Quiz Mathématiques : 4ème Année Secondaire — Série PB27

Question 1 sur 10 10:00

[{"id":71042,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2","option_d":"3x² + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme. La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71043,"question":"L'équation x² - 5x + 6 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = b² - 4ac = 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":71044,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour x tendant vers l'infini, on compare les termes de plus haut degré : f(x) ≈ 2x²\/x² = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71045,"question":"Soit une variable aléatoire X suivant une loi binomiale B(n=10, p=0.3). Quelle est l'espérance de X ?","option_a":"3","option_b":"0.3","option_c":"10","option_d":"7","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'espérance d'une loi binomiale B(n,p) est E(X) = n × p = 10 × 0.3 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71046,"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 elle n'est pas croissante sur [-2, 2].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71047,"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 \u003E 6","option_d":"x \u003C 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x - 5 \u003E 3x + 1 ⇒ -5 - 1 \u003E 3x - 2x ⇒ -6 \u003E x ⇒ x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71048,"question":"Soit un cube d'arête 4 cm. Quel est son volume ?","option_a":"64 cm³","option_b":"16 cm³","option_c":"48 cm³","option_d":"32 cm³","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le volume d'un cube est V = arête³ = 4³ = 64 cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71049,"question":"La fonction f(x) = 1\/x est dérivable 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, donc elle n'est pas dérivable en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71050,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"1\/2","option_b":"1\/3","option_c":"1\/6","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles, donc P(pair) = 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71051,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 3. Quelle est la valeur de u₃ ?","option_a":"54","option_b":"18","option_c":"162","option_d":"6","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Donc u₃ = 2 × 3³ = 2 × 27 = 54.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]