Quiz de révision : Mathématiques 3ème année secondaire

Question 1 sur 10 10:00

[{"id":50741,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x + 2x","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50742,"question":"L'équation x² - 5x + 6 = 0 admet deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = 25 - 24 = 1 \u003E 0, donc l'équation admet deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50743,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"2","option_b":"0","option_c":"1\/2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour les limites à l'infini des fonctions rationnelles, on compare les degrés des polynômes : ici, la limite est égale au rapport des coefficients dominants, soit 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50744,"question":"La fonction f(x) = x³ - 3x est 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. La fonction est décroissante sur [-1 ; 1], donc pas croissante sur [-2 ; 2].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50745,"question":"Quelle est la solution de l'inéquation 2x - 7 ≤ 5 ?","option_a":"x ≤ 6","option_b":"x ≥ 6","option_c":"x ≤ -6","option_d":"x ≥ -6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x - 7 ≤ 5, on obtient 2x ≤ 12, soit x ≤ 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50746,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un dé a 6 faces, dont 3 paires (2, 4, 6). La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50747,"question":"Quelle est la primitive de la fonction f(x) = 4x³ - 2x + 1 ?","option_a":"x⁴ - x² + x + C","option_b":"x⁴ - x² + C","option_c":"4x⁴ - 2x² + x + C","option_d":"x⁴ - 2x² + x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive se calcule en intégrant chaque terme : ∫4x³ dx = x⁴, ∫-2x dx = -x², ∫1 dx = x. La constante C est ajoutée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50748,"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},{"id":50749,"question":"Quelle est la solution de l'équation |2x - 3| = 5 ?","option_a":"x = 4 ou x = -1","option_b":"x = 4 ou x = 1","option_c":"x = -4 ou x = 1","option_d":"x = -4 ou x = -1","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation |2x - 3| = 5 donne deux cas : 2x - 3 = 5 (x = 4) ou 2x - 3 = -5 (x = -1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50750,"question":"La suite définie par uₙ = 2n + 1 est arithmétique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc la suite est arithmétique de raison 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]