Maths Bac : Testez vos connaissances en séries et problèmes

Question 1 sur 10 10:00

[{"id":28288,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x² + 2","option_d":"f'(x) = 3x² + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n·a·x^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28289,"question":"La suite définie par uₙ = 2n + 1 est-elle 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 elle est arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28290,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"1\/6","option_b":"1\/12","option_c":"1\/36","option_d":"1\/18","option_e":"","option_f":"","bonne_reponse":"C","explication":"Il y a 36 issues possibles (6 faces × 6 faces). Une seule issue correspond à (6,6), donc P = 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28291,"question":"La fonction f(x) = 1\/x est-elle définie en 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 interdite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28292,"question":"Quel est le coefficient directeur de la droite d'équation y = -2x + 3 ?","option_a":"-2","option_b":"2","option_c":"3","option_d":"-3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans l'équation réduite y = mx + p, m représente le coefficient directeur. Ici, m = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28293,"question":"La suite géométrique de premier terme u₀ = 4 et de raison q = 2 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite géométrique est croissante si q \u003E 1 et u₀ \u003E 0. Ici, u₀ = 4 \u003E 0 et q = 2 \u003E 1, donc elle est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28294,"question":"Quelle est la limite de la fonction f(x) = (x² - 4)\/(x - 2) lorsque x tend vers 2 ?","option_a":"0","option_b":"4","option_c":"2","option_d":"La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"B","explication":"En factorisant, f(x) = (x-2)(x+2)\/(x-2) = x+2 pour x ≠ 2. Donc lim(x→2) f(x) = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28295,"question":"L'équation x² + 4x + 5 = 0 admet-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = 16 - 20 = -4 \u003C 0. L'équation n'a donc pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28296,"question":"Quel est le volume d'un cube d'arête 3 cm ?","option_a":"9 cm³","option_b":"27 cm³","option_c":"81 cm³","option_d":"3 cm³","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le volume d'un cube est donné par V = arête³. Ici, V = 3³ = 27 cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28297,"question":"La fonction f(x) = x³ - 3x est-elle impaire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction est impaire si f(-x) = -f(x). Ici, f(-x) = (-x)³ - 3(-x) = -x³ + 3x = -(x³ - 3x) = -f(x), donc elle est impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]