Quiz : Maîtrisez les bases des mathématiques en 4ème secondaire

Question 1 sur 10 10:00

[{"id":49311,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -12","option_d":"x = 10","option_e":"","option_f":"","bonne_reponse":"A","explication":"On isole x : 3x - 2x = 5 + 7 → x = 12. Vérifiez en remplaçant x par 12 dans l'équation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49312,"question":"La fonction f(x) = x² - 4x + 3 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction est un polynôme du second degré avec un discriminant positif (Δ = 16 - 12 = 4 \u003E 0), donc elle s'annule en deux points et n'est pas toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49313,"question":"Quel est le résultat de √(49) + √(16) ?","option_a":"11","option_b":"13","option_c":"9","option_d":"15","option_e":"","option_f":"","bonne_reponse":"B","explication":"√(49) = 7 et √(16) = 4. Donc 7 + 4 = 11. Attention à ne pas confondre avec √(49 + 16).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49314,"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 le théorème de Pythagore : c² = a² + b², où c est l'hypoténuse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49315,"question":"Résolvez l'inéquation 2x - 5 \u003E 3x + 1.","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003C 6","option_d":"x \u003E 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"On isole x : 2x - 3x \u003E 1 + 5 → -x \u003E 6 → x \u003C -6 (en multipliant par -1, l'inégalité change de sens).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49316,"question":"La dérivée de f(x) = 3x² + 2x - 1 est f'(x) = 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -1 est 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49317,"question":"Calculez l'aire d'un triangle de base 8 cm et de hauteur 5 cm.","option_a":"20 cm²","option_b":"40 cm²","option_c":"13 cm²","option_d":"24 cm²","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire d'un triangle est (base × hauteur) \/ 2 = (8 × 5) \/ 2 = 20 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49318,"question":"La somme des angles d'un triangle est toujours égale à 180°.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une propriété fondamentale de la géométrie euclidienne.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49319,"question":"Résolvez le système d'équations : {2x + y = 5; x - y = 1}.","option_a":"x = 2, y = 1","option_b":"x = 1, y = 2","option_c":"x = 3, y = -1","option_d":"x = 0, y = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En additionnant les deux équations : 3x = 6 → x = 2. Puis y = 5 - 2x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49320,"question":"La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité d'un événement impossible est 0, et celle d'un événement certain est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]