Quiz — Lycée Pilote Sfax - DC 3 2016.pdf

Question 1 sur 10 20:00

[{"id":20539,"question":"Quelle est la solution de l’équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L’équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0. Les solutions sont donc x = 2 et x = 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\": \"x = 2 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4},{"id":20540,"question":"La fonction f(x) = x³ - 3x est-elle croissante sur l’intervalle [-2, 2] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f’(x) = 3x² - 3 s’annule en x = ±1. Sur [-2, -1] et [1, 2], la fonction est croissante, mais décroissante sur [-1, 1]. Elle n’est donc pas croissante sur tout l’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":20541,"question":"Quel est le résultat de lim(x→+∞) (3x² + 2x - 5) \/ (x² - x + 1) ?","option_a":"0","option_b":"3","option_c":"2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par x², on obtient lim(x→+∞) (3 + 2\/x - 5\/x²) \/ (1 - 1\/x + 1\/x²) = 3\/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\": \"2\", \"d\": \"1\"}}","_debug_options_count":4},{"id":20542,"question":"Dans un triangle rectangle, si cos(θ) = 3\/5, quelle est la valeur de sin(θ) ?","option_a":"4\/5","option_b":"3\/4","option_c":"5\/3","option_d":"1\/5","option_e":"","option_f":"","bonne_reponse":"a","explication":"D’après le théorème de Pythagore, sin²(θ) + cos²(θ) = 1. Donc sin(θ) = √(1 - (3\/5)²) = √(16\/25) = 4\/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\": \"4\/5\", \"b\": \"3\/4\", \"c\": \"5\/3\", \"d\": \"1\/5\"}}","_debug_options_count":4},{"id":20543,"question":"La dérivée de la fonction f(x) = e^(2x) est-elle f’(x) = 2e^(2x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^(u(x)) est u’(x)e^(u(x)). Ici, u(x) = 2x, donc u’(x) = 2. Ainsi, f’(x) = 2e^(2x).","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":20544,"question":"Quel est le discriminant de l’équation 2x² + 4x - 6 = 0 ?","option_a":"16","option_b":"32","option_c":"64","option_d":"48","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = b² - 4ac = 4² - 4*2*(-6) = 16 + 48 = 64. Cependant, pour l’équation 2x² + 4x - 6 = 0, Δ = 16 + 48 = 64. Correction : Δ = 64.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"16\", \"b\": \"32\", \"c\": \"64\", \"d\": \"48\"}}","_debug_options_count":4},{"id":20545,"question":"Dans un cercle de rayon 5 cm, quelle est la longueur d’un arc correspondant à un angle de 60° ?","option_a":"5π\/3 cm","option_b":"5π cm","option_c":"10π\/3 cm","option_d":"π\/3 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"La longueur d’un arc est donnée par L = (θ\/360°) * 2πR. Ici, L = (60\/360) * 2π*5 = (1\/6)*10π = 5π\/3 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"5π\/3 cm\", \"b\": \"5π cm\", \"c\": \"10π\/3 cm\", \"d\": \"π\/3 cm\"}}","_debug_options_count":4},{"id":20546,"question":"La fonction f(x) = ln(x) est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction logarithme népérien ln(x) n’est définie que pour x \u003E 0. Elle n’est donc pas définie en x = 0.","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":20547,"question":"Quel est le résultat de ∫(2x + 3) dx ?","option_a":"x² + 3x + C","option_b":"x² + 3x","option_c":"2x² + 3x + C","option_d":"x² + 6x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L’intégrale de 2x est x² et celle de 3 est 3x. On ajoute la constante d’intégration C. Donc ∫(2x + 3) dx = x² + 3x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x² + 3x + C\", \"b\": \"x² + 3x\", \"c\": \"2x² + 3x + C\", \"d\": \"x² +","_debug_options_count":4},{"id":20548,"question":"Si A et B sont deux événements incompatibles, quelle est la probabilité de A ∪ B ?","option_a":"P(A) + P(B)","option_b":"P(A) * P(B)","option_c":"P(A) - P(B)","option_d":"P(A) \/ P(B)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour deux événements incompatibles, P(A ∪ B) = P(A) + P(B). C’est une propriété fondamentale des probabilités.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"P(A) + P(B)\", \"b\": \"P(A) * P(B)\", \"c\": \"P(A) - P(B)\", \"d\": \"P(A) ","_debug_options_count":4}]