Quiz — 65708e8266e00_Corrigé-Révision DS1.pdf

Question 1 sur 10 20:00

[{"id":41280,"question":"Quelle est la solution de l’équation 3x - 5 = 2x + 7 ?","option_a":"x = -12","option_b":"x = 12","option_c":"x = -2","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"En soustrayant 2x des deux côtés, on obtient x - 5 = 7. Puis en ajoutant 5, on trouve x = 12.","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 = -12\", \"b\": \"x = 12\", \"c\": \"x = -2\", \"d\": \"x = 2\"}}","_debug_options_count":4},{"id":41281,"question":"La fonction f(x) = 2x + 3 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur de la fonction affine est positif (2), donc la fonction est bien croissante.","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":41282,"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":"Il s’agit d’une différence de carrés : x² - 9 = (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":41283,"question":"Dans un triangle rectangle, le carré de l’hypoténuse est égal à la somme des carrés des deux autres côtés. Cette propriété s’appelle :","option_a":"Théorème de Thalès","option_b":"Théorème de Pythagore","option_c":"Propriété des angles","option_d":"Formule d’Al-Khwarizmi","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Pythagore énonce que dans un triangle rectangle, a² + b² = c² où c est l’hypoténuse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Théorème de Thalès\", \"b\": \"Théorème de Pythagore\", \"c\": \"Pro","_debug_options_count":4},{"id":41284,"question":"L’inéquation 2x + 1 \u003E 5 a pour solution :","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E 3","option_d":"x \u003C 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En soustrayant 1 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\": \"a\", \"options\": {\"a\": \"x \u003E 2\", \"b\": \"x \u003C 2\", \"c\": \"x \u003E 3\", \"d\": \"x \u003C 3\"}}","_debug_options_count":4},{"id":41285,"question":"Quelle est l’image de 4 par la fonction g(x) = -x² + 5x - 3 ?","option_a":"-3","option_b":"3","option_c":"7","option_d":"13","option_e":"","option_f":"","bonne_reponse":"c","explication":"En remplaçant x par 4, on obtient g(4) = -16 + 20 - 3 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"-3\", \"b\": \"3\", \"c\": \"7\", \"d\": \"13\"}}","_debug_options_count":4},{"id":41286,"question":"Deux droites parallèles ont toujours le même coefficient directeur.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si deux droites sont parallèles, leurs coefficients directeurs sont égaux (même pente).","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":41287,"question":"Résoudre le système : { 2x + y = 5 ; x - y = 1 }. La solution est :","option_a":"(2, 1)","option_b":"(1, 3)","option_c":"(3, -1)","option_d":"(0, 5)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En additionnant les deux équations, on obtient 3x = 6, donc x = 2. En remplaçant, y = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"(2, 1)\", \"b\": \"(1, 3)\", \"c\": \"(3, -1)\", \"d\": \"(0, 5)\"}}","_debug_options_count":4},{"id":41288,"question":"La droite d’équation y = -2x + 4 passe par le point :","option_a":"(0, 4)","option_b":"(1, 2)","option_c":"(2, 0)","option_d":"(3, -2)","option_e":"","option_f":"","bonne_reponse":"c","explication":"En remplaçant x par 2, on obtient y = -4 + 4 = 0. Le point (2, 0) appartient donc à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"(0, 4)\", \"b\": \"(1, 2)\", \"c\": \"(2, 0)\", \"d\": \"(3, -2)\"}}","_debug_options_count":4},{"id":41289,"question":"Le discriminant d’une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"Δ = b² - 4ac","option_b":"Δ = a² - 4bc","option_c":"Δ = b² + 4ac","option_d":"Δ = 4a² - b²c","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant est bien Δ = b² - 4ac, utilisé pour déterminer le nombre de 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\": \"Δ = b² - 4ac\", \"b\": \"Δ = a² - 4bc\", \"c\": \"Δ = b² + 4ac\", \"d","_debug_options_count":4}]