Quiz : Les fondamentaux de mathématiques pour la 4ème année Math

Question 1 sur 10 10:00

[{"id":26308,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -12","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 2x des deux côtés et en ajoutant 5, on obtient x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26309,"question":"La fonction f(x) = 2x² - 3x + 1 est une fonction polynôme de degré :","option_a":"1","option_b":"2","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le degré d'un polynôme est donné par l'exposant le plus élevé de x, ici 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26310,"question":"Vrai ou Faux ? La dérivée de f(x) = x³ est f'(x) = 3x².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x^n est n*x^(n-1), donc pour x³, on obtient bien 3x².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26311,"question":"Quelle est l'aire d'un triangle rectangle dont les côtés de l'angle droit mesurent 6 cm et 8 cm ?","option_a":"24 cm²","option_b":"48 cm²","option_c":"14 cm²","option_d":"30 cm²","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire d'un triangle rectangle est (base * hauteur)\/2 = (6*8)\/2 = 24 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26312,"question":"Vrai ou Faux ? Le théorème de Pythagore s'applique uniquement aux triangles rectangles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le théorème de Pythagore est une propriété spécifique aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26313,"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 \u003C 6","option_d":"x \u003E 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 3x et en ajoutant 5, on obtient -x \u003E 6, soit x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26314,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 4x + 5 ?","option_a":"f(x) = (x-2)² + 1","option_b":"f(x) = (x-2)² - 1","option_c":"f(x) = (x+2)² + 1","option_d":"f(x) = (x+2)² - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En complétant le carré : x² - 4x + 5 = (x² - 4x + 4) + 1 = (x-2)² + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26315,"question":"Vrai ou Faux ? La fonction f(x) = 1\/x est définie pour 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 car la division par zéro est interdite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26316,"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 : (x-2)(x-3) = 0, donc x = 2 ou x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26317,"question":"Quelle est la valeur de sin(30°) ?","option_a":"1\/2","option_b":"√2\/2","option_c":"√3\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans un triangle rectangle, sin(30°) = côté opposé\/hypoténuse = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]