Quiz — correction_exercices_semaine1.pdf

Question 1 sur 10 20:00

[{"id":67236,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12\/3","option_c":"x = 4\/3","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 = 12\/3\", \"c\": \"x = 4\/3\", \"d\": \"x = 2\"}}","_debug_options_count":4},{"id":67237,"question":"L'équation x² = 16 a deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"x² = 16 équivaut à x = 4 ou x = -4, donc il y a bien deux solutions réelles.","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":67238,"question":"Quelle est la forme développée de (x + 3)(x - 2) ?","option_a":"x² + x - 6","option_b":"x² - 6x + 1","option_c":"x² + 5x - 6","option_d":"x² + x + 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En développant (x + 3)(x - 2), on obtient x² - 2x + 3x - 6 = x² + x - 6.","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 + x - 6\", \"b\": \"x² - 6x + 1\", \"c\": \"x² + 5x - 6\", \"d\": \"x²","_debug_options_count":4},{"id":67239,"question":"La fonction f(x) = 2x + 1 est-elle linéaire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction linéaire s'écrit f(x) = ax, donc f(x) = 2x + 1 est affine, pas linéaire.","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":67240,"question":"Résoudre l'inéquation 2x - 3 \u003E 5.","option_a":"x \u003E 4","option_b":"x \u003E 1","option_c":"x \u003C 4","option_d":"x \u003E 8","option_e":"","option_f":"","bonne_reponse":"a","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 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 \u003E 4\", \"b\": \"x \u003E 1\", \"c\": \"x \u003C 4\", \"d\": \"x \u003E 8\"}}","_debug_options_count":4},{"id":67241,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par Δ = b² - 4ac.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule du discriminant est bien Δ = b² - 4ac.","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":67242,"question":"Quelle est la valeur de x si 5x = 20 ?","option_a":"x = 4","option_b":"x = 5","option_c":"x = 100","option_d":"x = 15","option_e":"","option_f":"","bonne_reponse":"a","explication":"5x = 20 ⇒ x = 20 \/ 5 = 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 = 5\", \"c\": \"x = 100\", \"d\": \"x = 15\"}}","_debug_options_count":4},{"id":67243,"question":"L'expression 3(x + 2) est-elle équivalente à 3x + 6 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En développant 3(x + 2), on obtient 3x + 6, donc les deux expressions sont équivalentes.","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":67244,"question":"Résoudre l'équation (x - 1)(x + 3) = 0.","option_a":"x = 1 ou x = -3","option_b":"x = -1 ou x = 3","option_c":"x = 0 ou x = 2","option_d":"x = 1 ou x = 3","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 + 3 = 0 ⇒ 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 = 1 ou x = -3\", \"b\": \"x = -1 ou x = 3\", \"c\": \"x = 0 ou x = 2\", ","_debug_options_count":4},{"id":67245,"question":"La fonction f(x) = x² est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = x² est décroissante sur ]-∞; 0] et croissante sur [0; +∞[, donc elle n'est pas croissante sur tout ℝ.","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}]