Quiz — 69999094dcb4a_Série 17.pdf

Question 1 sur 10 20:00

[{"id":145357,"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":"En isolant x, on obtient 3x - 2x = 5 + 7, soit 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 = -12\", \"c\": \"x = 2\", \"d\": \"x = -2\"}}","_debug_options_count":4},{"id":145358,"question":"La fonction f(x) = x² - 4x + 3 est-elle croissante sur l'intervalle [2 ; +∞[ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 2x - 4 est positive pour x \u003E 2, donc la fonction est croissante sur cet intervalle.","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":145359,"question":"Quel est le discriminant de l'équation x² + 5x + 6 = 0 ?","option_a":"Δ = 1","option_b":"Δ = 25","option_c":"Δ = 16","option_d":"Δ = -1","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le discriminant est Δ = b² - 4ac = 25 - 24 = 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\": \"Δ = 1\", \"b\": \"Δ = 25\", \"c\": \"Δ = 16\", \"d\": \"Δ = -1\"}}","_debug_options_count":4},{"id":145360,"question":"La limite de la fonction f(x) = (2x + 1)\/(x - 3) quand x tend vers 3⁺ est-elle +∞ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Quand x tend vers 3⁺, le dénominateur tend vers 0⁺ et le numérateur vers 7, donc la limite est +∞.","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":145361,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + x - 5 ?","option_a":"f'(x) = 9x² - 4x + 1","option_b":"f'(x) = 6x² - 4x + 1","option_c":"f'(x) = 9x² - 2x + 1","option_d":"f'(x) = 6x² - 2x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée est f'(x) = 9x² - 4x + 1 (dérivée terme à terme).","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) = 9x² - 4x + 1\", \"b\": \"f'(x) = 6x² - 4x + 1\", \"c\": \"f'(x)","_debug_options_count":4},{"id":145362,"question":"Un triangle rectangle a pour côtés 3 cm et 4 cm. Quelle est la longueur de l'hypoténuse ?","option_a":"5 cm","option_b":"6 cm","option_c":"7 cm","option_d":"8 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par le théorème de Pythagore, l'hypoténuse mesure √(3² + 4²) = 5 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"5 cm\", \"b\": \"6 cm\", \"c\": \"7 cm\", \"d\": \"8 cm\"}}","_debug_options_count":4},{"id":145363,"question":"La fonction f(x) = 1\/x est-elle définie en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car le dénominateur s'annule.","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":145364,"question":"Quelle est la solution de l'inéquation 2x + 3 ≤ 7 ?","option_a":"x ≤ 2","option_b":"x ≥ 2","option_c":"x ≤ -2","option_d":"x ≥ -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En isolant x, on obtient 2x ≤ 4, soit x ≤ 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 ≤ 2\", \"b\": \"x ≥ 2\", \"c\": \"x ≤ -2\", \"d\": \"x ≥ -2\"}}","_debug_options_count":4},{"id":145365,"question":"La fonction f(x) = x³ est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = -x³ ≠ f(x), donc elle n'est pas paire.","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":145366,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x² en x = 1 ?","option_a":"1","option_b":"2","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 2x donne f'(1) = 2, qui est le coefficient directeur de la tangente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\", \"b\": \"2\", \"c\": \"3\", \"d\": \"4\"}}","_debug_options_count":4}]