Quiz Mathématiques Seconde : Algèbre, Fonctions et Géométrie

Question 1 sur 10 10:00

[{"id":18918,"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 = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"On isole x en soustrayant 2x des deux côtés, puis en ajoutant 7 : 3x - 2x = 5 + 7 → x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18919,"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":18920,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 6x + 8 ?","option_a":"f(x) = (x - 3)² - 1","option_b":"f(x) = (x - 2)(x - 4)","option_c":"f(x) = x(x - 6) + 8","option_d":"f(x) = (x + 3)² - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique s'obtient par complétion du carré : f(x) = (x - 3)² - 9 + 8 = (x - 3)² - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18921,"question":"Si a et b sont deux nombres réels, quelle identité remarquable est correcte ?","option_a":"(a + b)² = a² + b²","option_b":"(a - b)² = a² - 2ab + b²","option_c":"(a + b)(a - b) = a² + b²","option_d":"(a + b)³ = a³ + b³","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'identité (a - b)² = a² - 2ab + b² est la seule correcte parmi les propositions.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18922,"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":18923,"question":"Quelle est la solution de l'inéquation 2x - 5 ≤ 7 ?","option_a":"x ≤ 6","option_b":"x ≥ 6","option_c":"x ≤ 1","option_d":"x ≥ 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"On ajoute 5 des deux côtés : 2x ≤ 12, puis on divise par 2 : x ≤ 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18924,"question":"Dans un triangle ABC rectangle en A, si AB = 3 cm et AC = 4 cm, quelle est la longueur de BC ?","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 → BC = 5 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18925,"question":"La fonction f(x) = x² est-elle toujours croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = x² est décroissante sur ]-∞, 0] et croissante sur [0, +∞[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18926,"question":"Quelle est la factorisation 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 : (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18927,"question":"Si deux droites sont parallèles, leurs coefficients directeurs sont-ils égaux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux droites parallèles ont des coefficients directeurs égaux (même pente).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]