Quiz : Maîtrisez les bases des mathématiques pour le Bac

Question 1 sur 10 10:00

[{"id":58807,"question":"Quelle est la solution de l'équation 2x - 5 = 3 ?","option_a":"x = 1","option_b":"x = 4","option_c":"x = -1","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"B","explication":"En ajoutant 5 des deux côtés, on obtient 2x = 8, puis en divisant par 2, x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58808,"question":"La fonction f(x) = x² - 4x + 4 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction est un carré parfait : f(x) = (x-2)² ≥ 0 pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58809,"question":"Quel est le coefficient directeur de la droite d'équation y = -3x + 2 ?","option_a":"-3","option_b":"2","option_c":"3","option_d":"-2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est le nombre devant x, ici -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58810,"question":"L'inéquation 3x + 1 \u003E 7 a pour solution :","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E -2","option_d":"x \u003C -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 1 et en divisant par 3, on obtient x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58811,"question":"Le triangle ABC avec AB = 5 cm, BC = 12 cm et AC = 13 cm est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"13² = 5² + 12² (169 = 25 + 144), donc le triangle est rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58812,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 2x + 1 ?","option_a":"f'(x) = 6x - 2","option_b":"f'(x) = 3x - 2","option_c":"f'(x) = 6x² - 2","option_d":"f'(x) = 3x² - 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'un polynôme se calcule terme à terme : 6x - 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58813,"question":"L'équation x² - 5x + 6 = 0 a pour solutions :","option_a":"x = 2 et x = 3","option_b":"x = -2 et x = -3","option_c":"x = 1 et x = 6","option_d":"x = 0 et x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En factorisant, (x-2)(x-3) = 0 donne x = 2 ou x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58814,"question":"La droite d'équation y = 4x - 1 passe-t-elle par le point A(2, 7) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En remplaçant x par 2, on obtient y = 4*2 - 1 = 7, donc le point A appartient à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58815,"question":"Quel est le résultat de l'intégrale ∫(2x + 1)dx ?","option_a":"x² + x + C","option_b":"x² + C","option_c":"2x² + x + C","option_d":"x² + 2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 2x est x² et celle de 1 est x, donc x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58816,"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}]