Quiz Maths Terminale : Testez vos connaissances en 10 questions !

Question 1 sur 10 10:00

[{"id":9693,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"A) 3","option_b":"B) 0","option_c":"C) -1","option_d":"D) +∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"La limite d'un polynôme de même degré au numérateur et au dénominateur est le rapport des coefficients dominants. Ici, 3x²\/x² = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9694,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 1 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite géométrique de raison q \u003E 1 et de premier terme positif est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9695,"question":"Soit f une fonction dérivable sur ℝ. Si f'(x) \u003E 0 pour tout x ∈ ℝ, alors f est :","option_a":"A) Décroissante","option_b":"B) Croissante","option_c":"C) Constante","option_d":"D) Non monotone","option_e":"","option_f":"","bonne_reponse":"B","explication":"Si la dérivée est positive sur un intervalle, la fonction est strictement croissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9696,"question":"La probabilité d'obtenir un double 6 en lançant deux dés équilibrés est :","option_a":"A) 1\/6","option_b":"B) 1\/12","option_c":"C) 1\/36","option_d":"D) 1\/18","option_e":"","option_f":"","bonne_reponse":"C","explication":"Il y a 36 issues possibles (6 x 6), et une seule issue favorable (6-6). Donc P = 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9697,"question":"L'équation z² + 4z + 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 = 16 - 20 = -4 \u003C 0, donc il n'y a pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9698,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x + 1) ?","option_a":"A) e^(2x + 1)","option_b":"B) 2e^(2x + 1)","option_c":"C) (2x + 1)e^(2x)","option_d":"D) e^(x + 1)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de e^u est u' * e^u. Ici, u = 2x + 1, donc u' = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9699,"question":"Dans un triangle ABC, si cos(A) = 0.5, alors l'angle A mesure :","option_a":"A) 30°","option_b":"B) 45°","option_c":"C) 60°","option_d":"D) 90°","option_e":"","option_f":"","bonne_reponse":"C","explication":"cos(60°) = 0.5, donc A = 60°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9700,"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 elle est impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9701,"question":"Quel est le nombre de solutions de l'équation sin(x) = 0.5 dans l'intervalle [0, 2π] ?","option_a":"A) 1","option_b":"B) 2","option_c":"C) 3","option_d":"D) 4","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation sin(x) = 0.5 admet deux solutions dans [0, 2π] : π\/6 et 5π\/6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9702,"question":"Si deux événements A et B sont indépendants, alors P(A ∩ B) = :","option_a":"A) P(A) + P(B)","option_b":"B) P(A) * P(B)","option_c":"C) P(A) - P(B)","option_d":"D) P(A) \/ P(B)","option_e":"","option_f":"","bonne_reponse":"B","explication":"Par définition, deux événements sont indépendants si P(A ∩ B) = P(A) * P(B).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]