Quiz : Algèbre et Géométrie — 3ème Année Secondaire

Question 1 sur 10 10:00

[{"id":67752,"question":"Quelle est la solution de l'équation 2x² - 8x + 6 = 0 ?","option_a":"x = 1 ou x = 3","option_b":"x = -1 ou x = -3","option_c":"x = 2 ou x = 4","option_d":"x = 0 ou x = 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'équation en utilisant la formule du discriminant : Δ = b² - 4ac. Ici, Δ = 64 - 48 = 16, donc x = (8 ± 4)\/4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67753,"question":"Le théorème de Pythagore 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 Pythagore ne s'applique qu'aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67754,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x - 5","option_d":"f'(x) = 3x² + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67755,"question":"Un triangle a des angles de 30°, 60° et 90°. Quelle est la longueur de l'hypoténuse si le côté opposé à 30° mesure 5 cm ?","option_a":"10 cm","option_b":"5√3 cm","option_c":"5 cm","option_d":"10√3 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans un triangle 30-60-90, l'hypoténuse est le double du côté opposé à 30°. Donc 5 × 2 = 10 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67756,"question":"L'inéquation 3x - 7 \u003E 2x + 5 a pour solution :","option_a":"x \u003E 12","option_b":"x \u003C 12","option_c":"x \u003E -12","option_d":"x \u003C -12","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'inéquation : 3x - 2x \u003E 5 + 7 → x \u003E 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67757,"question":"La fonction f(x) = -2x + 4 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le coefficient directeur est négatif (-2), donc la fonction est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67758,"question":"Quel est le volume d'un cylindre de rayon 3 cm et de hauteur 5 cm ? (π ≈ 3,14)","option_a":"141,3 cm³","option_b":"47,1 cm³","option_c":"94,2 cm³","option_d":"282,6 cm³","option_e":"","option_f":"","bonne_reponse":"A","explication":"Volume = π × r² × h = 3,14 × 9 × 5 ≈ 141,3 cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67759,"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 plane.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67760,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 ≤ 0 ?","option_a":"x ∈ [2, 3]","option_b":"x ∈ ]-∞, 2] ∪ [3, +∞[","option_c":"x ∈ [0, 5]","option_d":"x ∈ ]-∞, 0] ∪ [5, +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'inéquation en trouvant les racines (x=2 et x=3) et en testant les intervalles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67761,"question":"Un parallélogramme a des côtés de 6 cm et 8 cm. Quelle est son aire si la hauteur relative au côté de 6 cm mesure 4 cm ?","option_a":"24 cm²","option_b":"32 cm²","option_c":"48 cm²","option_d":"192 cm²","option_e":"","option_f":"","bonne_reponse":"A","explication":"Aire = base × hauteur = 6 × 4 = 24 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]