Quiz Maths 9ème : Équations, Pythagore et Calcul Littéral

Question 1 sur 10 10:00

[{"id":76442,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 5\/3","option_d":"x = 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 5 = 10 → 3x = 15 → x = 5. L'équation est résolue en isolant x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76443,"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":76444,"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":"Utilisez 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":76445,"question":"Si AB = 5 cm, BC = 12 cm et AC = 13 cm, alors le triangle ABC est rectangle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vérifiez avec Pythagore : 5² + 12² = 25 + 144 = 169 = 13². Le triangle est rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76446,"question":"Quelle est la valeur de x dans l'équation 2(x + 3) = 4x - 2 ?","option_a":"x = 4","option_b":"x = 2","option_c":"x = 5","option_d":"x = 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"2x + 6 = 4x - 2 → 6 + 2 = 4x - 2x → 8 = 2x → x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76447,"question":"Le théorème de Thalès s'applique uniquement aux triangles isocèles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. Le théorème de Thalès s'applique à deux droites sécantes coupées par des parallèles, quel que soit le type de triangle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76448,"question":"Factorisez l'expression 4x² - 9.","option_a":"(2x - 3)(2x + 3)","option_b":"(4x - 9)(x + 1)","option_c":"(2x - 9)(2x + 1)","option_d":"(x - 3)(4x + 3)","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une identité remarquable : a² - b² = (a - b)(a + b). Ici, 4x² = (2x)² et 9 = 3².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76449,"question":"Dans un triangle rectangle, si les côtés de l'angle droit mesurent 6 cm et 8 cm, quelle est la longueur de l'hypoténuse ?","option_a":"10 cm","option_b":"14 cm","option_c":"12 cm","option_d":"8 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après Pythagore : hypoténuse² = 6² + 8² = 36 + 64 = 100 → hypoténuse = 10 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76450,"question":"L'expression 3x + 5y est-elle une expression littérale ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. Une expression littérale contient des lettres représentant des nombres inconnus.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76451,"question":"Résolvez l'inéquation 2x + 7 \u003E 15.","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E -4","option_d":"x \u003C -4","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 7 \u003E 15 → 2x \u003E 8 → x \u003E 4. L'inégalité reste inchangée car on divise par un nombre positif.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]