Quiz Maths Bac : Testez vos connaissances en algèbre et analyse !

Question 1 sur 10 10:00

[{"id":17838,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0,5 ou x = 2","option_c":"x = -1 ou x = 2","option_d":"x = 1,5 ou x = 0,5","option_e":"","option_f":"","bonne_reponse":"B","explication":"Résolvons l'équation : Δ = (-5)² - 4*2*2 = 25 - 16 = 9. Les solutions sont x = (5 ± √9)\/4, soit x = 2 ou x = 0,5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17839,"question":"La fonction f(x) = x³ - 3x² + 2x est dérivable sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Toute fonction polynôme est dérivable sur ℝ. Ici, f'(x) = 3x² - 6x + 2 existe pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17840,"question":"Quelle est la limite de (3x² + 2x - 1)\/(x² - 4) quand x tend vers +∞ ?","option_a":"3","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x², on obtient (3 + 2\/x - 1\/x²)\/(1 - 4\/x²). Quand x → +∞, les termes en 1\/x tendent vers 0, donc la limite est 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17841,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = -0,5. Quelle est la valeur de u₃ ?","option_a":"-0,25","option_b":"0,25","option_c":"-0,5","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"La formule d'une suite géométrique est uₙ = u₀ * qⁿ. Donc u₃ = 2 * (-0,5)³ = 2 * (-0,125) = -0,25. Attention à l'erreur de signe !","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17842,"question":"L'intégrale ∫₀¹ (2x + 1) dx vaut 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calculons l'intégrale : ∫(2x + 1) dx = x² + x + C. Entre 0 et 1, cela donne (1 + 1) - (0 + 0) = 2. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17843,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x + 2) ?","option_a":"f'(x) = 1\/(3x + 2)","option_b":"f'(x) = 3\/(3x + 2)","option_c":"f'(x) = 3x\/(3x + 2)","option_d":"f'(x) = 1\/(x + 2)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 3x + 2, donc u' = 3. Ainsi, f'(x) = 3\/(3x + 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17844,"question":"Un sac contient 3 boules rouges et 2 boules bleues. On tire une boule au hasard. Quelle est la probabilité de tirer une boule bleue ?","option_a":"0,2","option_b":"0,4","option_c":"0,5","option_d":"0,6","option_e":"","option_f":"","bonne_reponse":"B","explication":"Il y a 5 boules au total. La probabilité de tirer une boule bleue est 2\/5 = 0,4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17845,"question":"La fonction f(x) = x² - 4x + 3 est croissante sur l'intervalle [2 ; +∞[.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 2x - 4. Pour x ≥ 2, f'(x) ≥ 0, donc la fonction est croissante sur [2 ; +∞[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17846,"question":"Quelle est la solution de l'inéquation -2x + 5 \u003C 3x - 7 ?","option_a":"x \u003C 12\/5","option_b":"x \u003E 12\/5","option_c":"x \u003C 2","option_d":"x \u003E 2","option_e":"","option_f":"","bonne_reponse":"B","explication":"Résolvons : -2x + 5 \u003C 3x - 7 → 5 + 7 \u003C 3x + 2x → 12 \u003C 5x → x \u003E 12\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17847,"question":"Soit une variable aléatoire X suivant une loi normale N(0 ; 1). Quelle est la probabilité P(X ≤ 1) ?","option_a":"0,6826","option_b":"0,8413","option_c":"0,9772","option_d":"0,9987","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour une loi normale centrée réduite, P(X ≤ 1) ≈ 0,8413 (valeur lue dans la table de la loi normale).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]