Quiz — 2006corrigé Maths-1.pdf

Question 1 sur 10 20:00

[{"id":76746,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 3","option_c":"x = 15\/3","option_d":"x = 15","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 10, on ajoute 5 des deux côtés : 3x = 15, puis on divise par 3 : x = 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\": \"x = 5\", \"b\": \"x = 3\", \"c\": \"x = 15\/3\", \"d\": \"x = 15\"}}","_debug_options_count":4},{"id":76747,"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":"a","explication":"En soustrayant 3 des deux côtés, on obtient 2x \u003E 4, puis en divisant par 2 : x \u003E 2. L'inégalité est donc 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},{"id":76748,"question":"Quelle est la valeur de f(2) si f(x) = 2x² - 3x + 1 ?","option_a":"3","option_b":"5","option_c":"7","option_d":"9","option_e":"","option_f":"","bonne_reponse":"b","explication":"En remplaçant x par 2 : f(2) = 2*(2)² - 3*(2) + 1 = 8 - 6 + 1 = 3. La réponse correcte est 3 (option A).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"3\", \"b\": \"5\", \"c\": \"7\", \"d\": \"9\"}}","_debug_options_count":4},{"id":76749,"question":"Le produit de deux nombres négatifs est toujours positif.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale des nombres : le produit de deux nombres négatifs est positif.","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":76750,"question":"Quelle est la solution de l'équation x² - 4x + 4 = 0 ?","option_a":"x = 2","option_b":"x = -2","option_c":"x = 4","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"Cette équation est un carré parfait : (x - 2)² = 0, donc x = 2 est la solution double.","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 = 4\", \"d\": \"x = 0\"}}","_debug_options_count":4},{"id":76751,"question":"L'expression (a + b)² est égale à :","option_a":"a² + b²","option_b":"a² + 2ab + b²","option_c":"a² - b²","option_d":"2a + 2b","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'identité remarquable (a + b)² = a² + 2ab + b² est une formule de base à connaître.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"a² + b²\", \"b\": \"a² + 2ab + b²\", \"c\": \"a² - b²\", \"d\": \"2a + ","_debug_options_count":4},{"id":76752,"question":"Si un triangle a deux angles de 60°, alors c'est un triangle équilatéral.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un triangle avec deux angles de 60° a un troisième angle de 60° (180° - 120°), donc tous ses angles sont égaux : c'est un triangle équilatéral.","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":76753,"question":"Quelle est la valeur de 3\/4 + 1\/2 ?","option_a":"4\/6","option_b":"5\/4","option_c":"7\/8","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"En mettant au même dénominateur : 3\/4 + 2\/4 = 5\/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\": \"4\/6\", \"b\": \"5\/4\", \"c\": \"7\/8\", \"d\": \"1\"}}","_debug_options_count":4},{"id":76754,"question":"L'équation 5x = 0 a pour solution :","option_a":"x = 5","option_b":"x = 0","option_c":"x = -5","option_d":"Aucune solution","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation 5x = 0 implique x = 0, car 5*0 = 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\": \"x = 5\", \"b\": \"x = 0\", \"c\": \"x = -5\", \"d\": \"Aucune solution\"}}","_debug_options_count":4},{"id":76755,"question":"La somme des angles d'un triangle est toujours égale à 180°.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété géométrique fondamentale : la somme des angles d'un triangle est toujours 180°.","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}]