Maths 1ère année : Équations et Géométrie — Quiz d'évaluation

Question 1 sur 10 10:00

[{"id":61177,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 2","option_b":"x = 12","option_c":"x = -2","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"B","explication":"En soustrayant 2x des deux côtés et en ajoutant 5, on obtient x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61178,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est l'énoncé du théorème de Pythagore, valable uniquement pour les triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61179,"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":"Il s'agit d'une différence de carrés : a² - b² = (a - b)(a + b).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61180,"question":"Le théorème de Thalès 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 Thalès nécessite des droites parallèles et ne s'applique qu'aux triangles en configuration de Thalès.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61181,"question":"Résoudre l'inéquation 2x + 3 ≤ 7.","option_a":"x ≤ 2","option_b":"x ≥ 2","option_c":"x ≤ -2","option_d":"x ≥ -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 3 puis en divisant par 2, on obtient x ≤ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61182,"question":"Quelle est la nature du triangle dont les côtés mesurent 5 cm, 12 cm et 13 cm ?","option_a":"Acute","option_b":"Rectangle","option_c":"Obtus","option_d":"Isocèle","option_e":"","option_f":"","bonne_reponse":"B","explication":"5² + 12² = 13², donc le triangle est rectangle d'après le théorème de Pythagore.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61183,"question":"La factorisation de 4x² - 25 est (2x - 5)(2x + 5).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une différence de carrés : 4x² - 25 = (2x)² - 5² = (2x - 5)(2x + 5).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61184,"question":"Quelle est la solution de l'équation (x - 4)(x + 2) = 0 ?","option_a":"x = 4 ou x = -2","option_b":"x = -4 ou x = 2","option_c":"x = 4 ou x = 2","option_d":"x = -4 ou x = -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un produit de facteurs est nul si l'un des facteurs est nul : x - 4 = 0 ou x + 2 = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61185,"question":"Le théorème de Pythagore permet de calculer la longueur d'un côté d'un triangle quelconque.","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":61186,"question":"Quelle est la valeur de x dans l'équation 5(x + 1) = 3x + 15 ?","option_a":"x = 2","option_b":"x = 5","option_c":"x = -5","option_d":"x = 10","option_e":"","option_f":"","bonne_reponse":"C","explication":"En développant et simplifiant, on obtient 5x + 5 = 3x + 15 → 2x = 10 → x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]