Quiz — contrôle 2020 avec sol.pdf

Question 1 sur 10 20:00

[{"id":61417,"question":"Quelle est la solution du système d'équations suivant : { 2x + y = 5 ; x - y = 1 } ?","option_a":"A) (2,1)","option_b":"B) (1,2)","option_c":"C) (2,3)","option_d":"D) (3,1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En additionnant les deux équations, on obtient 3x = 6, donc x = 2. En remplaçant dans la deuxième équation, y = 1. La solution est donc (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\": \"A) (2,1)\", \"b\": \"B) (1,2)\", \"c\": \"C) (2,3)\", \"d\": \"D) (3,1)\"}}","_debug_options_count":4},{"id":61418,"question":"La fonction f(x) = 3x - 2 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b, ce qui est le cas ici avec a = 3 et b = -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":61419,"question":"Quelle est l'image de x = -1 par la fonction g(x) = x² + 2x - 3 ?","option_a":"A) -4","option_b":"B) -2","option_c":"C) 0","option_d":"D) 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"En remplaçant x par -1 dans g(x), on obtient (-1)² + 2*(-1) - 3 = 1 - 2 - 3 = -4. L'image est donc -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A) -4\", \"b\": \"B) -2\", \"c\": \"C) 0\", \"d\": \"D) 2\"}}","_debug_options_count":4},{"id":61420,"question":"Deux événements A et B sont indépendants si P(A ∩ B) = P(A) × P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est la définition de l'indépendance de deux événements en probabilités.","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":61421,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"A) x = 2 ou x = 3","option_b":"B) x = -2 ou x = -3","option_c":"C) x = 1 ou x = 6","option_d":"D) x = -1 ou x = 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En factorisant l'équation, on obtient (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\": \"A) x = 2 ou x = 3\", \"b\": \"B) x = -2 ou x = -3\", \"c\": \"C) x = 1 ou","_debug_options_count":4},{"id":61422,"question":"La représentation graphique d'une fonction affine est toujours une droite.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine est de la forme f(x) = ax + b, et sa représentation graphique est une droite.","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":61423,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"A) 1\/6","option_b":"B) 1\/3","option_c":"C) 1\/2","option_d":"D) 2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Il y a 3 nombres pairs (2,4,6) sur 6 faces possibles, donc la probabilité est 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\": \"c\", \"options\": {\"a\": \"A) 1\/6\", \"b\": \"B) 1\/3\", \"c\": \"C) 1\/2\", \"d\": \"D) 2\/3\"}}","_debug_options_count":4},{"id":61424,"question":"La fonction h(x) = 4 est-elle une fonction constante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction constante prend la même valeur pour tout x, ce qui est le cas de h(x) = 4.","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":61425,"question":"Quelle est la solution du système d'équations : { 3x - 2y = 7 ; x + y = 5 } ?","option_a":"A) (3,2)","option_b":"B) (2,3)","option_c":"C) (4,1)","option_d":"D) (1,4)","option_e":"","option_f":"","bonne_reponse":"b","explication":"En résolvant le système, on trouve x = 2 et y = 3. La solution est donc (2,3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A) (3,2)\", \"b\": \"B) (2,3)\", \"c\": \"C) (4,1)\", \"d\": \"D) (1,4)\"}}","_debug_options_count":4},{"id":61426,"question":"La fonction k(x) = x³ - 2x + 1 est-elle une fonction polynôme ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction polynôme est une somme de termes de la forme ax^n, ce qui est le cas de k(x).","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}]