Quiz — Lycée Pilote Médenine - DC 3 2017.pdf

Question 1 sur 10 20:00

[{"id":33910,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x² - 4) quand x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. -∞","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"La limite d'un polynôme quand x tend vers l'infini est déterminée par le terme de plus haut degré. Ici, les termes dominants sont 2x² au numérateur et x² au dénominateur, donc la limite est 2x²\/x² = 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\": \"A. 0\", \"b\": \"B. 2\", \"c\": \"C. -∞\", \"d\": \"D. +∞\"}}","_debug_options_count":4},{"id":33911,"question":"Soit une suite géométrique de premier terme u₀ = 3 et de raison q = 2. Quelle est la valeur de u₃ ?","option_a":"A. 6","option_b":"B. 12","option_c":"C. 24","option_d":"D. 48","option_e":"","option_f":"","bonne_reponse":"c","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Donc u₃ = 3 × 2³ = 3 × 8 = 24.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 6\", \"b\": \"B. 12\", \"c\": \"C. 24\", \"d\": \"D. 48\"}}","_debug_options_count":4},{"id":33912,"question":"Dans une classe de 30 élèves, 12 sont des filles. Quelle est la probabilité de choisir une fille au hasard ?","option_a":"A. 0.3","option_b":"B. 0.4","option_c":"C. 0.5","option_d":"D. 0.6","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, 12 filles \/ 30 élèves = 0.4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 0.3\", \"b\": \"B. 0.4\", \"c\": \"C. 0.5\", \"d\": \"D. 0.6\"}}","_debug_options_count":4},{"id":33913,"question":"Vrai ou Faux : La fonction f(x) = x³ est strictement 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 sauf en x = 0 où elle est nulle. La fonction est donc strictement 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":33914,"question":"Quelle est l'équation de la tangente à la courbe de f(x) = x² + 3x - 1 au point d'abscisse x = 1 ?","option_a":"A. y = 5x - 2","option_b":"B. y = 5x + 2","option_c":"C. y = 3x - 1","option_d":"D. y = 3x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La tangente a pour équation y = f'(a)(x - a) + f(a). Ici, f'(x) = 2x + 3, donc f'(1) = 5 et f(1) = 3. L'équation est y = 5(x - 1) + 3 = 5x - 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\": \"A. y = 5x - 2\", \"b\": \"B. y = 5x + 2\", \"c\": \"C. y = 3x - 1\", \"d\": ","_debug_options_count":4},{"id":33915,"question":"Soit une variable aléatoire X suivant une loi binomiale de paramètres n = 10 et p = 0.3. Quelle est l'espérance de X ?","option_a":"A. 3","option_b":"B. 7","option_c":"C. 10","option_d":"D. 0.3","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance d'une loi binomiale est E(X) = n × p = 10 × 0.3 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 3\", \"b\": \"B. 7\", \"c\": \"C. 10\", \"d\": \"D. 0.3\"}}","_debug_options_count":4},{"id":33916,"question":"Vrai ou Faux : Deux droites parallèles dans l'espace sont toujours coplanaires.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Deux droites parallèles dans l'espace ne sont pas nécessairement coplanaires. Elles peuvent être parallèles sans appartenir au même plan (parallèles gauches).","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":33917,"question":"Quelle est la dérivée de la fonction f(x) = ln(x² + 1) ?","option_a":"A. 2x\/(x² + 1)","option_b":"B. 2x","option_c":"C. 1\/(x² + 1)","option_d":"D. x\/(x² + 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la formule de dérivation d'une fonction composée, f'(x) = (1\/(x² + 1)) × 2x = 2x\/(x² + 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\": \"A. 2x\/(x² + 1)\", \"b\": \"B. 2x\", \"c\": \"C. 1\/(x² + 1)\", \"d\": \"D. x","_debug_options_count":4},{"id":33918,"question":"Soit une suite arithmétique de premier terme u₀ = 5 et de raison r = -2. Quelle est la valeur de u₄ ?","option_a":"A. -3","option_b":"B. -1","option_c":"C. 3","option_d":"D. 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule d'une suite arithmétique est uₙ = u₀ + n × r. Donc u₄ = 5 + 4 × (-2) = 5 - 8 = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. -3\", \"b\": \"B. -1\", \"c\": \"C. 3\", \"d\": \"D. 5\"}}","_debug_options_count":4},{"id":33919,"question":"Vrai ou Faux : La fonction f(x) = eˣ est convexe sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée seconde de f(x) = eˣ est f''(x) = eˣ, qui est toujours positive. Donc la fonction est convexe 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}]