_a":"5","option_b":"√(13)","option_c":"√(25)","option_d":"√(10)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La distance entre deux points A(x₁; y₁) et B(x₂; y₂) est donnée par √[(x₂ - x₁)² + (y₂ - y₁)²]. Ici, √[(5-2)² + (7-3)²] = √(9 + 16) = √25 = 5. L'option √(13) est incorrecte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"5\", \"b\": \"√(13)\", \"c\": \"√(25)\", \"d\": \"√(10)\"}}","_debug_options_count":4},{"id":85404,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-1; 1].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour étudier la croissance, on calcule la dérivée f'(x) = 3x² - 3. Sur [-1; 1], f'(x) ≤ 0 (car 3x² ≤ 3), donc la fonction 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\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":85405,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x) \/ (x² - 1) quand x tend vers +∞ ?","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour les limites à l'infini, on compare les termes dominants : (2x²) \/ (x²) = 2. Donc la limite est 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\": \"0\", \"c\": \"1\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":85406,"question":"Un sac contient 4 boules rouges et 6 boules bleues. On tire une boule au hasard. Quelle est la probabilité de tirer une boule rouge ?","option_a":"2\/5","option_b":"3\/5","option_c":"4\/10","option_d":"1\/4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 4 boules rouges sur un total de 10 boules. La probabilité est donc 4\/10 = 2\/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\": \"2\/5\", \"b\": \"3\/5\", \"c\": \"4\/10\", \"d\": \"1\/4\"}}","_debug_options_count":4},{"id":85407,"question":"La fonction exponentielle f(x) = eˣ est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle eˣ est définie pour tout x réel et prend uniquement des valeurs strictement positives.","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":85408,"question":"Quelle est la solution de l'équation 2x + 5 = 11 ?","option_a":"x = 3","option_b":"x = 4","option_c":"x = 5","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"b","explication":"En résolvant l'équation : 2x + 5 = 11 → 2x = 6 → x = 3. L'option x = 4 est incorrecte.","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 = 3\", \"b\": \"x = 4\", \"c\": \"x = 5\", \"d\": \"x = 6\"}}","_debug_options_count":4},{"id":85409,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est l'énoncé du théorème de Pythagore, qui s'applique uniquement aux triangles rectangles.","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}]