Testez vos connaissances en mathématiques : Algèbre, Analyse et Géométrie

Question 1 sur 10 10:00

[{"id":41686,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 5\/3","option_d":"x = 15","option_e":"","option_f":"","bonne_reponse":"B","explication":"Résolvez l'équation en isolant x : 3x = 10 + 5 → 3x = 15 → x = 15\/3 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41687,"question":"La fonction f(x) = x² - 4x + 4 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Cette fonction est un carré parfait : f(x) = (x-2)² ≥ 0 pour tout x réel. Elle s'annule en x=2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41688,"question":"Quel est le discriminant de l'équation x² + 2x - 3 = 0 ?","option_a":"Δ = 16","option_b":"Δ = 4","option_c":"Δ = 8","option_d":"Δ = 12","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = b² - 4ac = 2² - 4(1)(-3) = 4 + 12 = 16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41689,"question":"La dérivée de f(x) = 3x² + 2x - 1 est f'(x) = 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -1 est 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41690,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"1\/2","option_b":"√2\/2","option_c":"√3\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"sin(π\/6) = sin(30°) = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41691,"question":"L'équation x² + 1 = 0 admet deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 0² - 4(1)(1) = -4 \u003C 0. Pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41692,"question":"La fonction f(x) = e^x est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = e^x \u003E 0 pour tout x réel, donc la fonction est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41693,"question":"Quelle est la solution de l'inéquation 2x + 3 \u003E 7 ?","option_a":"x \u003E 2","option_b":"x \u003E -2","option_c":"x \u003C 2","option_d":"x \u003C -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x \u003E 7 - 3 → 2x \u003E 4 → x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41694,"question":"La somme des angles d'un triangle est égale à 180°.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une propriété fondamentale de la géométrie plane.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41695,"question":"Quelle est la dérivée de f(x) = ln(x) ?","option_a":"f'(x) = 1\/x","option_b":"f'(x) = x","option_c":"f'(x) = e^x","option_d":"f'(x) = -1\/x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est 1\/x pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]