Quiz Maths Terminale : Testez vos connaissances en 10 questions

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[{"id":52251,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"A. 2x + 3","option_b":"B. x² + 3","option_c":"C. 2x + 5","option_d":"D. x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme est obtenue en appliquant la règle de dérivation terme à terme : (x²)' = 2x et (3x)' = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52252,"question":"La fonction f(x) = 1\/x est définie pour 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 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52253,"question":"Quelle est la limite de la fonction f(x) = (3x² - 2x + 1)\/(x² + 1) quand x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 3","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"Pour les fonctions rationnelles, la limite en l'infini est égale au rapport des coefficients dominants : 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52254,"question":"L'équation x² - 4x + 4 = 0 admet deux solutions distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0, donc l'équation admet une solution double : x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52255,"question":"Quelle est la primitive de la fonction f(x) = 4x³ - 2x + 1 ?","option_a":"A. x⁴ - x² + x + C","option_b":"B. x⁴ - x² + C","option_c":"C. 12x² - 2 + C","option_d":"D. 4x⁴ - 2x² + x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive s'obtient en augmentant chaque exposant de 1 et en divisant par le nouvel exposant : (4x³)' = x⁴, (-2x)' = -x², (1)' = x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52256,"question":"Dans un repère orthonormé, l'équation x² + y² = 25 représente un cercle de centre O(0,0) et de rayon 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² + y² = r² représente un cercle de centre O(0,0) et de rayon r. Ici, r² = 25 donc r = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52257,"question":"Quelle est la valeur de la somme S = 1 + 2 + 3 + ... + n ?","option_a":"A. n(n+1)\/2","option_b":"B. n²","option_c":"C. (n+1)²\/2","option_d":"D. n(n-1)\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La somme des n premiers entiers naturels est donnée par la formule S = n(n+1)\/2, démontrée par récurrence ou méthode des paires.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52258,"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":"La fonction exponentielle e^x est strictement positive pour tout x réel, car e^x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52259,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"A. x \u003C -6","option_b":"B. x \u003E -6","option_c":"C. x \u003C 6","option_d":"D. x \u003E 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant : 2x - 5 \u003E 3x + 1 → -x \u003E 6 → x \u003C -6 (en divisant par -1, l'inégalité change de sens).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52260,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, deux vecteurs sont orthogonaux si et seulement si leur produit scalaire est nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]