Quiz — Maths en tete - Algebre.pdf

Question 1 sur 10 20:00

[{"id":8015,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 1 ?","option_a":"x = 4","option_b":"x = 6","option_c":"x = -4","option_d":"x = -6","option_e":"","option_f":"","bonne_reponse":"b","explication":"En soustrayant 2x des deux côtés et en ajoutant 5, on obtient x = 6.","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 = 4\", \"b\": \"x = 6\", \"c\": \"x = -4\", \"d\": \"x = -6\"}}","_debug_options_count":4},{"id":8016,"question":"Un polynôme du second degré peut avoir au maximum deux racines réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un polynôme du second degré peut avoir 0, 1 ou 2 racines réelles selon son discriminant.","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":8017,"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 : (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":8018,"question":"L'inéquation 2x + 3 \u003E 7 a pour solution :","option_a":"x \u003E 2","option_b":"x \u003E 5","option_c":"x \u003C 2","option_d":"x \u003C 5","option_e":"","option_f":"","bonne_reponse":"b","explication":"En soustrayant 3 et en divisant par 2, on obtient x \u003E 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\": \"x \u003E 2\", \"b\": \"x \u003E 5\", \"c\": \"x \u003C 2\", \"d\": \"x \u003C 5\"}}","_debug_options_count":4},{"id":8019,"question":"La factorisation de 4x² - 12x + 9 est :","option_a":"(2x - 3)²","option_b":"(2x + 3)²","option_c":"(4x - 3)(x - 3)","option_d":"(2x - 1)(2x - 9)","option_e":"","option_f":"","bonne_reponse":"a","explication":"4x² - 12x + 9 est un carré parfait : (2x - 3)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\": \"(2x - 3)²\", \"b\": \"(2x + 3)²\", \"c\": \"(4x - 3)(x - 3)\", \"d\": \"(2x","_debug_options_count":4},{"id":8020,"question":"Le discriminant d'un polynôme du second degré ax² + bx + c est 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":8021,"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 ∈ [0, 5]","option_d":"x ∈ ]-∞, 0] ∪ [5, +∞[","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le polynôme x² - 5x + 6 se factorise en (x - 2)(x - 3). Les solutions sont 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":8022,"question":"La somme des racines d'un polynôme du second degré ax² + bx + c est égale à :","option_a":"-b\/a","option_b":"b\/a","option_c":"-c\/a","option_d":"c\/a","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après les relations de Viète, la somme des racines est -b\/a.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"-b\/a\", \"b\": \"b\/a\", \"c\": \"-c\/a\", \"d\": \"c\/a\"}}","_debug_options_count":4},{"id":8023,"question":"L'expression (x + 2)(x - 2) est égale à :","option_a":"x² - 4","option_b":"x² + 4","option_c":"x² - 2x + 4","option_d":"x² + 2x - 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"(x + 2)(x - 2) = x² - 4 (différence de carrés).","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 - 4\", \"b\": \"x² + 4\", \"c\": \"x² - 2x + 4\", \"d\": \"x² + 2x - 4","_debug_options_count":4},{"id":8024,"question":"Un polynôme du second degré avec un discriminant négatif n'a pas de racines réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si Δ \u003C 0, le polynôme n'a pas de racines réelles (mais des racines complexes).","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}]