Quiz Mathématiques : Équations et Géométrie pour la 1ère Année

Question 1 sur 10 10:00

[{"id":74442,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12\/3","option_c":"x = -4","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 5 = 7 ⇒ 3x = 12 ⇒ x = 4. La solution est donc x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74443,"question":"Dans un repère orthonormé, le milieu d'un segment AB avec A(2;3) et B(4;7) a pour coordonnées :","option_a":"(3;5)","option_b":"(6;10)","option_c":"(1;2)","option_d":"(5;3)","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le milieu M a pour coordonnées ((xA+xB)\/2 ; (yA+yB)\/2) = ((2+4)\/2 ; (3+7)\/2) = (3;5).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74444,"question":"L'inéquation 2x + 3 \u003E 5 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 3 \u003E 5 ⇒ 2x \u003E 2 ⇒ x \u003E 1. La solution est donc x \u003E 1, ce qui est vrai.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74445,"question":"Le théorème de Pythagore s'applique uniquement aux triangles rectangles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le théorème de Pythagore énonce que dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés. Il ne s'applique donc qu'aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74446,"question":"Quelle est la distance entre les points A(-1;2) et B(3;-4) dans un repère orthonormé ?","option_a":"√52","option_b":"10","option_c":"√26","option_d":"5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La distance AB = √[(3-(-1))² + (-4-2)²] = √[16 + 36] = √52.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74447,"question":"L'équation x² = 9 a pour solutions :","option_a":"x = 3","option_b":"x = -3","option_c":"x = 3 ou x = -3","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"C","explication":"x² = 9 ⇒ x = 3 ou x = -3. Les deux solutions sont valides.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74448,"question":"Dans un triangle ABC, si AB = AC, alors le triangle est isocèle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un triangle est isocèle si deux de ses côtés sont égaux. Si AB = AC, alors le triangle ABC est bien isocèle en A.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74449,"question":"Quelle est la solution de l'inéquation -2x + 1 ≤ 5 ?","option_a":"x ≥ -2","option_b":"x ≤ -2","option_c":"x ≥ 2","option_d":"x ≤ 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"-2x + 1 ≤ 5 ⇒ -2x ≤ 4 ⇒ x ≥ -2 (en divisant par un nombre négatif, le sens de l'inégalité change).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74450,"question":"Le point M(1;1) appartient-il à la droite d'équation y = 2x - 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour x = 1, y = 2(1) - 1 = 1. Le point M(1;1) vérifie bien l'équation de la droite, donc il appartient à cette droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74451,"question":"Quelle est la valeur de x dans l'équation 5(x + 2) = 3x + 10 ?","option_a":"x = 0","option_b":"x = 1","option_c":"x = -1","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"5(x + 2) = 3x + 10 ⇒ 5x + 10 = 3x + 10 ⇒ 2x = 0 ⇒ x = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]