Quiz — exercice.pdf

Question 1 sur 10 20:00

[{"id":14619,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = -1 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0, donc les solutions sont x = 2 et 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 = 2 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4},{"id":14620,"question":"La fonction f(x) = 3x² - 2x + 1 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant Δ = (-2)² - 4*3*1 = 4 - 12 = -8 \u003C 0, et le coefficient de x² est positif, donc la fonction est toujours positive.","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":14621,"question":"Quelle est la limite de la suite uₙ = (2n² + 3n - 1)\/(n² + 5) quand n tend vers l'infini ?","option_a":"2","option_b":"3","option_c":"1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par n², on obtient uₙ = (2 + 3\/n - 1\/n²)\/(1 + 5\/n²), donc la limite est 2\/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\": \"2\", \"b\": \"3\", \"c\": \"1\", \"d\": \"0\"}}","_debug_options_count":4},{"id":14622,"question":"Un triangle ABC est rectangle en A. Si AB = 3 cm et AC = 4 cm, quelle est la longueur de BC ?","option_a":"5 cm","option_b":"7 cm","option_c":"√7 cm","option_d":"√10 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, BC² = AB² + AC² = 9 + 16 = 25, donc BC = 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\": \"7 cm\", \"c\": \"√7 cm\", \"d\": \"√10 cm\"}}","_debug_options_count":4},{"id":14623,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est-elle de 1\/2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un dé équilibré a 3 nombres pairs (2, 4, 6) sur 6 faces, donc la probabilité est 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\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":14624,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 4x² + 5x - 2 ?","option_a":"f'(x) = 3x² - 8x + 5","option_b":"f'(x) = 3x² - 4x + 5","option_c":"f'(x) = x² - 8x + 5","option_d":"f'(x) = 3x² - 8x - 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x³ est 3x², celle de -4x² est -8x, celle de 5x est 5, et celle de -2 est 0, donc f'(x) = 3x² - 8x + 5.","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) = 3x² - 8x + 5\", \"b\": \"f'(x) = 3x² - 4x + 5\", \"c\": \"f'(x)","_debug_options_count":4},{"id":14625,"question":"Un carré a une aire de 16 cm². Quelle est la longueur de sa diagonale ?","option_a":"4√2 cm","option_b":"8 cm","option_c":"4 cm","option_d":"2√2 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le côté du carré est √16 = 4 cm. La diagonale d'un carré de côté c est c√2, donc 4√2 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\": \"4√2 cm\", \"b\": \"8 cm\", \"c\": \"4 cm\", \"d\": \"2√2 cm\"}}","_debug_options_count":4},{"id":14626,"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 la division par zéro est impossible.","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":14627,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C -1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant 2x - 3 \u003E 5, on obtient 2x \u003E 8, donc x \u003E 4.","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 4\", \"b\": \"x \u003C 4\", \"c\": \"x \u003E 1\", \"d\": \"x \u003C -1\"}}","_debug_options_count":4},{"id":14628,"question":"Un sac contient 5 boules rouges et 3 boules bleues. Quelle est la probabilité de tirer une boule bleue ?","option_a":"3\/8","option_b":"5\/8","option_c":"3\/5","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 3 boules bleues sur un total de 8 boules, donc la probabilité est 3\/8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3\/8\", \"b\": \"5\/8\", \"c\": \"3\/5\", \"d\": \"1\/2\"}}","_debug_options_count":4}]