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Question 1 sur 10 10:00

[{"id":31748,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 2 ou x = 1\/2","option_c":"x = -1 ou x = -2","option_d":"x = 1\/2 ou x = 2","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation 2x² - 5x + 2 = 0 se résout en utilisant le discriminant Δ = b² - 4ac = 25 - 16 = 9. Les solutions sont x = (5 ± 3)\/4, soit x = 2 ou x = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31749,"question":"La fonction f(x) = x³ - 3x + 1 est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction n'est donc pas croissante sur tout ℝ, car elle admet des intervalles de décroissance.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31750,"question":"Quelle est la limite de (3x² + 2x - 5)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"0","option_b":"3","option_c":"∞","option_d":"1\/4","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par x², on obtient (3 + 2\/x - 5\/x²)\/(1 - 4\/x²). Lorsque x tend vers +∞, cette expression tend vers 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31751,"question":"Dans un triangle rectangle, si sin(θ) = 3\/5, alors cos(θ) = ?","option_a":"4\/5","option_b":"3\/4","option_c":"5\/3","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, si sin(θ) = 3\/5, alors le côté adjacent est 4 (car 3² + 4² = 5²). Ainsi, cos(θ) = adjacent\/hypoténuse = 4\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31752,"question":"La dérivée de f(x) = e^(2x) est f'(x) = 2e^(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^(u(x)) est u'(x)e^(u(x)). Ici, u(x) = 2x, donc u'(x) = 2. Ainsi, f'(x) = 2e^(2x), ce qui est correct.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31753,"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 ∈ ]-∞ ; 3[","option_d":"x ∈ ]1 ; +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'inéquation x² - 4x + 3 \u003C 0 se résout en trouvant les racines 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":31754,"question":"Dans une expérience aléatoire, si P(A) = 0,2 et P(B) = 0,5, alors P(A ∪ B) = ? (A et B sont incompatibles)","option_a":"0,7","option_b":"0,3","option_c":"0,1","option_d":"0,8","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si A et B sont incompatibles, alors P(A ∪ B) = P(A) + P(B) = 0,2 + 0,5 = 0,7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31755,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0. Elle n'est pas définie pour x ≤ 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31756,"question":"Quelle est l'équation de la tangente à la courbe y = x² + 3x - 2 au point d'abscisse x = 1 ?","option_a":"y = 5x - 3","option_b":"y = 5x + 3","option_c":"y = x + 5","option_d":"y = 3x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La pente de la tangente est f'(1) = 2*1 + 3 = 5. L'équation est y = f'(1)(x - 1) + f(1) = 5(x - 1) + 2 = 5x - 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31757,"question":"Si une variable aléatoire X suit une loi normale N(μ, σ²), alors P(μ - σ ≤ X ≤ μ + σ) ≈ ?","option_a":"0,68","option_b":"0,95","option_c":"0,997","option_d":"0,5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi normale, environ 68% des valeurs se situent dans l'intervalle [μ - σ ; μ + σ].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]