Quiz — img011.pdf

Question 1 sur 10 20:00

[{"id":4376,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 2 ou x = 1\/2","option_c":"x = -1 ou x = -2","option_d":"x = 1\/2 ou x = 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"La solution s'obtient en utilisant la formule du discriminant Δ = b² - 4ac = 25 - 16 = 9. Les solutions sont x = (5 ± 3)\/4, soit x = 2 ou x = 1\/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 = 1 ou x = 2\", \"b\": \"x = 2 ou x = 1\/2\", \"c\": \"x = -1 ou x = -2\"","_debug_options_count":4},{"id":4377,"question":"La fonction f(x) = x³ - 3x² + 4 est croissante sur l'intervalle [-1, 1].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² - 6x. Sur [-1, 1], f'(x) est négative (ex: f'(-1) = 9 \u003E 0, mais f'(1) = -3 \u003C 0). La fonction n'est pas croissante sur tout l'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":4378,"question":"Quelle est la limite de (3x² + 2x - 1)\/(x² - 4) quand x tend vers l'infini ?","option_a":"0","option_b":"3","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par x², on obtient (3 + 2\/x - 1\/x²)\/(1 - 4\/x²). Quand x → ∞, les termes en 1\/x tendent vers 0, donc la limite est 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"3\", \"c\": \"1\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":4379,"question":"Dans un triangle ABC, si AB = 5, AC = 7 et BC = 8, alors l'angle B est aigu.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"D'après le théorème d'Al-Kashi, cos(B) = (AB² + BC² - AC²)\/(2·AB·BC) = (25 + 64 - 49)\/80 = 40\/80 = 0,5. Donc B = 60° (aigu).","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":4380,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) + ln(x) ?","option_a":"f'(x) = 2e^(2x) + 1\/x","option_b":"f'(x) = e^(2x) + 1\/x","option_c":"f'(x) = 2e^(2x) + ln(x)","option_d":"f'(x) = e^(2x) + x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^(2x) est 2e^(2x) (dérivée d'une fonction composée) et celle de ln(x) est 1\/x. Donc f'(x) = 2e^(2x) + 1\/x.","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) = 2e^(2x) + 1\/x\", \"b\": \"f'(x) = e^(2x) + 1\/x\", \"c\": \"f'(x) ","_debug_options_count":4},{"id":4381,"question":"L'intégrale de 0 à π de sin(x) dx est égale à 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de sin(x) est -cos(x). Évaluée entre 0 et π, on obtient -cos(π) - (-cos(0)) = -(-1) - (-1) = 1 + 1 = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":4382,"question":"Quelle est la solution de l'inéquation x² - 4x + 3 \u003C 0 ?","option_a":"x ∈ ]1, 3[","option_b":"x ∈ ]-∞, 1[ ∪ ]3, +∞[","option_c":"x ∈ ]0, 4[","option_d":"x ∈ ]-1, 1[","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les racines de x² - 4x + 3 = 0 sont x = 1 et x = 3. Le polynôme est négatif entre ses racines, donc x ∈ ]1, 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, 3[\", \"b\": \"x ∈ ]-∞, 1[ ∪ ]3, +∞[\", \"c\": \"x ∈ ","_debug_options_count":4},{"id":4383,"question":"Dans une expérience aléatoire, la probabilité d'un événement A est P(A) = 0,6. Alors P(A̅) = 0,4.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"P(A̅) = 1 - P(A) = 1 - 0,6 = 0,4. L'affirmation est donc vraie.","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":4384,"question":"Quelle est la valeur de l'intégrale ∫(2x + 1) dx entre 0 et 2 ?","option_a":"6","option_b":"4","option_c":"5","option_d":"7","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale de 2x + 1 est x² + x. Évaluée entre 0 et 2, on obtient (4 + 2) - (0 + 0) = 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\": \"6\", \"b\": \"4\", \"c\": \"5\", \"d\": \"7\"}}","_debug_options_count":4},{"id":4385,"question":"La fonction f(x) = 1\/x est définie et continue sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction 1\/x n'est pas définie en x = 0 et présente une discontinuité en ce point. Elle n'est donc pas continue sur ℝ.","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}]