Quiz : Maîtrisez les dérivées et équations en 4ème année secondaire !

Question 1 sur 10 10:00

[{"id":45196,"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":"6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45197,"question":"L'équation x² - 4x + 3 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = b² - 4ac = 16 - 12 = 4 \u003E 0, donc l'équation admet deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45198,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 7 ?","option_a":"x \u003E 5","option_b":"x \u003E 2","option_c":"x \u003C 5","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'inéquation : 2x \u003E 10 → x \u003E 5. La solution est donc x \u003E 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45199,"question":"La fonction f(x) = x³ est-elle dérivable en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction f(x) = x³ est dérivable en tout point, y compris x = 0, car elle est polynomiale.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45200,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x) \/ x lorsque x tend vers 0 ?","option_a":"0","option_b":"2","option_c":"3","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"Simplifiez f(x) = 2x + 3. Lorsque x → 0, f(x) → 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45201,"question":"L'équation 3x² + 6x + 3 = 0 admet une solution double.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = 36 - 36 = 0, donc l'équation admet une solution double : x = -1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45202,"question":"Quelle est la dérivée de la fonction f(x) = 1\/x ?","option_a":"-1\/x²","option_b":"1\/x²","option_c":"-x","option_d":"x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de f(x) = 1\/x est f'(x) = -1\/x², car (1\/x)' = -1\/x².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45203,"question":"La fonction f(x) = √x est-elle dérivable en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction √x n'est pas dérivable en x = 0 car sa dérivée f'(x) = 1\/(2√x) tend vers l'infini lorsque x → 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45204,"question":"Quelle est la solution de l'équation 5x + 7 = 3x - 1 ?","option_a":"x = -4","option_b":"x = -3","option_c":"x = 4","option_d":"x = 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'équation : 5x - 3x = -1 - 7 → 2x = -8 → x = -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45205,"question":"La fonction f(x) = |x| est-elle dérivable en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction valeur absolue n'est pas dérivable en x = 0 car ses dérivées à gauche et à droite ne sont pas égales.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]