Quiz — exam-i-corrige-4.pdf

Question 1 sur 10 20:00

[{"id":10253,"question":"Quelle est la solution de l’équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L’équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3)=0, donc les solutions sont x=2 et 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 = 2 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4},{"id":10254,"question":"La dérivée de la fonction 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 est correct.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":10255,"question":"Quel est le volume d’un cube d’arête 4 cm ?","option_a":"16 cm³","option_b":"32 cm³","option_c":"64 cm³","option_d":"128 cm³","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le volume d’un cube est donné par V = arête³ = 4³ = 64 cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"16 cm³\", \"b\": \"32 cm³\", \"c\": \"64 cm³\", \"d\": \"128 cm³\"}}","_debug_options_count":4},{"id":10256,"question":"La probabilité d’obtenir un nombre pair en lançant un dé équilibré est 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un dé a 6 faces : 1, 2, 3, 4, 5, 6. Les nombres pairs sont 2, 4, 6, soit 3 cas favorables sur 6 possibles. Donc P(pair) = 3\/6 = 1\/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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":10257,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 1) lorsque x tend vers l’infini ?","option_a":"0","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"Pour x → ∞, on garde les termes de plus haut degré : f(x) ≈ 2x²\/x² = 2. Donc la limite est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"2\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":10258,"question":"L’inéquation 3x - 5 ≤ 7 a pour solution x ≤ 4.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 5 ≤ 7 ⇒ 3x ≤ 12 ⇒ x ≤ 4. La solution est donc correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":10259,"question":"Quelle est l’équation de la tangente à la courbe y = x² + 1 au point d’abscisse x = 1 ?","option_a":"y = 2x + 1","option_b":"y = 2x - 1","option_c":"y = x + 2","option_d":"y = 3x - 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"La tangente a pour équation y = f’(a)(x-a) + f(a). Ici, f’(x)=2x, f(1)=2, donc y = 2(x-1) + 2 = 2x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"y = 2x + 1\", \"b\": \"y = 2x - 1\", \"c\": \"y = x + 2\", \"d\": \"y = 3x - ","_debug_options_count":4},{"id":10260,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":10261,"question":"Quel est le résultat de l’intégrale ∫(3x² + 2x) dx ?","option_a":"x³ + x² + C","option_b":"x³ + x + C","option_c":"3x³ + x² + C","option_d":"x³ + 2x² + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L’intégrale de 3x² est x³, celle de 2x est x², donc ∫(3x² + 2x) dx = x³ + x² + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x³ + x² + C\", \"b\": \"x³ + x + C\", \"c\": \"3x³ + x² + C\", \"d\": \"","_debug_options_count":4},{"id":10262,"question":"La médiane d’une série statistique est toujours égale à la moyenne.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La médiane et la moyenne sont des indicateurs différents. La médiane est la valeur centrale, tandis que la moyenne est la somme des valeurs divisée par leur nombre. Elles ne sont égales que dans des cas particuliers.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]