Quiz : Maîtrisez les fondamentaux des mathématiques de Terminale !

Question 1 sur 10 10:00

[{"id":62682,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2x","option_d":"3x² + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62683,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle ]-∞, -1[.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 est négative sur ]-∞, -1[, donc la fonction est décroissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62684,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 2 ou x = 1\/2","option_b":"x = -2 ou x = -1\/2","option_c":"x = 1 ou x = 2","option_d":"x = -1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant l'équation du second degré, on trouve x = 2 ou x = 1\/2 grâce à la formule des racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62685,"question":"La limite de la fonction f(x) = (x² + 1)\/x quand x tend vers +∞ est égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La limite est +∞, car le terme dominant au numérateur est x² et au dénominateur x, donc f(x) ~ x quand x tend vers +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62686,"question":"Quelle est la matrice inverse de A = [[1, 2], [3, 4]] ?","option_a":"[[ -2, 1 ], [ 1.5, -0.5 ]]","option_b":"[[ 4, -2 ], [ -3, 1 ]]","option_c":"[[ 1, -2 ], [ -3, 4 ]]","option_d":"[[ -1, 2 ], [ 3, -4 ]]","option_e":"","option_f":"","bonne_reponse":"A","explication":"La matrice inverse de A est calculée par la formule A⁻¹ = (1\/det(A)) * [[d, -b], [-c, a]], où det(A) = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62687,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62688,"question":"Quelle est la limite de la suite uₙ = (n² + 1)\/n quand n tend vers +∞ ?","option_a":"0","option_b":"1","option_c":"+∞","option_d":"n","option_e":"","option_f":"","bonne_reponse":"C","explication":"En simplifiant, uₙ = n + 1\/n, donc la limite est +∞ quand n tend vers +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62689,"question":"La fonction f(x) = e^x est convexe sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée seconde f''(x) = e^x est toujours positive, donc la fonction est convexe sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62690,"question":"Quelle est la solution de l'inéquation x² - 4x + 3 \u003C 0 ?","option_a":"x ∈ ]1, 3[","option_b":"x ∈ ]-∞, 1[ ∪ ]3, +∞[","option_c":"x ∈ ]-∞, +∞[","option_d":"x ∈ ∅","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines de l'équation x² - 4x + 3 = 0 sont x = 1 et x = 3. Le polynôme est négatif entre ces deux racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62691,"question":"La suite uₙ définie par u₀ = 1 et uₙ₊₁ = 2uₙ est une suite géométrique de raison 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La relation de récurrence uₙ₊₁ = 2uₙ montre que chaque terme est multiplié par 2, donc la suite est géométrique de raison 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]