Quiz interactif : Algèbre et géométrie en Seconde

Question 1 sur 10 10:00

[{"id":75702,"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":"Pour résoudre 3x - 5 = 10, on ajoute 5 des deux côtés : 3x = 15, puis on divise par 3 : x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75703,"question":"Dans un triangle ABC, si AB = 5 cm, BC = 12 cm et AC = 13 cm, alors ce triangle est rectangle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant le théorème de Pythagore : 5² + 12² = 25 + 144 = 169 = 13². Le triangle est donc rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75704,"question":"La fonction f(x) = 2x + 3 est une fonction affine. Quelle est sa pente ?","option_a":"2","option_b":"3","option_c":"0","option_d":"-2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine s'écrit f(x) = ax + b, où a est la pente. Ici, a = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75705,"question":"Quelle est la solution de l'inéquation 2x + 7 \u003E 11 ?","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E -2","option_d":"x \u003C -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 2x + 7 \u003E 11, on soustrait 7 : 2x \u003E 4, puis on divise par 2 : x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75706,"question":"Le centre de symétrie d'un parallélogramme est le point d'intersection de ses diagonales.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, le centre de symétrie d'un parallélogramme est le point d'intersection de ses diagonales.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75707,"question":"Quelle est l'image de -3 par la fonction f(x) = -4x + 1 ?","option_a":"13","option_b":"-11","option_c":"11","option_d":"-13","option_e":"","option_f":"","bonne_reponse":"B","explication":"En remplaçant x par -3 : f(-3) = -4*(-3) + 1 = 12 + 1 = 13. L'image est donc 13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75708,"question":"Dans un repère orthonormé, la distance entre les points A(1; 2) et B(4; 6) est :","option_a":"5","option_b":"√25","option_c":"√(3² + 4²)","option_d":"Toutes les réponses sont correctes","option_e":"","option_f":"","bonne_reponse":"D","explication":"La distance est calculée par √[(4-1)² + (6-2)²] = √(9 + 16) = √25 = 5. Toutes les réponses sont donc correctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75709,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant est bien Δ = b² - 4ac, formule fondamentale pour résoudre les équations du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75710,"question":"Quelle est la solution de l'équation x² - 6x + 9 = 0 ?","option_a":"x = 3","option_b":"x = -3","option_c":"x = 9","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 6x + 9 = 0 peut s'écrire (x - 3)² = 0, donc x = 3 est la solution double.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75711,"question":"Dans un cercle de centre O et de rayon 5 cm, la longueur d'un arc de 60° est :","option_a":"5π\/3 cm","option_b":"5π cm","option_c":"π\/3 cm","option_d":"10π\/3 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"La longueur d'un arc est donnée par (θ\/360) * 2πr, soit (60\/360)*2π*5 = (1\/6)*10π = 5π\/3 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]