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Question 1 sur 10 10:00

[{"id":46561,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x² + 2x","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme f(x) = ax^n est f'(x) = nax^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46562,"question":"L'équation x² - 4x + 4 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0. L'équation admet donc une solution double (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46563,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 1) quand x tend vers l'infini ?","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour les fonctions rationnelles, la limite en l'infini est le rapport des coefficients dominants : 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46564,"question":"Le théorème de Thalès s'applique uniquement dans un triangle rectangle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Thalès s'applique à tout triangle, qu'il soit rectangle ou non, tant que les droites sont parallèles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46565,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4. L'inéquation est vérifiée pour x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46566,"question":"La fonction f(x) = x³ est croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² est toujours positive (sauf en x=0 où elle est nulle), donc la fonction est croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46567,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé à 6 faces ?","option_a":"1\/2","option_b":"1\/3","option_c":"1\/6","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles. La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46568,"question":"L'intégrale de f(x) = 2x entre 0 et 2 est égale à 4.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale ∫(0 à 2) 2x dx = [x²](0 à 2) = 4 - 0 = 4. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46569,"question":"Quelle est la forme canonique de l'expression x² - 6x + 10 ?","option_a":"(x - 3)² + 1","option_b":"(x - 6)² + 10","option_c":"(x - 3)² + 4","option_d":"(x - 2)² + 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 6x + 10 = (x² - 6x + 9) + 1 = (x - 3)² + 1. La forme canonique est (x - 3)² + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46570,"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 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]