Quiz — correction ex(1--3) S33 mr arbii.pdf

Question 1 sur 10 20:00

[{"id":2520,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -12","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 7 = 2x + 5, soustrayez 2x des deux côtés : x - 7 = 5, puis ajoutez 7 : x = 12.","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 = 12\", \"b\": \"x = 2\", \"c\": \"x = -12\", \"d\": \"x = 5\"}}","_debug_options_count":4},{"id":2521,"question":"Vrai ou Faux : La fonction f(x) = 2x² + 3x - 5 est une fonction affine.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction affine est de la forme f(x) = ax + b. Ici, f(x) = 2x² + 3x - 5 est une fonction du second degré (polynôme de degré 2).","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":2522,"question":"Quelle est la probabilité de tirer un as dans un jeu de 52 cartes ?","option_a":"1\/13","option_b":"1\/52","option_c":"4\/52","option_d":"13\/52","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un jeu de 52 cartes contient 4 as. La probabilité est donc 4\/52, soit 1\/13 après simplification.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\/13\", \"b\": \"1\/52\", \"c\": \"4\/52\", \"d\": \"13\/52\"}}","_debug_options_count":4},{"id":2523,"question":"Vrai ou Faux : 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 : dans un triangle rectangle, l'hypoténuse au carré est égale à la somme des carrés des deux autres côtés.","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":2524,"question":"Quelle est la dérivée de la fonction f(x) = 4x³ - 2x² + x - 7 ?","option_a":"f'(x) = 12x² - 4x + 1","option_b":"f'(x) = 12x² - 4x","option_c":"f'(x) = 4x² - 2x + 1","option_d":"f'(x) = 12x³ - 4x² + x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : (4x³)' = 12x², (-2x²)' = -4x, (x)' = 1, (-7)' = 0. Donc f'(x) = 12x² - 4x + 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\": \"f'(x) = 12x² - 4x + 1\", \"b\": \"f'(x) = 12x² - 4x\", \"c\": \"f'(x) =","_debug_options_count":4},{"id":2525,"question":"Quelle est la médiane d'un jeu de données : 5, 7, 8, 10, 12 ?","option_a":"7","option_b":"8","option_c":"10","option_d":"12","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour trouver la médiane, rangez les données par ordre croissant : 5, 7, 8, 10, 12. La médiane est la valeur centrale, ici 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"7\", \"b\": \"8\", \"c\": \"10\", \"d\": \"12\"}}","_debug_options_count":4},{"id":2526,"question":"Vrai ou Faux : Une fonction linéaire est toujours croissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction linéaire f(x) = ax + b est croissante si a \u003E 0, décroissante si a \u003C 0, et constante si a = 0. Elle n'est donc pas toujours croissante.","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":2527,"question":"Quelle est la solution du système d'équations : { 2x + y = 5 ; x - y = 1 } ?","option_a":"x = 2, y = 1","option_b":"x = 1, y = 3","option_c":"x = 3, y = -1","option_d":"x = 0, y = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"En additionnant les deux équations : 3x = 6 → x = 2. En remplaçant x dans la deuxième équation : 2 - y = 1 → y = 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\": \"x = 2, y = 1\", \"b\": \"x = 1, y = 3\", \"c\": \"x = 3, y = -1\", \"d\": \"x","_debug_options_count":4},{"id":2528,"question":"Quelle est l'aire d'un cercle de rayon 3 cm ? (π ≈ 3,14)","option_a":"9π cm²","option_b":"6π cm²","option_c":"18π cm²","option_d":"3π cm²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'aire d'un cercle est donnée par la formule A = πr². Avec r = 3 cm, A = π × 3² = 9π cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"9π cm²\", \"b\": \"6π cm²\", \"c\": \"18π cm²\", \"d\": \"3π cm²\"}}","_debug_options_count":4},{"id":2529,"question":"Vrai ou Faux : La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'un événement impossible est égale à 0. La probabilité d'un événement certain est égale à 1.","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}]