Maths Bac : Testez vos connaissances en séries d'exercices

Question 1 sur 10 10:00

[{"id":30718,"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 = -1 ou x = -6","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0, donc les solutions sont x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30719,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle ]-∞, -1[.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 est négative sur ]-∞, -1[, donc la fonction est décroissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30720,"question":"Quelle est la limite de (2x + 1)\/(x - 3) lorsque x tend vers +∞ ?","option_a":"2","option_b":"0","option_c":"1\/3","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x, on obtient (2 + 1\/x)\/(1 - 3\/x) → 2\/1 = 2 lorsque x → +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30721,"question":"La dérivée de la fonction f(x) = ln(x) est f'(x) = 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est bien 1\/x, c'est une propriété fondamentale des logarithmes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30722,"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 simplifiant, on obtient -x \u003E 6, soit x \u003C -6 après multiplication par -1 (inversion du sens de l'inégalité).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30723,"question":"La fonction f(x) = e^x est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle e^x est strictement positive pour tout x réel, car e^x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30724,"question":"Quelle est la valeur de la dérivée de f(x) = sin(2x) en x = π\/4 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"C","explication":"La dérivée est f'(x) = 2cos(2x). En x = π\/4, f'(π\/4) = 2cos(π\/2) = 2*0 = 0. (Correct: 0)","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30725,"question":"L'équation x³ - 4x = 0 admet trois solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation se factorise en x(x² - 4) = 0, soit x = 0, x = 2, x = -2. Il y a donc trois solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30726,"question":"Quelle est la limite de (x² + 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"-∞","option_e":"","option_f":"","bonne_reponse":"D","explication":"Lorsque x → 1, le numérateur tend vers 2 et le dénominateur tend vers 0 par valeurs positives, donc la limite est +∞. (Correct: ∞)","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30727,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]