Quiz Maths : Algèbre et Analyse — Niveau Secondaire

Question 1 sur 10 10:00

[{"id":65362,"question":"Quelle est la solution de l'équation 2x + 5 = 11 ?","option_a":"x = 3","option_b":"x = 4","option_c":"x = 5","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 5 des deux côtés, on obtient 2x = 6, puis en divisant par 2, x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65363,"question":"La fonction f(x) = x² est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction carrée est toujours positive ou nulle, car x² ≥ 0 pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65364,"question":"Quelle est la limite de (3x² + 2x - 1) \/ (x² + 1) quand x tend vers l'infini ?","option_a":"3","option_b":"2","option_c":"1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x², on obtient (3 + 2\/x - 1\/x²) \/ (1 + 1\/x²), dont la limite est 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65365,"question":"Un triangle rectangle a des côtés de 3 cm et 4 cm. Quelle est la longueur de l'hypoténuse ?","option_a":"5 cm","option_b":"6 cm","option_c":"7 cm","option_d":"8 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, l'hypoténuse est √(3² + 4²) = √25 = 5 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65366,"question":"La dérivée de f(x) = x³ est-elle f'(x) = 3x² ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x³ est bien 3x², car d\/dx(x^n) = n*x^(n-1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65367,"question":"Quelle est la solution de l'inéquation 2x - 7 \u003E 3 ?","option_a":"x \u003E 5","option_b":"x \u003E 10","option_c":"x \u003C 5","option_d":"x \u003C 10","option_e":"","option_f":"","bonne_reponse":"A","explication":"En ajoutant 7 des deux côtés, on obtient 2x \u003E 10, puis en divisant par 2, x \u003E 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65368,"question":"Un cercle a un rayon de 5 cm. Quelle est son aire ?","option_a":"25π cm²","option_b":"10π cm²","option_c":"50π cm²","option_d":"100π cm²","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire d'un cercle est πr², donc π*5² = 25π cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65369,"question":"La suite u_n = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La différence entre deux termes consécutifs est constante (u_{n+1} - u_n = 2), donc la suite est arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65370,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = 1 ou x = 6","option_c":"x = -2 ou x = -3","option_d":"x = 0 ou x = 5","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},{"id":65371,"question":"La fonction f(x) = 1\/x est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction 1\/x n'est pas définie en x = 0, car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]