Quiz — Lycée Pilote Sousse - DS 3 2018 (+Corrigé).pdf

Question 1 sur 10 20:00

[{"id":5736,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"3x - 5","option_c":"6x² - 5x","option_d":"3x² - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule en appliquant la règle : (ax^n)' = n*ax^(n-1). Ici, 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 - 5x\", \"d\": \"3x² - 5\"}}","_debug_options_count":4},{"id":5737,"question":"Dans une classe de 30 élèves, 12 sont des filles. Quelle est la probabilité de choisir une fille au hasard ?","option_a":"0.4","option_b":"0.3","option_c":"0.5","option_d":"0.6","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité se calcule par le rapport du nombre de cas favorables sur le nombre total de cas. Ici, 12\/30 = 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\": \"0.4\", \"b\": \"0.3\", \"c\": \"0.5\", \"d\": \"0.6\"}}","_debug_options_count":4},{"id":5738,"question":"Vrai ou Faux ? La fonction f(x) = x³ est croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = x³ est strictement croissante sur ℝ car sa dérivée f'(x) = 3x² est toujours positive (sauf en x=0 où elle est nulle).","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":5739,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour trouver la limite d'une suite rationnelle, on divise numérateur et dénominateur par n. On obtient lim (2 + 1\/n)\/(1 + 3\/n) = 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":5740,"question":"Vrai ou Faux ? Dans un cube, la diagonale d'une face est égale à la moitié de la diagonale de l'espace.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La diagonale d'une face d'un cube de côté a est a√2, tandis que la diagonale de l'espace est a√3. a√2 ≠ (a√3)\/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":5741,"question":"Quelle est l'équation de la tangente à la courbe y = x² + 1 au point d'abscisse x = 1 ?","option_a":"y = 2x + 1","option_b":"y = 2x - 1","option_c":"y = x + 1","option_d":"y = x - 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation de la tangente en x = a est y = f'(a)(x - a) + f(a). Ici, f(1) = 2 et f'(1) = 2, donc y = 2(x - 1) + 2 = 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\": \"y = 2x + 1\", \"b\": \"y = 2x - 1\", \"c\": \"y = x + 1\", \"d\": \"y = x - 1","_debug_options_count":4},{"id":5742,"question":"Quelle est la probabilité d'obtenir exactement 2 fois pile en 3 lancers d'une pièce équilibrée ?","option_a":"1\/8","option_b":"3\/8","option_c":"1\/4","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une loi binomiale de paramètres n=3 et p=0.5. P(X=2) = C(3,2) * (0.5)^2 * (0.5)^1 = 3\/8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\/8\", \"b\": \"3\/8\", \"c\": \"1\/4\", \"d\": \"1\/2\"}}","_debug_options_count":4},{"id":5743,"question":"Vrai ou Faux ? Toute fonction continue sur un intervalle fermé est dérivable sur cet intervalle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction continue n'est pas nécessairement dérivable (exemple : f(x) = |x| en x=0). La dérivabilité est une condition plus forte.","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":5744,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003C 6","option_d":"x \u003E 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant 2x - 5 \u003E 3x + 1, on obtient -x \u003E 6, soit x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x \u003C -6\", \"b\": \"x \u003E -6\", \"c\": \"x \u003C 6\", \"d\": \"x \u003E 6\"}}","_debug_options_count":4},{"id":5745,"question":"Quelle est l'aire totale d'un cube de côté 4 cm ?","option_a":"24 cm²","option_b":"48 cm²","option_c":"96 cm²","option_d":"12 cm²","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un cube a 6 faces carrées. L'aire d'une face est 4² = 16 cm². L'aire totale est 6 * 16 = 96 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"24 cm²\", \"b\": \"48 cm²\", \"c\": \"96 cm²\", \"d\": \"12 cm²\"}}","_debug_options_count":4}]