Maths 4ème année : Testez vos connaissances en 10 questions

Question 1 sur 10 10:00

[{"id":14063,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0.5 ou x = 2","option_c":"x = -1 ou x = -2","option_d":"x = 0.5 ou x = 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la formule des racines du second degré, on trouve x = 0.5 ou x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14064,"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 est correcte : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14065,"question":"Quel est le théorème qui permet de calculer la longueur d'un côté dans un triangle rectangle ?","option_a":"Théorème de Pythagore","option_b":"Théorème de Thalès","option_c":"Théorème des milieux","option_d":"Théorème de l'angle inscrit","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le théorème de Pythagore s'applique dans un triangle rectangle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14066,"question":"Si f(x) = x³ - 3x + 1, que vaut f'(2) ?","option_a":"3","option_b":"6","option_c":"9","option_d":"12","option_e":"","option_f":"","bonne_reponse":"C","explication":"f'(x) = 3x² - 3, donc f'(2) = 3*(2)² - 3 = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14067,"question":"Dans un triangle ABC, si AB = 5 cm, BC = 4 cm et AC = 3 cm, alors le triangle est rectangle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"5² = 4² + 3² (25 = 16 + 9), donc le triangle est rectangle en C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14068,"question":"Quelle est la forme canonique de l'expression 2x² - 8x + 5 ?","option_a":"2(x - 2)² - 3","option_b":"2(x - 2)² + 1","option_c":"2(x - 1)² - 3","option_d":"2(x - 1)² + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x² - 8x + 5 = 2(x² - 4x) + 5 = 2(x - 2)² - 8 + 5 = 2(x - 2)² - 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14069,"question":"Si sin(θ) = 0.6, quelle est la valeur de cos(θ) dans un triangle rectangle ?","option_a":"0.4","option_b":"0.8","option_c":"1","option_d":"0.6","option_e":"","option_f":"","bonne_reponse":"B","explication":"D'après le théorème de Pythagore, cos(θ) = √(1 - 0.6²) = 0.8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14070,"question":"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 (division par zéro).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14071,"question":"Quelle est la limite de (x² - 4)\/(x - 2) quand x tend vers 2 ?","option_a":"0","option_b":"2","option_c":"4","option_d":"indéterminée","option_e":"","option_f":"","bonne_reponse":"C","explication":"En simplifiant, (x² - 4)\/(x - 2) = x + 2 → limite = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14072,"question":"Si une droite a pour équation y = 3x + 1, quelle est sa pente ?","option_a":"1","option_b":"3","option_c":"-1","option_d":"-3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Dans l'équation y = mx + p, m représente la pente. Ici, m = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]