Quiz — DC1-3-16M.pdf

Question 1 sur 10 20:00

[{"id":5686,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = -4","option_c":"x = 12","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 7, on ajoute 5 des deux côtés : 3x = 12, puis on divise par 3 : 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\": \"x = 4\", \"b\": \"x = -4\", \"c\": \"x = 12\", \"d\": \"x = 2\"}}","_debug_options_count":4},{"id":5687,"question":"L'équation x² - 5x + 6 = 0 a pour solutions x = 2 et x = 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En factorisant, on obtient (x-2)(x-3)=0, donc les solutions sont bien 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":5688,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x-3)(x+3)","option_b":"(x-9)(x+1)","option_c":"(x-3)²","option_d":"(x-3)(x-3)","option_e":"","option_f":"","bonne_reponse":"a","explication":"x² - 9 est une différence de carrés : (x)² - (3)² = (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\": \"(x-3)(x-3)\"","_debug_options_count":4},{"id":5689,"question":"L'équation 2x + 3 = 5x - 6 a pour solution x = 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"En résolvant : 2x - 5x = -6 - 3 → -3x = -9 → x = 3. La solution est donc correcte.","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":5690,"question":"Quelle est la solution de l'équation (x-1)(x+2) = 0 ?","option_a":"x = 1 et x = -2","option_b":"x = -1 et x = 2","option_c":"x = 1 et x = 2","option_d":"x = -1 et x = -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un produit de facteurs est nul si l'un des facteurs est nul : x-1=0 → x=1 ou x+2=0 → x=-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 = 1 et x = -2\", \"b\": \"x = -1 et x = 2\", \"c\": \"x = 1 et x = 2\", ","_debug_options_count":4},{"id":5691,"question":"L'équation x² + 4x + 4 = 0 a une solution double.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant est Δ = 16 - 16 = 0, donc l'équation a une solution double : x = -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":5692,"question":"Quelle est la solution de l'équation 4x - 8 = 0 ?","option_a":"x = 2","option_b":"x = -2","option_c":"x = 0","option_d":"x = 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"4x = 8 → x = 8\/4 = 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 = 2\", \"b\": \"x = -2\", \"c\": \"x = 0\", \"d\": \"x = 4\"}}","_debug_options_count":4},{"id":5693,"question":"L'équation x² - 4x + 3 = 0 a pour solutions x = 1 et x = 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En factorisant : (x-1)(x-3)=0, donc les solutions sont x=1 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":5694,"question":"Quelle est la forme développée de (x+2)² ?","option_a":"x² + 4x + 4","option_b":"x² + 2x + 4","option_c":"x² + 4","option_d":"x² + 2x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant (a+b)² = a² + 2ab + b², on obtient x² + 4x + 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\": \"x² + 4x + 4\", \"b\": \"x² + 2x + 4\", \"c\": \"x² + 4\", \"d\": \"x² + 2","_debug_options_count":4},{"id":5695,"question":"L'équation 5(x-2) = 3x + 10 a pour solution x = 10.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En développant : 5x - 10 = 3x + 10 → 2x = 20 → x = 10. La solution est correcte.","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}]