Quiz — 62d03dd1690ec_Enoncé.pdf

Question 1 sur 10 20:00

[{"id":46648,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -5","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 5 = 2x + 7 → 3x - 2x = 7 + 5 → x = 12.","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 = 2\", \"c\": \"x = -5\", \"d\": \"x = 5\"}}","_debug_options_count":4},{"id":46649,"question":"La fonction f(x) = 2x² - 3x + 1 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction affine a la forme f(x) = ax + b. Ici, le terme x² indique qu'il s'agit d'une fonction polynôme de degré 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":46650,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 10 cm et un côté 6 cm, quelle est la longueur du troisième côté ?","option_a":"8 cm","option_b":"√(100-36) cm","option_c":"4 cm","option_d":"16 cm","option_e":"","option_f":"","bonne_reponse":"b","explication":"D'après le théorème de Pythagore : c² = a² + b² → c = √(10² - 6²) = √64 = 8 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"8 cm\", \"b\": \"√(100-36) cm\", \"c\": \"4 cm\", \"d\": \"16 cm\"}}","_debug_options_count":4},{"id":46651,"question":"Le nombre 0,75 est-il un nombre rationnel ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un nombre rationnel s'écrit sous forme de fraction a\/b avec a et b entiers. 0,75 = 3\/4, donc c'est un nombre rationnel.","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":46652,"question":"Quelle est la dérivée de la fonction f(x) = 5x³ - 2x² + x - 4 ?","option_a":"f'(x) = 15x² - 4x + 1","option_b":"f'(x) = 15x² - 4x","option_c":"f'(x) = 5x² - 2x + 1","option_d":"f'(x) = 15x - 4x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en multipliant chaque terme par son exposant et en réduisant l'exposant de 1 : f'(x) = 15x² - 4x + 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\": \"f'(x) = 15x² - 4x + 1\", \"b\": \"f'(x) = 15x² - 4x\", \"c\": \"f'(x) =","_debug_options_count":4},{"id":46653,"question":"Si deux droites sont parallèles, alors leurs coefficients directeurs sont égaux.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux droites parallèles ont le même coefficient directeur. C'est une propriété fondamentale des droites dans le plan.","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":46654,"question":"Résoudre l'inéquation : 2(x - 3) \u003E 5x + 1.","option_a":"x \u003C -7\/3","option_b":"x \u003E -7\/3","option_c":"x \u003C 7\/3","option_d":"x \u003E 7\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"2x - 6 \u003E 5x + 1 → -3x \u003E 7 → x \u003C -7\/3 (en divisant par un nombre négatif, on inverse le sens de l'inégalité).","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 \u003C -7\/3\", \"b\": \"x \u003E -7\/3\", \"c\": \"x \u003C 7\/3\", \"d\": \"x \u003E 7\/3\"}}","_debug_options_count":4},{"id":46655,"question":"Le nombre π est-il un nombre irrationnel ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"π ne peut pas s'écrire comme une fraction d'entiers, donc c'est un nombre irrationnel.","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":46656,"question":"Quelle est l'image de -2 par la fonction f(x) = -3x² + 2x + 5 ?","option_a":"f(-2) = 15","option_b":"f(-2) = -3","option_c":"f(-2) = 21","option_d":"f(-2) = -11","option_e":"","option_f":"","bonne_reponse":"c","explication":"f(-2) = -3(-2)² + 2(-2) + 5 = -3(4) - 4 + 5 = -12 - 4 + 5 = -11.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"f(-2) = 15\", \"b\": \"f(-2) = -3\", \"c\": \"f(-2) = 21\", \"d\": \"f(-2) = ","_debug_options_count":4},{"id":46657,"question":"Dans un repère orthonormé, la distance entre les points A(1; 2) et B(4; 6) est égale à :","option_a":"5","option_b":"√(3² + 4²)","option_c":"√25","option_d":"Toutes les réponses sont correctes","option_e":"","option_f":"","bonne_reponse":"d","explication":"La distance AB = √[(4-1)² + (6-2)²] = √(9 + 16) = √25 = 5. Toutes les réponses sont donc correctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"5\", \"b\": \"√(3² + 4²)\", \"c\": \"√25\", \"d\": \"Toutes les répons","_debug_options_count":4}]