Quiz de révision : Algèbre et Fonctions — Seconde Maths

Question 1 sur 10 10:00

[{"id":50161,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12","option_c":"x = 2","option_d":"x = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résoudre l'équation : 3x - 5 = 7 → 3x = 12 → x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50162,"question":"La fonction f(x) = x² + 3x - 4 est une fonction affine.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction affine s'écrit f(x) = ax + b. Ici, f(x) = x² + 3x - 4 est un polynôme du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50163,"question":"Quelle est la forme canonique de la fonction f(x) = 2x² - 8x + 5 ?","option_a":"f(x) = 2(x - 2)² - 3","option_b":"f(x) = 2(x - 4)² + 5","option_c":"f(x) = 2(x - 1)² - 1","option_d":"f(x) = 2(x + 2)² - 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Forme canonique : f(x) = 2(x² - 4x) + 5 = 2[(x - 2)² - 4] + 5 = 2(x - 2)² - 8 + 5 = 2(x - 2)² - 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50164,"question":"Dans un triangle rectangle, le cosinus d'un angle est égal au rapport :","option_a":"Côté opposé \/ Hypoténuse","option_b":"Côté adjacent \/ Hypoténuse","option_c":"Côté opposé \/ Côté adjacent","option_d":"Hypoténuse \/ Côté adjacent","option_e":"","option_f":"","bonne_reponse":"B","explication":"Par définition, cos(θ) = côté adjacent \/ hypoténuse dans un triangle rectangle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50165,"question":"L'inéquation 2x + 3 \u003E 5 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Résoudre l'inéquation : 2x + 3 \u003E 5 → 2x \u003E 2 → x \u003E 1. La solution est x \u003E 1, donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50166,"question":"Quelle est la dérivée de la fonction f(x) = 4x³ - 2x² + x - 7 ?","option_a":"f'(x) = 12x² - 4x + 1","option_b":"f'(x) = 12x² - 4x - 7","option_c":"f'(x) = 4x² - 2x + 1","option_d":"f'(x) = 12x³ - 4x² + x","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dérivée terme à terme : f'(x) = 12x² - 4x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50167,"question":"Le théorème de Pythagore s'applique uniquement aux triangles rectangles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le théorème de Pythagore énonce que dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50168,"question":"Résoudre l'équation (x - 3)(2x + 5) = 0 :","option_a":"x = 3 ou x = -5\/2","option_b":"x = -3 ou x = 5\/2","option_c":"x = 3 ou x = 5\/2","option_d":"x = -3 ou x = -5\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un produit de facteurs est nul si et seulement si l'un des facteurs est nul : x - 3 = 0 ou 2x + 5 = 0 → x = 3 ou x = -5\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50169,"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":50170,"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 ∈ ]-∞ ; -2] ∪ [3 ; +∞[","option_d":"x ∈ [1 ; 6]","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résoudre l'inéquation : x² - 5x + 6 ≤ 0 → (x - 2)(x - 3) ≤ 0. Le produit est négatif ou nul entre les racines 2 et 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]