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[{"id":1133,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x² + 2x","option_d":"f'(x) = 6x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d’une fonction polynôme se calcule terme par terme en utilisant la règle : (ax^n)' = n·a·x^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1134,"question":"Résolvez l’équation 2x² - 5x + 2 = 0. Quelles sont les solutions ?","option_a":"x = 1 et x = 2","option_b":"x = 2 et x = 1\/2","option_c":"x = -1 et x = -2","option_d":"x = 1\/2 et x = 2","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la formule des racines d’un polynôme du second degré (Δ = b² - 4ac), on trouve x1 = 2 et x2 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1135,"question":"Quelle est l’équation de la tangente à la courbe y = x³ au point d’abscisse x = 1 ?","option_a":"y = 3x - 2","option_b":"y = 3x + 2","option_c":"y = x³ + 2","option_d":"y = 3x² - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La tangente en x = 1 a pour équation y = f'(1)(x - 1) + f(1). Ici, f'(1) = 3 et f(1) = 1, donc y = 3x - 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1136,"question":"Dans un sac contenant 4 boules rouges et 6 boules bleues, quelle est la probabilité de tirer une boule rouge ?","option_a":"0,4","option_b":"0,6","option_c":"0,25","option_d":"0,5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La probabilité est le rapport du nombre de cas favorables sur le nombre total de cas : 4\/10 = 0,4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1137,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x) \/ (x² - 1) lorsque x tend vers l’infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour les fonctions rationnelles, on compare les termes de plus haut degré : lim (2x² \/ x²) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]