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Question 1 sur 10 10:00

[{"id":54851,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2","option_d":"6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la formule (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54852,"question":"L'équation x² - 5x + 6 = 0 admet deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = (-5)² - 4*1*6 = 25 - 24 = 1 \u003E 0, donc l'équation admet bien deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54853,"question":"Quelle est l'intégrale de f(x) = 4x³ entre 0 et 2 ?","option_a":"8","option_b":"16","option_c":"32","option_d":"64","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégrale de 4x³ est x⁴. Entre 0 et 2, cela donne 2⁴ - 0⁴ = 16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54854,"question":"La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité d'un événement impossible est égale à 0. La probabilité d'un événement certain est égale à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54855,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"0","option_b":"1\/2","option_c":"√2\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"sin(π\/6) = sin(30°) = 1\/2, une valeur fondamentale à connaître en trigonométrie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54856,"question":"Une suite géométrique de raison q = -2 et de premier terme u₀ = 3 est décroissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite géométrique de raison négative n'est ni croissante ni décroissante, car ses termes alternent en signe.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54857,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 1","option_b":"x \u003E 4","option_c":"x \u003C 4","option_d":"x \u003E -1","option_e":"","option_f":"","bonne_reponse":"B","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4. La solution est donc x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54858,"question":"La fonction f(x) = 1\/x est dérivable en x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0, donc elle n'est pas dérivable en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54859,"question":"Quelle est la valeur de la limite lim (x→∞) (3x² + 2x) \/ (x² - 5) ?","option_a":"0","option_b":"3","option_c":"∞","option_d":"1\/5","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par x², on obtient (3 + 2\/x) \/ (1 - 5\/x²) → 3\/1 = 3 quand x→∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54860,"question":"Un cube de côté 4 cm a un volume de 64 cm³.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le volume d'un cube est donné par V = côté³. Ici, V = 4³ = 64 cm³, donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]