Quiz — Série d'exercices Math - Probabilité + Fonctions trigonométriques - 3ème Math (2009-2010) Mr Abdessatar El Faleh.pdf

Question 1 sur 10 20:00

[{"id":27880,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"1\/6","option_b":"1\/2","option_c":"1\/3","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"b","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles. La probabilité est donc 3\/6 = 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\": \"1\/6\", \"b\": \"1\/2\", \"c\": \"1\/3\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":27881,"question":"La fonction f(x) = sin(x) est-elle périodique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction sinus est périodique de période 2π, car sin(x + 2π) = sin(x) pour tout x réel.","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":27882,"question":"Dans un sac contenant 5 boules rouges et 3 boules bleues, quelle est la probabilité de tirer une boule bleue ?","option_a":"3\/5","option_b":"3\/8","option_c":"5\/8","option_d":"8\/3","option_e":"","option_f":"","bonne_reponse":"b","explication":"Il y a 3 boules bleues sur un total de 8 boules. La probabilité est donc 3\/8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"3\/5\", \"b\": \"3\/8\", \"c\": \"5\/8\", \"d\": \"8\/3\"}}","_debug_options_count":4},{"id":27883,"question":"L'identité trigonométrique sin²(x) + cos²(x) = 1 est-elle toujours vraie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Cette identité est valable pour tout nombre réel x, elle est donc toujours 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":27884,"question":"Quelle est la valeur de cos(π\/3) ?","option_a":"0","option_b":"1\/2","option_c":"√2\/2","option_d":"√3\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"cos(π\/3) = 1\/2, car π\/3 correspond à 60 degrés et le cosinus de 60° est 0,5.","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\": \"1\/2\", \"c\": \"√2\/2\", \"d\": \"√3\/2\"}}","_debug_options_count":4},{"id":27885,"question":"Dans une urne contenant 4 boules vertes et 6 boules jaunes, quelle est la probabilité de tirer deux boules vertes successivement sans remise ?","option_a":"2\/15","option_b":"4\/15","option_c":"6\/25","option_d":"1\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité est (4\/10) * (3\/9) = 12\/90 = 2\/15.","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\/15\", \"b\": \"4\/15\", \"c\": \"6\/25\", \"d\": \"1\/3\"}}","_debug_options_count":4},{"id":27886,"question":"La fonction f(x) = tan(x) est-elle définie pour tout x réel ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction tangente n'est pas définie pour x = π\/2 + kπ (k entier), car cos(x) = 0 à ces points, ce qui rend tan(x) indéfini.","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":27887,"question":"Quelle est la probabilité d'obtenir au moins un 6 en lançant deux dés équilibrés ?","option_a":"1\/6","option_b":"11\/36","option_c":"1\/3","option_d":"5\/12","option_e":"","option_f":"","bonne_reponse":"b","explication":"","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\/6\", \"b\": \"11\/36\", \"c\": \"1\/3\", \"d\": \"5\/12\"}}","_debug_options_count":4},{"id":27888,"question":"L'équation sin(x) = 0 a-t-elle une infinité de solutions ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation sin(x) = 0 a une infinité de solutions car sin(x) = 0 pour x = kπ (k entier).","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":27889,"question":"Dans une classe de 30 élèves, 12 étudient l'anglais et 8 étudient l'espagnol. Si 5 élèves étudient les deux langues, combien d'élèves n'étudient ni l'anglais ni l'espagnol ?","option_a":"9","option_b":"11","option_c":"15","option_d":"20","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le nombre d'élèves étudiant au moins une langue est 12 + 8 - 5 = 15. Donc, 30 - 15 = 15 élèves n'étudient ni l'anglais ni l'espagnol.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"9\", \"b\": \"11\", \"c\": \"15\", \"d\": \"20\"}}","_debug_options_count":4}]