Quiz Maths 4ème : Algèbre & Géométrie — Niveau Intermédiaire

Question 1 sur 10 10:00

[{"id":78872,"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 = 15","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour résoudre 3x - 5 = 10, on ajoute 5 des deux côtés (3x = 15), puis on divise par 3 (x = 5). La bonne réponse est donc x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78873,"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, une propriété fondamentale en géométrie des triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78874,"question":"Quelle est la dérivée de la fonction f(x) = 2x² + 3x - 1 ?","option_a":"f'(x) = 4x + 3","option_b":"f'(x) = 2x + 3","option_c":"f'(x) = 4x² + 3x","option_d":"f'(x) = 2x² + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (2x²)' = 4x, (3x)' = 3, et (-1)' = 0. Donc f'(x) = 4x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78875,"question":"Si un cercle a un rayon de 5 cm, quelle est son aire ?","option_a":"25π cm²","option_b":"10π cm²","option_c":"5π cm²","option_d":"50π cm²","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire d'un cercle se calcule avec la formule A = πr². Avec r = 5 cm, on obtient A = π × 5² = 25π cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78876,"question":"La fonction f(x) = x² est toujours croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = x² est décroissante sur ]-∞, 0] et croissante sur [0, +∞[. Elle n'est donc pas toujours croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78877,"question":"Quelle est la solution de 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 résolvant 2x + 7 \u003E 3x - 1, on soustrait 2x (x + 7 \u003E -1), puis on soustrait 7 (x \u003E -8). La solution est donc x \u003E -8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78878,"question":"Dans un parallélogramme, les diagonales se coupent en leur milieu.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une propriété fondamentale des parallélogrammes : leurs diagonales se bisectent mutuellement.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78879,"question":"Quelle est la valeur de sin(30°) ?","option_a":"1\/2","option_b":"√2\/2","option_c":"√3\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans un triangle rectangle isocèle, sin(30°) = côté opposé \/ hypoténuse = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78880,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78881,"question":"Quelle est la solution de l'équation x² - 4x + 4 = 0 ?","option_a":"x = 2","option_b":"x = -2","option_c":"x = 4","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 4x + 4 = 0 peut s'écrire (x - 2)² = 0. La solution est donc x = 2 (racine double).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]