Quiz : Testez vos connaissances sur les exercices types

Question 1 sur 10 10:00

[{"id":22218,"question":"Quelle est la formule de la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"f'(x) = 2x + 3","option_b":"f'(x) = x² + 3","option_c":"f'(x) = 2x - 5","option_d":"f'(x) = 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":22219,"question":"L'équation x² - 4x + 4 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = (-4)² - 4*1*4 = 16 - 16 = 0. Une seule solution réelle double (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22220,"question":"Quelle est la solution de l'inéquation 3x - 7 \u003E 2x + 1 ?","option_a":"x \u003E 8","option_b":"x \u003C 8","option_c":"x \u003E -6","option_d":"x \u003C -6","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 7 \u003E 2x + 1 ⇒ 3x - 2x \u003E 1 + 7 ⇒ x \u003E 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22221,"question":"La fonction exponentielle f(x) = e^x est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout x réel, e^x \u003E 0. La fonction exponentielle est strictement positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22222,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx ?","option_a":"x² + x + C","option_b":"2x² + x + C","option_c":"x² + 2x + C","option_d":"2x² + 2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"∫2x dx = x² et ∫1 dx = x. Donc ∫(2x + 1) dx = x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22223,"question":"La loi de Newton F = m*a s'applique uniquement aux mouvements rectilignes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La loi de Newton s'applique à tout mouvement, qu'il soit rectiligne ou non.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22224,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"1\/2","option_b":"√2\/2","option_c":"√3\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"sin(π\/6) = sin(30°) = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22225,"question":"Un triangle rectangle a toujours deux angles aigus.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un triangle rectangle a un angle droit (90°) et deux angles aigus dont la somme est 90°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22226,"question":"Quelle est la solution de l'équation 2^(x+1) = 8 ?","option_a":"x = 1","option_b":"x = 2","option_c":"x = 3","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"B","explication":"2^(x+1) = 8 ⇒ 2^(x+1) = 2³ ⇒ x + 1 = 3 ⇒ x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22227,"question":"La résistance équivalente de deux résistances en série est toujours supérieure à chacune d'elles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En série, R_eq = R1 + R2. Donc R_eq \u003E R1 et R_eq \u003E R2 si R1 et R2 sont positives.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]