Quiz — Exam 2021-2022.pdf

Question 1 sur 10 20:00

[{"id":41865,"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":"Les solutions de l'équation x² - 5x + 6 = 0 s'obtiennent en factorisant : (x - 2)(x - 3) = 0, donc x = 2 ou 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":41866,"question":"La fonction f(x) = 2x + 3 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = 2x + 3 est une fonction affine de coefficient directeur 2, donc elle est strictement croissante.","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":41867,"question":"Quel est le vecteur directeur de la droite d'équation y = -3x + 2 ?","option_a":"Vecteur (1, -3)","option_b":"Vecteur (-3, 1)","option_c":"Vecteur (2, -3)","option_d":"Vecteur (3, -1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le vecteur directeur d'une droite d'équation y = mx + p est (1, m). Ici, m = -3, donc le vecteur directeur est (1, -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\": \"Vecteur (1, -3)\", \"b\": \"Vecteur (-3, 1)\", \"c\": \"Vecteur (2, -3)\",","_debug_options_count":4},{"id":41868,"question":"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, tandis que celle 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},{"id":41869,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + x ?","option_a":"f'(x) = 3x² - 4x + 1","option_b":"f'(x) = 3x² - 2x + 1","option_c":"f'(x) = x² - 4x + 1","option_d":"f'(x) = 3x - 4x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = x³ - 2x² + x est f'(x) = 3x² - 4x + 1, obtenue en appliquant les règles de dérivation.","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) = 3x² - 4x + 1\", \"b\": \"f'(x) = 3x² - 2x + 1\", \"c\": \"f'(x)","_debug_options_count":4},{"id":41870,"question":"Un angle de 120° est-il un angle aigu ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un angle aigu est un angle dont la mesure est strictement inférieure à 90°. 120° est donc un angle obtus.","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":41871,"question":"Quelle est la médiane d'une série statistique dont les valeurs sont 5, 7, 8, 10, 12 ?","option_a":"8","option_b":"7","option_c":"9","option_d":"10","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une série de 5 valeurs, la médiane est la 3ème valeur lorsque les données sont ordonnées : 5, 7, 8, 10, 12. La médiane est donc 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\": \"8\", \"b\": \"7\", \"c\": \"9\", \"d\": \"10\"}}","_debug_options_count":4},{"id":41872,"question":"La somme des angles d'un triangle est-elle toujours égale à 180° ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans un triangle, la somme des mesures des trois angles est toujours égale à 180°, que ce soit un triangle rectangle, isocèle ou quelconque.","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":41873,"question":"Quelle est la solution de l'inéquation 3x - 5 \u003E 1 ?","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E -2","option_d":"x \u003C -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvons l'inéquation : 3x - 5 \u003E 1 → 3x \u003E 6 → x \u003E 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 \u003E 2\", \"b\": \"x \u003C 2\", \"c\": \"x \u003E -2\", \"d\": \"x \u003C -2\"}}","_debug_options_count":4},{"id":41874,"question":"Un vecteur de norme 5 peut-il avoir des coordonnées (3, 4) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La norme d'un vecteur (a, b) est calculée par √(a² + b²). Ici, √(3² + 4²) = √(9 + 16) = √25 = 5, donc le vecteur (3, 4) a bien une norme de 5.","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}]