Quiz — 654cf4d514947_énoncé_Série 18 (3).pdf

Question 1 sur 10 20:00

[{"id":53267,"question":"Quelle est la solution de l'équation 2x + 5 = 11 ?","option_a":"x = 3","option_b":"x = 4","option_c":"x = 5","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En soustrayant 5 des deux côtés, on obtient 2x = 6. En divisant par 2, on trouve 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 = 4\", \"c\": \"x = 5\", \"d\": \"x = 6\"}}","_debug_options_count":4},{"id":53268,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":53269,"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 + 2x","option_d":"f'(x) = 5x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 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 + 2x\",","_debug_options_count":4},{"id":53270,"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":"16 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant le théorème de Pythagore : 6² + x² = 10² → 36 + x² = 100 → x² = 64 → x = 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\": \"16 cm\"}}","_debug_options_count":4},{"id":53271,"question":"La fonction f(x) = x² est-elle toujours croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = x² est décroissante pour x \u003C 0 et croissante pour x \u003E 0.","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":53272,"question":"Quelle est la solution de l'inéquation 3x - 7 ≤ 2x + 5 ?","option_a":"x ≤ 12","option_b":"x ≥ 12","option_c":"x ≤ -12","option_d":"x ≥ -12","option_e":"","option_f":"","bonne_reponse":"a","explication":"En soustrayant 2x des deux côtés, on obtient x - 7 ≤ 5. En ajoutant 7, on trouve 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 ≥ 12\", \"c\": \"x ≤ -12\", \"d\": \"x ≥ -12\"}}","_debug_options_count":4},{"id":53273,"question":"Dans un cercle de rayon 5 cm, quelle est la longueur d'un arc correspondant à un angle de 60° ?","option_a":"5π\/3 cm","option_b":"10π\/3 cm","option_c":"5π cm","option_d":"10π cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"La longueur de l'arc est donnée par (θ\/360) × 2πr = (60\/360) × 2π × 5 = (1\/6) × 10π = 5π\/3 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\": \"5π\/3 cm\", \"b\": \"10π\/3 cm\", \"c\": \"5π cm\", \"d\": \"10π cm\"}}","_debug_options_count":4},{"id":53274,"question":"La probabilité d'un événement impossible est-elle égale à 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, la probabilité d'un événement impossible est 0.","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":53275,"question":"Quelle est la solution du système d'équations suivant : { 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, on obtient 3x = 6 → x = 2. En remplaçant dans la deuxième équation, on trouve 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\":","_debug_options_count":4},{"id":53276,"question":"La fonction f(x) = 1\/x est-elle 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 pour 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}]