Quiz Maths Terminale : Maîtrisez les fondamentaux !

Question 1 sur 10 10:00

[{"id":56941,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"6x² + 2","option_c":"3x + 2","option_d":"6x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation terme à terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56942,"question":"La limite de la suite uₙ = (n² + 1)\/n² quand n tend vers l'infini est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En simplifiant uₙ = 1 + 1\/n², on voit que la limite est bien 1 car 1\/n² tend vers 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56943,"question":"Quel est le résultat de l'intégrale ∫(2x + 3) dx ?","option_a":"x² + 3x + C","option_b":"x² + 3x","option_c":"2x² + 3x + C","option_d":"x² + 2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale d'une somme est la somme des intégrales : ∫2x dx + ∫3 dx = x² + 3x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56944,"question":"Une fonction dérivable sur un intervalle est toujours continue sur cet intervalle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est un théorème fondamental : la dérivabilité entraîne la continuité.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56945,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"e²","option_b":"2","option_c":"1\/2","option_d":"ln(2)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En exponentiant les deux côtés, on obtient x = e².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56946,"question":"La suite définie par uₙ = (-1)ⁿ est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Cette suite alterne entre -1 et 1, donc elle n'a pas de limite (diverge).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56947,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x³ au point d'abscisse 2 ?","option_a":"6","option_b":"12","option_c":"3","option_d":"8","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le coefficient directeur est f'(2) = 3*(2)² = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56948,"question":"La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout x réel, eˣ \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56949,"question":"Quelle est la valeur de l'intégrale ∫₀¹ (3x² + 2x) dx ?","option_a":"2","option_b":"1","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calcul : [x³ + x²]₀¹ = (1 + 1) - (0 + 0) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56950,"question":"La fonction f(x) = 1\/x est définie en x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction 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}]