Quiz Maths 2ème année secondaire : Fonctions, Équations et Géométrie

Question 1 sur 10 10:00

[{"id":40666,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"A. 6x - 5","option_b":"B. 3x - 5","option_c":"C. 6x² - 5","option_d":"D. 3x² - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40667,"question":"L'équation x² - 4x + 4 = 0 admet-elle 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 = 0, donc l'équation admet une solution double (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40668,"question":"Dans un triangle rectangle, si cos(θ) = 0,8, quelle est la valeur de sin(θ) ?","option_a":"A. 0,2","option_b":"B. 0,4","option_c":"C. 0,6","option_d":"D. 0,8","option_e":"","option_f":"","bonne_reponse":"C","explication":"D'après la relation sin²(θ) + cos²(θ) = 1, si cos(θ) = 0,8 alors sin(θ) = √(1 - 0,64) = 0,6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40669,"question":"La fonction f(x) = 2x³ - 3x² + 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) = 6x² - 6x = 6x(x - 1) change de signe, donc la fonction n'est pas croissante partout.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40670,"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, on obtient -x \u003E 6, soit x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40671,"question":"Le théorème de Thalès s'applique-t-il uniquement aux triangles rectangles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Thalès s'applique à tous les triangles, pas seulement aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40672,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 1) lorsque x tend vers +∞ ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 3","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) ≈ 3 pour x → +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40673,"question":"Un triangle a des côtés de longueurs 3, 4 et 5. Est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, 3² + 4² = 5², donc le triangle est rectangle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40674,"question":"Quelle est la solution de l'équation |2x - 3| = 5 ?","option_a":"A. x = 4 ou x = -1","option_b":"B. x = 4 ou x = 1","option_c":"C. x = -4 ou x = 1","option_d":"D. x = -4 ou x = -1","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation |2x - 3| = 5 donne 2x - 3 = 5 ou 2x - 3 = -5, soit x = 4 ou x = -1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40675,"question":"La fonction f(x) = x² - 4x + 3 admet-elle un minimum en x = 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 s'annule en x = 2, et f''(x) = 2 \u003E 0, donc c'est un minimum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]