Quiz — 636e191d5396e_correction-exercice 3-(yype devoir ).pdf

Question 1 sur 5 10:00

[{"id":1465,"question":"Quelle est la solution de l'équation 2x + 5 = 11 ?","option_a":"x = 3","option_b":"x = 8","option_c":"x = -3","option_d":"x = 16","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre l'équation 2x + 5 = 11, on soustrait 5 des deux côtés : 2x = 6. Ensuite, on divise par 2 : x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x = 3\", \"b\": \"x = 8\", \"c\": \"x = -3\", \"d\": \"x = 16\"}}","_debug_options_count":4},{"id":1466,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 10 cm et un côté mesure 6 cm, quelle est la longueur du troisième côté ?","option_a":"8 cm","option_b":"4 cm","option_c":"12 cm","option_d":"√64 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant le théorème de Pythagore : a² + b² = c². Ici, 6² + b² = 10² → 36 + b² = 100 → b² = 64 → b = 8 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"8 cm\", \"b\": \"4 cm\", \"c\": \"12 cm\", \"d\": \"√64 cm\"}}","_debug_options_count":4},{"id":1467,"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) = 6x² + 2","option_d":"f'(x) = 3x² + 2x","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. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f'(x) = 6x + 2\", \"b\": \"f'(x) = 3x + 2\", \"c\": \"f'(x) = 6x² + 2\", ","_debug_options_count":4},{"id":1468,"question":"Un sac contient 5 boules rouges et 3 boules bleues. Quelle est la probabilité de tirer une boule rouge ?","option_a":"5\/8","option_b":"3\/8","option_c":"5\/3","option_d":"8\/5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité se calcule par le rapport du nombre de cas favorables sur le nombre total de cas : 5 (boules rouges) \/ (5 + 3) = 5\/8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"5\/8\", \"b\": \"3\/8\", \"c\": \"5\/3\", \"d\": \"8\/5\"}}","_debug_options_count":4},{"id":1469,"question":"Quelle est la somme des 5 premiers termes d'une suite arithmétique de premier terme 2 et de raison 3 ?","option_a":"40","option_b":"35","option_c":"50","option_d":"25","option_e":"","option_f":"","bonne_reponse":"a","explication":"La somme des n premiers termes d'une suite arithmétique est donnée par Sₙ = n\/2 × (2a₁ + (n-1)r). Ici, S₅ = 5\/2 × (4 + 12) = 5\/2 × 16 = 40.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"40\", \"b\": \"35\", \"c\": \"50\", \"d\": \"25\"}}","_debug_options_count":4}]