Quiz — DC2-3-13-14M.pdf

Question 1 sur 10 20:00

[{"id":17399,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = -12","option_c":"x = 2","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 2x = 5 + 7 → x = 12. Il faut regrouper les termes en x et les constantes.","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 = 12\", \"b\": \"x = -12\", \"c\": \"x = 2\", \"d\": \"x = -2\"}}","_debug_options_count":4},{"id":17400,"question":"L'équation x² - 5x + 6 = 0 admet deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant Δ = 25 - 24 = 1 \u003E 0, donc deux solutions réelles distinctes : x = 2 et 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":17401,"question":"Quelle méthode permet de résoudre l'équation x² - 4 = 0 ?","option_a":"Factorisation par identité remarquable","option_b":"Utilisation du discriminant","option_c":"Résolution graphique","option_d":"Factorisation par x","option_e":"","option_f":"","bonne_reponse":"a","explication":"x² - 4 = (x - 2)(x + 2) = 0 → solutions x = 2 et x = -2. C'est une identité remarquable (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\": \"Factorisation par identité remarquable\", \"b\": \"Utilisation du di","_debug_options_count":4},{"id":17402,"question":"L'inéquation 2x + 3 \u003E 7 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":"2x \u003E 4 → x \u003E 2. Il faut isoler x en divisant par un nombre positif (2), donc le sens de l'inégalité reste inchangé.","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":17403,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant est bien Δ = b² - 4ac. Cette formule permet de déterminer le nombre et la nature des solutions.","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":17404,"question":"Quelle est la solution de l'équation (x - 1)(x + 3) = 0 ?","option_a":"x = 1 ou x = -3","option_b":"x = -1 ou x = 3","option_c":"x = 1 ou x = 3","option_d":"x = -1 ou x = -3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un produit de facteurs est nul si et seulement 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 = 1 ou x = 3\", ","_debug_options_count":4},{"id":17405,"question":"L'inéquation -3x + 5 ≤ 2 a pour solution :","option_a":"x ≥ 1","option_b":"x ≤ 1","option_c":"x ≥ -1","option_d":"x ≤ -1","option_e":"","option_f":"","bonne_reponse":"b","explication":"-3x ≤ -3 → x ≥ 1. En divisant par un nombre négatif (-3), le sens de l'inégalité est inversé.","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 ≥ 1\", \"b\": \"x ≤ 1\", \"c\": \"x ≥ -1\", \"d\": \"x ≤ -1\"}}","_debug_options_count":4},{"id":17406,"question":"Une équation du second degré peut avoir :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai. Une équation du second degré peut avoir 0, 1 ou 2 solutions réelles selon le 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\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":17407,"question":"Quelle est la solution de l'équation 4x² - 12x + 9 = 0 ?","option_a":"x = 3\/2 (solution double)","option_b":"x = 1 et x = 2","option_c":"x = -3\/2 et x = 3\/2","option_d":"Pas de solution réelle","option_e":"","option_f":"","bonne_reponse":"a","explication":"4x² - 12x + 9 = (2x - 3)² = 0 → solution double x = 3\/2. Le discriminant Δ = 0.","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\/2 (solution double)\", \"b\": \"x = 1 et x = 2\", \"c\": \"x = -3\/2","_debug_options_count":4},{"id":17408,"question":"L'ensemble des solutions de l'inéquation x² - 9 \u003C 0 est :","option_a":"]-3 ; 3[","option_b":"[-3 ; 3]","option_c":"]-∞ ; -3[ ∪ ]3 ; +∞[","option_d":"]-∞ ; +∞[","option_e":"","option_f":"","bonne_reponse":"a","explication":"x² - 9 \u003C 0 → x² \u003C 9 → -3 \u003C x \u003C 3. L'ensemble des solutions est l'intervalle ouvert ]-3 ; 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\": \"]-3 ; 3[\", \"b\": \"[-3 ; 3]\", \"c\": \"]-∞ ; -3[ ∪ ]3 ; +∞[\", \"d","_debug_options_count":4}]