Quiz Maths BAC : Testez vos connaissances en algèbre et analyse !

Question 1 sur 10 10:00

[{"id":43016,"question":"Quelle est la solution de l'équation 2x² - 5x - 3 = 0 ?","option_a":"x = 3 ou x = -1\/2","option_b":"x = -3 ou x = 1\/2","option_c":"x = 3 ou x = 1\/2","option_d":"x = -3 ou x = -1\/2","option_e":"","option_f":"","bonne_reponse":"C","explication":"Résolvez l'équation en utilisant la formule du discriminant Δ = b² - 4ac. Ici, Δ = 25 + 24 = 49, donc x = (5 ± 7)\/4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43017,"question":"La fonction f(x) = x³ - 3x est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = -x³ + 3x ≠ f(x), donc la fonction n'est pas paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43018,"question":"Quelle est la limite de (3x² + 2x - 1)\/(x² - 4) quand x tend vers l'infini ?","option_a":"3","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Divisez le numérateur et le dénominateur par x². La limite devient (3 + 2\/x - 1\/x²)\/(1 - 4\/x²) → 3 quand x → ∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43019,"question":"L'inéquation x² - 4x + 3 \u003E 0 a pour solution :","option_a":"x ∈ ]1, 3[","option_b":"x ∈ ]-∞, 1[ ∪ ]3, +∞[","option_c":"x ∈ ]-∞, 1[","option_d":"x ∈ ]3, +∞[","option_e":"","option_f":"","bonne_reponse":"B","explication":"Résolvez l'inéquation en étudiant le signe du polynôme. Les racines sont x=1 et x=3, et le polynôme est positif à l'extérieur de ces racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43020,"question":"La suite définie par uₙ = (2n + 1)\/n est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calculez la limite de uₙ quand n → ∞. uₙ = 2 + 1\/n → 2, donc la suite est convergente vers 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43021,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x + 1) ?","option_a":"f'(x) = 1\/(2x + 1)","option_b":"f'(x) = 2\/(2x + 1)","option_c":"f'(x) = 1\/(x + 1)","option_d":"f'(x) = 2x\/(2x + 1)","option_e":"","option_f":"","bonne_reponse":"B","explication":"Appliquez la formule de dérivation des fonctions composées : (ln(u))' = u'\/u. Ici, u = 2x + 1, donc u' = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43022,"question":"Un sac contient 5 boules rouges et 3 boules bleues. Quelle est la probabilité de tirer deux boules rouges sans remise ?","option_a":"10\/28","option_b":"15\/28","option_c":"25\/64","option_d":"5\/14","option_e":"","option_f":"","bonne_reponse":"A","explication":"La probabilité est (5\/8) * (4\/7) = 20\/56 = 10\/28. Utilisez la formule des probabilités conditionnelles pour deux tirages sans remise.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43023,"question":"La fonction f(x) = e^x est-elle toujours croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de f(x) = e^x est f'(x) = e^x \u003E 0 pour tout x, donc la fonction est toujours croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43024,"question":"Résolvez l'inéquation |x - 2| ≤ 3 :","option_a":"x ∈ [-1, 5]","option_b":"x ∈ ]-∞, -1] ∪ [5, +∞[","option_c":"x ∈ [2, 5]","option_d":"x ∈ [-3, 3]","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'inégalité |x - 2| ≤ 3 équivaut à -3 ≤ x - 2 ≤ 3, donc -1 ≤ x ≤ 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43025,"question":"Quelle est la primitive de f(x) = 3x² + 2x qui s'annule en x = 1 ?","option_a":"F(x) = x³ + x² + 2","option_b":"F(x) = x³ + x² - 2","option_c":"F(x) = x³ + x² + 1","option_d":"F(x) = x³ + x² - 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Trouvez une primitive F(x) = x³ + x² + C. Comme F(1) = 0, alors 1 + 1 + C = 0 ⇒ C = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]