Quiz Mathématiques Bac : Algèbre, Fonctions et Géométrie

Question 1 sur 10 10:00

[{"id":9463,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -2","option_d":"x = 7","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x, on obtient 3x - 2x = 5 + 7 → x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9464,"question":"La fonction f(x) = 2x² - 3x + 1 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 est de la forme f(x) = ax + b. Ici, le terme x² indique qu'il s'agit d'une fonction du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9465,"question":"Quel est le coefficient directeur de la droite d'équation y = -4x + 7 ?","option_a":"-4","option_b":"7","option_c":"4","option_d":"-7","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans l'équation y = ax + b, 'a' représente le coefficient directeur. Ici, a = -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9466,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés. Ce théorème s'appelle :","option_a":"Théorème de Thalès","option_b":"Théorème de Pythagore","option_c":"Théorème de Gauss","option_d":"Théorème de Bézout","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Pythagore énonce que dans un triangle rectangle, c² = a² + b² où c est l'hypoténuse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9467,"question":"Si sin(θ) = 0.5, alors θ mesure environ :","option_a":"30°","option_b":"45°","option_c":"60°","option_d":"90°","option_e":"","option_f":"","bonne_reponse":"A","explication":"sin(30°) = 0.5. C'est une valeur trigonométrique fondamentale à connaître.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9468,"question":"L'inéquation 2x + 3 \u003E 7 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x \u003E 4 → x \u003E 2. L'inégalité est donc vraie pour x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9469,"question":"Quelle est l'image de 3 par la fonction f(x) = x² - 2x + 1 ?","option_a":"4","option_b":"6","option_c":"8","option_d":"10","option_e":"","option_f":"","bonne_reponse":"B","explication":"f(3) = 3² - 2*3 + 1 = 9 - 6 + 1 = 4. L'image est donc 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9470,"question":"Dans un cercle de rayon 5 cm, quelle est la longueur d'un arc correspondant à un angle au centre de 60° ?","option_a":"5π\/3 cm","option_b":"5π cm","option_c":"10π\/3 cm","option_d":"π\/3 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"La longueur d'un arc est donnée par (θ\/360) * 2πr. Ici, (60\/360)*2π*5 = 5π\/3 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9471,"question":"La dérivée de la fonction f(x) = 3x³ - 2x² + x est f'(x) = 9x² - 4x + 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En dérivant terme à terme : f'(x) = 9x² - 4x + 1 est correct.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9472,"question":"Quel est le PGCD de 48 et 60 ?","option_a":"6","option_b":"12","option_c":"16","option_d":"24","option_e":"","option_f":"","bonne_reponse":"B","explication":"Les diviseurs de 48 sont 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Ceux de 60 sont 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Le PGCD est 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]