Quiz : Équations, inéquations et fonctions — 4ème année secondaire

Question 1 sur 10 10:00

[{"id":13193,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 5\/3","option_d":"x = 15","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 5 = 10 ⇒ 3x = 15 ⇒ x = 5. La solution est donc x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13194,"question":"L'inéquation 2x + 3 \u003E 7 a pour solution x \u003E 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 3 \u003E 7 ⇒ 2x \u003E 4 ⇒ x \u003E 2. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13195,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 4x + 3 ?","option_a":"f(x) = (x - 2)² - 1","option_b":"f(x) = (x - 1)² + 1","option_c":"f(x) = (x + 2)² - 1","option_d":"f(x) = (x - 2)² + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"f(x) = x² - 4x + 3 = (x² - 4x + 4) - 1 = (x - 2)² - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13196,"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":13197,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 ≤ 0 ?","option_a":"x ∈ [2 ; 3]","option_b":"x ∈ ]-∞ ; 2] ∪ [3 ; +∞[","option_c":"x ∈ [0 ; 5]","option_d":"x ∈ {2, 3}","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 5x + 6 = (x - 2)(x - 3). Le produit est ≤ 0 pour x ∈ [2 ; 3].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13198,"question":"La fonction f(x) = √(x - 1) est définie pour x ≥ 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La racine carrée est définie pour x - 1 ≥ 0, soit x ≥ 1. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13199,"question":"Quelle est la solution de l'équation |x - 3| = 5 ?","option_a":"x = 8 ou x = -2","option_b":"x = 2 ou x = -8","option_c":"x = 3 ± 5","option_d":"x = 8","option_e":"","option_f":"","bonne_reponse":"A","explication":"|x - 3| = 5 ⇒ x - 3 = 5 ou x - 3 = -5 ⇒ x = 8 ou x = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13200,"question":"La fonction f(x) = x³ est une fonction paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Or (-x)³ = -x³ ≠ x³. La fonction est donc impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13201,"question":"Quelle est la solution de l'inéquation (x + 1)(x - 4) \u003E 0 ?","option_a":"x ∈ ]-∞ ; -1[ ∪ ]4 ; +∞[","option_b":"x ∈ [-1 ; 4]","option_c":"x ∈ ]-1 ; 4[","option_d":"x ∈ { -1, 4 }","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le produit (x + 1)(x - 4) est \u003E 0 lorsque x \u003C -1 ou x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13202,"question":"La fonction f(x) = 2x + 1 est une fonction affine.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine s'écrit f(x) = ax + b. Ici, f(x) = 2x + 1 est bien affine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]