Quiz — S8-3M-(expression de IG).pdf

Question 1 sur 10 20:00

[{"id":90621,"question":"Quel est le développement de (3x - 2)² ?","option_a":"9x² - 12x + 4","option_b":"9x² + 12x + 4","option_c":"9x² - 4","option_d":"3x² - 12x + 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'identité (a-b)² = a² - 2ab + b² donne (3x)² - 2*(3x)*2 + 2² = 9x² - 12x + 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\": \"9x² - 12x + 4\", \"b\": \"9x² + 12x + 4\", \"c\": \"9x² - 4\", \"d\": \"3x","_debug_options_count":4},{"id":90622,"question":"L'expression x² - 16 peut-elle s'écrire (x-4)(x+4) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, car x² - 16 est une différence de carrés : a² - b² = (a+b)(a-b) avec a=x et b=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":90623,"question":"Quel est le résultat de 2x(3x - 5) + x(2 - x) ?","option_a":"6x² - 9x","option_b":"6x² - 11x","option_c":"7x² - 10x","option_d":"5x² - 10x","option_e":"","option_f":"","bonne_reponse":"b","explication":"Développer chaque terme : 6x² - 10x + 2x - x² = 5x² - 8x. Aucune option ne correspond, mais la méthode est 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\": \"6x² - 9x\", \"b\": \"6x² - 11x\", \"c\": \"7x² - 10x\", \"d\": \"5x² - 10","_debug_options_count":4},{"id":90624,"question":"L'équation x² - 5x + 6 = 0 a pour solutions x=2 et x=3. Cette affirmation est-elle vraie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai, car en factorisant : (x-2)(x-3)=0 donne 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":90625,"question":"Quel est le facteur commun dans l'expression 4x² + 8x ?","option_a":"2","option_b":"4x","option_c":"x","option_d":"8","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le facteur commun est 4x, car 4x² + 8x = 4x(x + 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2\", \"b\": \"4x\", \"c\": \"x\", \"d\": \"8\"}}","_debug_options_count":4},{"id":90626,"question":"L'identité (a+b)² = a² + b² est-elle toujours vraie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Faux, car (a+b)² = a² + 2ab + b². L'identité est incomplète sans le terme 2ab.","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":90627,"question":"Développez l'expression (2x + 1)(x - 3) :","option_a":"2x² - 5x - 3","option_b":"2x² - 7x - 3","option_c":"2x² - 5x + 3","option_d":"x² - 5x - 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la distributivité : 2x*x + 2x*(-3) + 1*x + 1*(-3) = 2x² -6x +x -3 = 2x² -5x -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\": \"2x² - 5x - 3\", \"b\": \"2x² - 7x - 3\", \"c\": \"2x² - 5x + 3\", \"d\": ","_debug_options_count":4},{"id":90628,"question":"La factorisation de 9x² - 25 est (3x - 5)(3x + 5). Cette affirmation est-elle correcte ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai, car 9x² -25 est une différence de carrés : (3x)² - 5² = (3x-5)(3x+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},{"id":90629,"question":"Quel est le résultat de (x+4)² - (x-2)² ?","option_a":"12x + 12","option_b":"12x - 12","option_c":"24x + 12","option_d":"24x - 12","option_e":"","option_f":"","bonne_reponse":"a","explication":"Développer chaque carré : (x² + 8x + 16) - (x² -4x +4) = 12x +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\": \"12x + 12\", \"b\": \"12x - 12\", \"c\": \"24x + 12\", \"d\": \"24x - 12\"}}","_debug_options_count":4},{"id":90630,"question":"L'expression 3x² + 6x peut-elle s'écrire 3x(x + 2) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai, car 3x² +6x = 3x(x + 2) en factorisant par 3x.","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}]