Quiz Maths 2ème Année : Algèbre, Fonctions et Géométrie

Question 1 sur 10 10:00

[{"id":41636,"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 = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x, on obtient 3x - 2x = 5 + 7, soit x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41637,"question":"La fonction f(x) = x² - 4x + 3 admet-elle un minimum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction est une parabole ouverte vers le haut, donc elle admet un minimum en son sommet.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41638,"question":"Quel est le résultat de lim(x→2) (x² - 4)\/(x - 2) ?","option_a":"0","option_b":"2","option_c":"4","option_d":"indéterminé","option_e":"","option_f":"","bonne_reponse":"C","explication":"En factorisant, on obtient lim(x→2) (x-2)(x+2)\/(x-2) = lim(x→2) (x+2) = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41639,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 5 cm et un côté mesure 3 cm, quelle est la longueur du troisième côté ?","option_a":"4 cm","option_b":"6 cm","option_c":"√34 cm","option_d":"2 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore : 5² = 3² + x² → x = √(25-9) = 4 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41640,"question":"La dérivée de f(x) = 3x³ - 2x² + x - 1 est f'(x) = 9x² - 4x + 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En dérivant terme à terme : f'(x) = 9x² - 4x + 1, ce qui correspond bien à l'énoncé.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41641,"question":"Quelle est la solution de l'inéquation 2x + 3 ≤ 7 ?","option_a":"x ≤ 2","option_b":"x ≥ 2","option_c":"x ≤ -2","option_d":"x ≥ -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x, on obtient 2x ≤ 4 → x ≤ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41642,"question":"Soit f(x) = (x² - 1)\/(x - 1). Quelle est la limite de f(x) quand x tend vers 1 ?","option_a":"1","option_b":"0","option_c":"2","option_d":"indéterminé","option_e":"","option_f":"","bonne_reponse":"A","explication":"En simplifiant, f(x) = x + 1 pour x ≠ 1, donc lim(x→1) f(x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41643,"question":"Un cercle a un rayon de 4 cm. Quelle est son aire ?","option_a":"16π cm²","option_b":"8π cm²","option_c":"4π cm²","option_d":"π cm²","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire d'un cercle est πr² = π × 4² = 16π cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41644,"question":"La fonction f(x) = sin(x) est-elle périodique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction sin(x) a une période de 2π, donc elle est périodique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41645,"question":"Quelle est la solution de l'équation x² + 5x + 6 = 0 ?","option_a":"x = -2 ou x = -3","option_b":"x = 2 ou x = 3","option_c":"x = -1 ou x = -6","option_d":"x = 1 ou x = 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En factorisant, on obtient (x+2)(x+3) = 0, donc x = -2 ou x = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]