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Question 1 sur 10 10:00

[{"id":39715,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x + 5","option_d":"x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc f'(x) = 2x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39716,"question":"Une suite géométrique de raison q = -2 et de premier terme u₀ = 3 est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite géométrique converge uniquement si |q| \u003C 1. Ici, |q| = 2 \u003E 1, donc elle diverge.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39717,"question":"Quel est le résultat de l'intégrale ∫(3x² + 2x) dx ?","option_a":"x³ + x² + C","option_b":"x³ + x + C","option_c":"3x³ + x² + C","option_d":"x³ + 2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 3x² est x³, celle de 2x est x², et on ajoute la constante d'intégration C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39718,"question":"Dans une expérience aléatoire, si P(A) = 0.4 et P(B) = 0.5 avec A et B incompatibles, quelle est P(A ∪ B) ?","option_a":"0.1","option_b":"0.9","option_c":"0.2","option_d":"0.45","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour deux événements incompatibles, P(A ∪ B) = P(A) + P(B) = 0.4 + 0.5 = 0.9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39719,"question":"Le nombre complexe z = 3 + 4i a pour module |z| = 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module de z = a + bi est √(a² + b²) = √(9 + 16) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39720,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"y = Ce^(-2x)","option_b":"y = Ce^(2x)","option_c":"y = Cx","option_d":"y = C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation différentielle linéaire du premier ordre y' + 2y = 0 a pour solution générale y = Ce^(-2x), où C est une constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39721,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 10 cm et un côté mesure 6 cm, quelle est la longueur de l'autre côté ?","option_a":"8 cm","option_b":"4 cm","option_c":"√64 cm","option_d":"16 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, l'autre côté mesure √(10² - 6²) = √(100 - 36) = √64 = 8 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39722,"question":"La fonction exponentielle est-elle 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 e^x est strictement positive pour tout x réel, car e^x \u003E 0 pour tout x ∈ ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39723,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"1\/6","option_b":"1\/12","option_c":"1\/36","option_d":"1\/18","option_e":"","option_f":"","bonne_reponse":"C","explication":"Il y a 6 × 6 = 36 issues possibles. Une seule issue correspond à (6,6), donc la probabilité est 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39724,"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":"La formule du discriminant est bien Δ = b² - 4ac, utilisée pour déterminer le nombre de solutions réelles de l'équation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]