Quiz Maths — 4ème Année Secondaire : Algèbre & Fonctions

Question 1 sur 10 10:00

[{"id":53621,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 2","option_c":"x = 12","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 5 = 7, on ajoute 5 des deux côtés : 3x = 12, puis on divise par 3 : x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53622,"question":"La fonction f(x) = 2x + 3 est-elle 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 sous la forme f(x) = ax + b, ce qui est le cas ici avec a = 2 et b = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53623,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 1 ?","option_a":"f'(x) = 2x + 3","option_b":"f'(x) = x² + 3","option_c":"f'(x) = 2x - 1","option_d":"f'(x) = x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -1 est 0. Donc f'(x) = 2x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53624,"question":"L'inéquation 2x + 1 \u003E 5 a pour solution :","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E 3","option_d":"x \u003C 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 1 des deux côtés, on obtient 2x \u003E 4, puis en divisant par 2 : x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53625,"question":"La fonction f(x) = 1\/x est-elle 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":53626,"question":"Quelle est la solution de l'inéquation -3x + 2 ≤ 8 ?","option_a":"x ≥ -2","option_b":"x ≤ -2","option_c":"x ≥ 2","option_d":"x ≤ 2","option_e":"","option_f":"","bonne_reponse":"B","explication":"En soustrayant 2 des deux côtés, on obtient -3x ≤ 6. En divisant par -3 (et inversant le sens de l'inégalité), on obtient x ≥ -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53627,"question":"La fonction f(x) = x³ est-elle 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). Ici, f(-x) = (-x)³ = -x³ ≠ x³ = f(x). Donc elle n'est pas paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53628,"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 = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En factorisant, on obtient (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":53629,"question":"La fonction f(x) = √x est-elle définie pour x = -4 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La racine carrée d'un nombre négatif n'est pas définie dans les réels. Donc f(-4) n'existe pas.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53630,"question":"Quelle est la solution de l'équation 4(x - 1) = 2x + 6 ?","option_a":"x = 5","option_b":"x = 3","option_c":"x = 7","option_d":"x = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant, on obtient 4x - 4 = 2x + 6. En soustrayant 2x des deux côtés, on a 2x - 4 = 6. Puis en ajoutant 4 : 2x = 10, donc x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]