Quiz — rattrapage Alg3 15-16.pdf

Question 1 sur 10 20:00

[{"id":18579,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 2","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 = 2\", \"c\": \"x = 12\", \"d\": \"x = -2\"}}","_debug_options_count":4},{"id":18580,"question":"Un polynôme du second degré a toujours deux racines réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un polynôme du second degré peut avoir 0, 1 ou 2 racines réelles selon son discriminant (Δ \u003C 0, Δ = 0 ou Δ \u003E 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":18581,"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)²","option_e":"","option_f":"","bonne_reponse":"a","explication":"x² - 9 est une différence de carrés : x² - 3² = (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":18582,"question":"L'inéquation 2x + 1 \u003E 5 a pour solution :","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E -2","option_d":"x \u003C -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 2x + 1 \u003E 5, on soustrait 1 : 2x \u003E 4, puis on divise par 2 : x \u003E 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 \u003E 2\", \"b\": \"x \u003C 2\", \"c\": \"x \u003E -2\", \"d\": \"x \u003C -2\"}}","_debug_options_count":4},{"id":18583,"question":"La fonction f(x) = x² est toujours 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; +∞[.","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":18584,"question":"Quelle est la valeur de x pour laquelle le polynôme P(x) = x³ - 4x² + 5x - 2 s'annule ?","option_a":"x = 1","option_b":"x = 2","option_c":"x = -1","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"En testant x = 1 : P(1) = 1 - 4 + 5 - 2 = 0. Donc 1 est une racine.","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\", \"b\": \"x = 2\", \"c\": \"x = -1\", \"d\": \"x = 0\"}}","_debug_options_count":4},{"id":18585,"question":"L'équation x² + 4x + 4 = 0 a pour discriminant :","option_a":"Δ = 0","option_b":"Δ = 8","option_c":"Δ = 16","option_d":"Δ = -12","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0. L'équation a une racine 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\": \"Δ = 0\", \"b\": \"Δ = 8\", \"c\": \"Δ = 16\", \"d\": \"Δ = -12\"}}","_debug_options_count":4},{"id":18586,"question":"La fonction f(x) = 2x + 3 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 f(x) = ax + b, ce qui est le cas ici avec a = 2 et b = 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":18587,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 ≤ 0 ?","option_a":"x ∈ [2; 3]","option_b":"x ∈ ]-∞; 2] ∪ [3; +∞[","option_c":"x ∈ [1; 6]","option_d":"x ∈ ℝ","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le polynôme x² - 5x + 6 se factorise en (x - 2)(x - 3). Il est négatif ou nul entre ses racines : x ∈ [2; 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 ∈ [2; 3]\", \"b\": \"x ∈ ]-∞; 2] ∪ [3; +∞[\", \"c\": \"x ∈ ","_debug_options_count":4},{"id":18588,"question":"La dérivée de f(x) = 3x² + 2x - 1 est f'(x) = 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -1 est 0. Donc f'(x) = 6x + 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}]