Quiz — Lycée Pilote Bizerte - Test de controle 2.pdf

Question 1 sur 10 20:00

[{"id":31850,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -12","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En isolant x, on obtient 3x - 2x = 7 + 5, soit 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 = -2\"}}","_debug_options_count":4},{"id":31851,"question":"Dans un repère orthonormé, le milieu du segment [AB] avec A(2 ; 3) et B(-4 ; 1) a pour coordonnées :","option_a":"(-1 ; 2)","option_b":"(-2 ; 4)","option_c":"(3 ; -1)","option_d":"(-3 ; -1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le milieu M a pour coordonnées ((2 + (-4))\/2 ; (3 + 1)\/2) = (-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\": \"(-1 ; 2)\", \"b\": \"(-2 ; 4)\", \"c\": \"(3 ; -1)\", \"d\": \"(-3 ; -1)\"}}","_debug_options_count":4},{"id":31852,"question":"L'inéquation 2x + 3 \u003E 7 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La solution est x \u003E 2, donc l'affirmation est fausse.","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":31853,"question":"Quelle est la distance entre les points A(1 ; 2) et B(4 ; 6) dans un repère orthonormé ?","option_a":"5","option_b":"√13","option_c":"7","option_d":"√10","option_e":"","option_f":"","bonne_reponse":"b","explication":"La distance AB = √[(4-1)² + (6-2)²] = √(9 + 16) = √25 = 5. La réponse correcte est 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"5\", \"b\": \"√13\", \"c\": \"7\", \"d\": \"√10\"}}","_debug_options_count":4},{"id":31854,"question":"La fonction f(x) = 2x + 1 est 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.","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":31855,"question":"Résoudre l'inéquation -3x + 4 ≤ 10 :","option_a":"x ≥ -2","option_b":"x ≤ -2","option_c":"x ≥ 2","option_d":"x ≤ 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"En isolant x, on obtient -3x ≤ 6, soit x ≥ -2 (car division par un nombre négatif inverse le sens de l'inégalité).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x ≥ -2\", \"b\": \"x ≤ -2\", \"c\": \"x ≥ 2\", \"d\": \"x ≤ 2\"}}","_debug_options_count":4},{"id":31856,"question":"Le point C(3 ; -2) appartient-il à la droite d'équation y = -2x + 4 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant x par 3 dans l'équation, on obtient y = -2(3) + 4 = -2. Le point C(3 ; -2) appartient bien à la 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":31857,"question":"Quelle est la forme factorisée de l'expression x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'expression x² - 9 est une différence de carrés : (x - 3)(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)(x + 3)\", \"b\": \"(x - 9)(x + 1)\", \"c\": \"(x - 3)²\", \"d\": \"(","_debug_options_count":4},{"id":31858,"question":"La fonction f(x) = x² - 4x + 3 a pour sommet :","option_a":"(2 ; -1)","option_b":"(1 ; 0)","option_c":"(0 ; 3)","option_d":"(4 ; 3)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le sommet d'une parabole f(x) = ax² + bx + c a pour abscisse x = -b\/(2a) = 2. En remplaçant, on obtient f(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\": \"(2 ; -1)\", \"b\": \"(1 ; 0)\", \"c\": \"(0 ; 3)\", \"d\": \"(4 ; 3)\"}}","_debug_options_count":4},{"id":31859,"question":"L'équation x² + 4 = 0 a des solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation x² = -4 n'a pas de solution réelle car un carré est toujours positif.","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}]