Maths 3ème année secondaire : Algèbre, Géométrie et Probabilités

Question 1 sur 10 10:00

[{"id":20848,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12","option_c":"x = -4","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":20849,"question":"Le théorème de Pythagore s'applique-t-il à tous les triangles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Pythagore ne s'applique qu'aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20850,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 6x + 10 ?","option_a":"f(x) = (x - 3)² + 1","option_b":"f(x) = (x - 2)² + 6","option_c":"f(x) = (x + 3)² - 1","option_d":"f(x) = (x - 1)² + 9","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique est obtenue en complétant le carré : f(x) = (x - 3)² + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20851,"question":"Si on lance un dé équilibré, quelle est la probabilité d'obtenir un nombre pair ?","option_a":"1\/6","option_b":"1\/2","option_c":"1\/3","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20852,"question":"Dans un triangle ABC, si AB = 5 cm, BC = 12 cm et AC = 13 cm, alors le triangle est rectangle en B.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"On vérifie avec le théorème de Pythagore : 5² + 12² = 25 + 144 = 169 = 13², donc le triangle est rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20853,"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","option_c":"f'(x) = 4x² - 2x + 1","option_d":"f'(x) = 12x³ - 4x² + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée est obtenue en appliquant les règles de dérivation : f'(x) = 12x² - 4x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20854,"question":"Un sac contient 4 boules rouges et 6 boules bleues. On tire une boule au hasard. Quelle est la probabilité de tirer une boule rouge ?","option_a":"2\/5","option_b":"3\/5","option_c":"1\/4","option_d":"1\/10","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 4 boules rouges sur un total de 10 boules, donc la probabilité est 4\/10 = 2\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20855,"question":"La fonction f(x) = 2x + 3 est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction affine f(x) = 2x + 3 a un coefficient directeur positif (2), donc elle est croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20856,"question":"Quelle est la solution de l'inéquation 2x + 5 \u003E 11 ?","option_a":"x \u003E 3","option_b":"x \u003E -3","option_c":"x \u003C 3","option_d":"x \u003C -3","option_e":"","option_f":"","bonne_reponse":"A","explication":"On soustrait 5 des deux côtés : 2x \u003E 6, puis on divise par 2 : x \u003E 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20857,"question":"Dans un repère orthonormé, quelle est la distance entre les points A(2, 3) et B(5, 7) ?","option_a":"5","option_b":"√(13)","option_c":"√(25)","option_d":"7","option_e":"","option_f":"","bonne_reponse":"B","explication":"La distance est calculée avec la formule √[(5-2)² + (7-3)²] = √(9 + 16) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]