Quiz — img536.pdf

Question 1 sur 5 10:00

[{"id":3316,"question":"Quelle est la valeur de sin(π\/6) + cos(π\/3) ?","option_a":"1","option_b":"√3\/2","option_c":"1\/2","option_d":"√2\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"sin(π\/6) = 1\/2 et cos(π\/3) = 1\/2. Donc sin(π\/6) + cos(π\/3) = 1\/2 + 1\/2 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"1\", \"b\": \"√3\/2\", \"c\": \"1\/2\", \"d\": \"√2\/2\"}}","_debug_options_count":4},{"id":3317,"question":"Soit f(x) = 2x² - 3x + 1. Quelle est la dérivée f'(x) ?","option_a":"4x - 3","option_b":"2x - 3","option_c":"4x² - 3x","option_d":"x² - 3x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme f(x) = ax² + bx + c est f'(x) = 2ax + b. Ici, a=2 et b=-3, donc f'(x) = 4x - 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\": \"4x - 3\", \"b\": \"2x - 3\", \"c\": \"4x² - 3x\", \"d\": \"x² - 3x + 1\"}}","_debug_options_count":4},{"id":3318,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 5 cm et un côté mesure 3 cm, quelle est la longueur du troisième côté ?","option_a":"4 cm","option_b":"√34 cm","option_c":"2 cm","option_d":"√16 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore : hypoténuse² = côté1² + côté2². Donc côté2 = √(5² - 3²) = √(25 - 9) = √16 = 4 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\": \"4 cm\", \"b\": \"√34 cm\", \"c\": \"2 cm\", \"d\": \"√16 cm\"}}","_debug_options_count":4},{"id":3319,"question":"Résolvez l'équation exponentielle : 2^(x+1) = 8.","option_a":"x = 2","option_b":"x = 1","option_c":"x = 3","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"2^(x+1) = 8 peut s'écrire 2^(x+1) = 2³. Donc x+1 = 3, soit x = 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\": \"x = 2\", \"b\": \"x = 1\", \"c\": \"x = 3\", \"d\": \"x = 0\"}}","_debug_options_count":4},{"id":3320,"question":"Quelle est la limite de la fonction f(x) = (3x² - 2x + 1)\/(x² + 1) quand x tend vers l'infini ?","option_a":"3","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour x tendant vers l'infini, les termes dominants sont 3x² dans le numérateur et x² dans le dénominateur. Donc la limite est 3x²\/x² = 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\": \"3\", \"b\": \"1\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4}]