Quiz de révision : Mathématiques 3ème année secondaire

Question 1 sur 10 10:00

[{"id":49401,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = -1 ou x = 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"On factorise l'équation : (x-2)(x-3)=0, donc les solutions sont x=2 et x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49402,"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":"B","explication":"La dérivée f'(x) = 2x - 4 est négative pour x \u003C 2, donc la fonction est décroissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49403,"question":"Quel est le discriminant de l'équation 3x² + 2x - 1 = 0 ?","option_a":"Δ = 16","option_b":"Δ = 4","option_c":"Δ = 8","option_d":"Δ = 12","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant est Δ = b² - 4ac = 2² - 4*3*(-1) = 4 + 12 = 16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49404,"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":"2\/5","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, cos(θ) = √(1 - sin²(θ)) = √(1 - 9\/25) = 4\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49405,"question":"L'équation x³ - 2x² + x = 0 admet trois solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"On factorise : x(x² - 2x + 1) = x(x-1)² = 0, donc les solutions sont x=0 (double) et x=1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49406,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3)\/(x² - 1) lorsque x tend vers +∞ ?","option_a":"2","option_b":"0","option_c":"1","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) = (2 + 3\/x²)\/(1 - 1\/x²), donc la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49407,"question":"Un triangle ABC a pour côtés AB=5, BC=7 et AC=8. Quelle est la mesure de l'angle B ?","option_a":"30°","option_b":"45°","option_c":"60°","option_d":"90°","option_e":"","option_f":"","bonne_reponse":"C","explication":"D'après la loi des cosinus : cos(B) = (AB² + BC² - AC²)\/(2*AB*BC) = (25 + 49 - 64)\/70 = 10\/70 = 1\/7 ≈ 0,866, donc B ≈ 30°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49408,"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 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":49409,"question":"Quel est le centre de symétrie de la fonction f(x) = x³ - 3x ?","option_a":"x=0","option_b":"x=1","option_c":"x=-1","option_d":"Aucun","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction est impaire (f(-x) = -f(x)), donc son centre de symétrie est l'origine (0,0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49410,"question":"Si f(x) = e^x et g(x) = ln(x), alors (f∘g)(x) = x pour tout x \u003E 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La composition (f∘g)(x) = e^(ln(x)) = x, donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]