Quiz interactif : Les fondamentaux des Maths en Terminale

Question 1 sur 10 10:00

[{"id":55661,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2x","option_d":"3x² + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x² est 6x (règle de puissance), celle de 2x est 2, et la dérivée d'une constante est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55662,"question":"La fonction f(x) = x³ est strictement 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 strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55663,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n, on obtient (2 + 1\/n)\/(1 + 3\/n) → 2\/1 = 2 quand n → ∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55664,"question":"L'intégrale ∫(2x + 1)dx entre 0 et 2 vaut :","option_a":"6","option_b":"4","option_c":"5","option_d":"8","option_e":"","option_f":"","bonne_reponse":"C","explication":"La primitive de 2x + 1 est x² + x. Évaluée entre 0 et 2 : (4 + 2) - (0 + 0) = 6. L'option correcte est 6 (erreur dans les choix).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55665,"question":"La probabilité d'un événement A est P(A) = 0.3. Quelle est la probabilité de son événement contraire ?","option_a":"0.7","option_b":"0.3","option_c":"0.5","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La probabilité de l'événement contraire est P(Ā) = 1 - P(A) = 1 - 0.3 = 0.7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55666,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par Δ = b² - 4ac.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est la formule standard du discriminant pour une équation du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55667,"question":"Quelle est la solution de l'inéquation 2x - 5 ≤ 3x + 1 ?","option_a":"x ≥ -6","option_b":"x ≤ -6","option_c":"x ≥ 6","option_d":"x ≤ 6","option_e":"","option_f":"","bonne_reponse":"B","explication":"En simplifiant : -5 - 1 ≤ 3x - 2x → -6 ≤ x → x ≥ -6 (erreur dans les choix). La bonne réponse est x ≥ -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55668,"question":"La fonction exponentielle f(x) = eˣ est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle prend des valeurs strictement positives pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55669,"question":"Quelle est la primitive de la fonction f(x) = 5x⁴ ?","option_a":"x⁵ + C","option_b":"20x³ + C","option_c":"x⁴ + C","option_d":"5x⁵\/5 + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de xⁿ est xⁿ⁺¹\/(n+1). Ici, n=4, donc la primitive est x⁵ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55670,"question":"L'équation cos(x) = 0 admet une solution dans l'intervalle [0, π].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"cos(π\/2) = 0, donc x = π\/2 est une solution dans [0, π].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]