Quiz interactif : Fonctions, équations et inéquations — Niveau Seconde

Question 1 sur 10 10:00

[{"id":58216,"question":"Quelle est l’image de 2 par la fonction f(x) = 3x² - 5x + 1 ?","option_a":"A. 3","option_b":"B. -1","option_c":"C. 1","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calculez f(2) = 3*(2)² - 5*(2) + 1 = 12 - 10 + 1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58217,"question":"L’équation 2x - 5 = 0 a pour solution x = 2,5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l’équation : 2x = 5 → x = 5\/2 = 2,5. La solution est donc correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58218,"question":"Quelle est la solution de l’inéquation 3x - 7 \u003E 2 ?","option_a":"A. x \u003E 3","option_b":"B. x \u003E 1","option_c":"C. x \u003C 3","option_d":"D. x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez : 3x \u003E 9 → x \u003E 3. La solution est x \u003E 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58219,"question":"La fonction f(x) = x² - 4x + 4 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Factorisez : f(x) = (x-2)² ≥ 0. La fonction est toujours positive ou nulle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58220,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 6x + 5 ?","option_a":"A. (x-3)² - 4","option_b":"B. (x-2)² - 3","option_c":"C. (x-1)² - 5","option_d":"D. (x-4)² - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Complétez le carré : f(x) = (x² - 6x + 9) - 4 = (x-3)² - 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58221,"question":"L’inéquation x² - 5x + 6 ≤ 0 a pour solutions x ∈ [2 ; 3].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Factorisez : (x-2)(x-3) ≤ 0. Les solutions sont bien x ∈ [2 ; 3].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58222,"question":"Quelle est la solution de l’équation (x+1)(x-3) = 0 ?","option_a":"A. x = -1 ou x = 3","option_b":"B. x = 1 ou x = -3","option_c":"C. x = 0 ou x = 2","option_d":"D. x = -2 ou x = 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un produit de facteurs est nul si l’un des facteurs est nul : x+1=0 → x=-1 ou x-3=0 → x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58223,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n’est pas définie en x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58224,"question":"Quelle est la solution de l’équation 4x² - 9 = 0 ?","option_a":"A. x = 3\/2 ou x = -3\/2","option_b":"B. x = 2 ou x = -2","option_c":"C. x = 1\/2 ou x = -1\/2","option_d":"D. x = 3 ou x = -3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez : 4x² = 9 → x² = 9\/4 → x = ±3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58225,"question":"L’inéquation -2x + 5 ≥ 1 a pour solution x ≤ 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez : -2x ≥ -4 → x ≤ 2 (en divisant par un nombre négatif, l’inégalité change de sens).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]