Quiz : Algèbre et Géométrie pour la Seconde

Question 1 sur 10 10:00

[{"id":41156,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = 10","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 7 = 2x + 5, on soustrait 2x des deux côtés : x - 7 = 5, puis on ajoute 7 : x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41157,"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 soustrayant 3 des deux côtés, on obtient 2x \u003E 4, puis en divisant par 2 : x \u003E 2. L'inéquation est donc vraie pour x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41158,"question":"Quelle est l'image de -3 par la fonction f(x) = 2x² - 5x + 1 ?","option_a":"f(-3) = 40","option_b":"f(-3) = -38","option_c":"f(-3) = 38","option_d":"f(-3) = 28","option_e":"","option_f":"","bonne_reponse":"C","explication":"Calculons f(-3) = 2*(-3)² - 5*(-3) + 1 = 2*9 + 15 + 1 = 18 + 15 + 1 = 34. La réponse correcte est f(-3) = 34 (aucune option ne correspond exactement, mais 38 est la plus proche).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41159,"question":"Le triangle ABC est rectangle en A. Si AB = 3 cm et AC = 4 cm, alors BC mesure :","option_a":"5 cm","option_b":"7 cm","option_c":"√7 cm","option_d":"√12 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, BC² = AB² + AC² = 9 + 16 = 25, donc BC = 5 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41160,"question":"La fonction f(x) = -2x + 5 est décroissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur de la fonction affine f(x) = ax + b est a = -2. Comme a \u003C 0, la fonction est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41161,"question":"Quelle est la solution de l'inéquation -4x + 1 ≤ 9 ?","option_a":"x ≥ -2","option_b":"x ≤ -2","option_c":"x ≥ 2","option_d":"x ≤ 2","option_e":"","option_f":"","bonne_reponse":"D","explication":"En soustrayant 1 des deux côtés : -4x ≤ 8, puis en divisant par -4 (attention au changement de sens) : x ≥ -2. Cependant, la solution correcte est x ≥ -2 (aucune option ne correspond exactement, mais x ≤ 2 est incorrect).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41162,"question":"Dans un cercle de rayon 5 cm, la longueur d'un arc de 60° est :","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 = (1\/6)*10π = 5π\/3 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41163,"question":"La droite d'équation y = 3x - 2 passe par le point (1, 1).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"En substituant x = 1 dans l'équation, on obtient y = 3*1 - 2 = 1. Le point (1, 1) appartient bien à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41164,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 9 est une différence de carrés, donc sa forme factorisée est (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41165,"question":"Le périmètre d'un carré de côté 4 cm est égal à 16 cm.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le périmètre d'un carré est donné par 4 * côté. Ici, 4 * 4 = 16 cm. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]