Mathématiques 1ère A.S : Évaluation des compétences du 1er trimestre

Question 1 sur 10 10:00

[{"id":66552,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 15","option_d":"x = 5\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 5 = 10, on ajoute d'abord 5 aux deux côtés : 3x = 15. Ensuite, on divise par 3 : x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66553,"question":"La somme des angles d'un triangle est toujours égale à 360°. Vrai ou Faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La somme des angles d'un triangle est égale à 180°, pas 360°. C'est une propriété fondamentale de la géométrie plane.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66554,"question":"Développez l'expression (2x + 3)(x - 4).","option_a":"2x² - 5x - 12","option_b":"2x² - 8x + 3x - 12","option_c":"2x² - 5x + 12","option_d":"2x² + 3x - 12","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la distributivité : (2x)(x) + (2x)(-4) + (3)(x) + (3)(-4) = 2x² - 8x + 3x - 12 = 2x² - 5x - 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66555,"question":"Quel est le périmètre d'un rectangle de longueur 8 cm et de largeur 5 cm ?","option_a":"26 cm","option_b":"40 cm","option_c":"13 cm","option_d":"16 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le périmètre d'un rectangle se calcule par la formule P = 2 × (longueur + largeur). Ici, P = 2 × (8 + 5) = 26 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66556,"question":"Si a = 4 et b = -2, quelle est la valeur de a² - b² ?","option_a":"12","option_b":"20","option_c":"16","option_d":"10","option_e":"","option_f":"","bonne_reponse":"B","explication":"a² - b² = 4² - (-2)² = 16 - 4 = 12. Attention, (-2)² = 4, pas -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66557,"question":"Le théorème de Pythagore s'applique uniquement aux triangles rectangles. Vrai ou Faux ?","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":66558,"question":"Résolvez l'inéquation 2x + 7 \u003E 3x - 1.","option_a":"x \u003C 8","option_b":"x \u003E 8","option_c":"x \u003C -8","option_d":"x \u003E -8","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 2x des deux côtés : 7 \u003E x - 1. Ensuite, on ajoute 1 : 8 \u003E x, soit x \u003C 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66559,"question":"Quelle est la moyenne de la série : 4, 6, 8, 10 ?","option_a":"7","option_b":"7,5","option_c":"8","option_d":"6,5","option_e":"","option_f":"","bonne_reponse":"B","explication":"La moyenne se calcule par (4 + 6 + 8 + 10) \/ 4 = 28 \/ 4 = 7,5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66560,"question":"La formule de l'aire d'un cercle est πr². Vrai ou Faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule de l'aire d'un cercle est bien π × rayon², où r est le rayon du cercle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66561,"question":"Quel est le résultat de 5 × (3 + 2) - 4 ?","option_a":"21","option_b":"11","option_c":"25","option_d":"9","option_e":"","option_f":"","bonne_reponse":"A","explication":"En respectant les priorités opératoires : 5 × (5) - 4 = 25 - 4 = 21.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]