Quiz Mathématiques — Série 39 : Testez vos connaissances !

Question 1 sur 10 10:00

[{"id":60617,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = -2","option_c":"x = 2","option_d":"x = -12","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 7 = 2x + 5 → 3x - 2x = 5 + 7 → x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60618,"question":"La dérivée de la fonction f(x) = x² + 3x - 4 est f'(x) = 2x + 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -4 est 0. Donc f'(x) = 2x + 3 est correct.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60619,"question":"Quel est le discriminant de l'équation quadratique 2x² - 5x + 3 = 0 ?","option_a":"Δ = 1","option_b":"Δ = -1","option_c":"Δ = 25 - 24 = 1","option_d":"Δ = 16","option_e":"","option_f":"","bonne_reponse":"C","explication":"Pour ax² + bx + c = 0, Δ = b² - 4ac. Ici, Δ = (-5)² - 4*2*3 = 25 - 24 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60620,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est l'énoncé du théorème de Pythagore, valable uniquement pour les triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60621,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"3","option_b":"∞","option_c":"0","option_d":"2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour les limites à l'infini des fonctions rationnelles, on compare les degrés des polynômes. Ici, les termes dominants sont 3x²\/x² = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60622,"question":"La médiane d'un triangle est une droite qui passe par un sommet et le milieu du côté opposé.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est la définition exacte d'une médiane dans un triangle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60623,"question":"Résoudre l'inéquation : -2x + 5 \u003E 3x - 7.","option_a":"x \u003C 2","option_b":"x \u003E 2","option_c":"x \u003C 12\/5","option_d":"x \u003E 12\/5","option_e":"","option_f":"","bonne_reponse":"D","explication":"-2x + 5 \u003E 3x - 7 → 5 + 7 \u003E 3x + 2x → 12 \u003E 5x → x \u003C 12\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60624,"question":"Le centre de symétrie d'un cercle est le point équidistant de tous ses points.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, le centre d'un cercle est le point équidistant de tous les points du cercle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60625,"question":"Quelle est la dérivée de la fonction f(x) = e^(3x) ?","option_a":"f'(x) = e^(3x)","option_b":"f'(x) = 3e^(3x)","option_c":"f'(x) = e^(x)","option_d":"f'(x) = 3x e^(3x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de e^(u(x)) est u'(x) * e^(u(x)). Ici, u(x) = 3x → u'(x) = 3, donc f'(x) = 3e^(3x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60626,"question":"Dans une série statistique, la moyenne est toujours égale à la médiane.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La moyenne et la médiane sont égales uniquement si la distribution est symétrique. Sinon, elles peuvent différer.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]