Quiz — Examen S1 2011-2012.doc

Question 1 sur 10 20:00

[{"id":20699,"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 = 0 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. Les solutions sont donc 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":20700,"question":"La fonction f(x) = 2x + 3 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b. Ici, a = 2 et b = 3, donc c'est bien une fonction affine.","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":20701,"question":"Quel est le discriminant de l'équation 3x² - 4x + 1 = 0 ?","option_a":"Δ = 4","option_b":"Δ = -4","option_c":"Δ = 16","option_d":"Δ = 0","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le discriminant Δ = b² - 4ac = (-4)² - 4*3*1 = 16 - 12 = 4. Ici, Δ = 16 est incorrect, la bonne réponse est Δ = 4.","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 = 4\", \"b\": \"Δ = -4\", \"c\": \"Δ = 16\", \"d\": \"Δ = 0\"}}","_debug_options_count":4},{"id":20702,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 5 cm et un côté mesure 3 cm, quelle est la longueur du troisième côté ?","option_a":"4 cm","option_b":"6 cm","option_c":"2 cm","option_d":"√34 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore : 3² + x² = 5² → 9 + x² = 25 → x² = 16 → x = 4 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 cm\", \"b\": \"6 cm\", \"c\": \"2 cm\", \"d\": \"√34 cm\"}}","_debug_options_count":4},{"id":20703,"question":"La fonction f(x) = x² - 4x + 5 admet-elle un minimum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = x² - 4x + 5 est une parabole tournée vers le haut (coefficient de x² positif), donc elle admet un minimum en x = -b\/(2a) = 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":20704,"question":"Quelle est l'image de 2 par la fonction f(x) = 1\/x ?","option_a":"0.5","option_b":"2","option_c":"-2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"f(2) = 1\/2 = 0.5. L'image de 2 par cette fonction est donc 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0.5\", \"b\": \"2\", \"c\": \"-2\", \"d\": \"1\"}}","_debug_options_count":4},{"id":20705,"question":"Dans un cercle de rayon 4 cm, quelle est la longueur d'un arc correspondant à un angle au centre de 60° ?","option_a":"4π\/3 cm","option_b":"2π cm","option_c":"π cm","option_d":"8π cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"La longueur d'un arc est donnée par L = (θ\/360) × 2πr. Ici, L = (60\/360) × 2π × 4 = (1\/6) × 8π = 4π\/3 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\": \"4π\/3 cm\", \"b\": \"2π cm\", \"c\": \"π cm\", \"d\": \"8π cm\"}}","_debug_options_count":4},{"id":20706,"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) = (-x)³ = -x³ ≠ x³ = f(x). Donc f(x) 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":20707,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 1 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x² + 2","option_d":"f'(x) = 3x² + 2x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = 3x² + 2x - 1 est f'(x) = 6x + 2 (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) = 6x + 2\", \"b\": \"f'(x) = 3x + 2\", \"c\": \"f'(x) = 6x² + 2\", ","_debug_options_count":4},{"id":20708,"question":"Dans une classe de 30 élèves, 18 sont des filles. Quel est le pourcentage de garçons dans cette classe ?","option_a":"40%","option_b":"60%","option_c":"30%","option_d":"50%","option_e":"","option_f":"","bonne_reponse":"a","explication":"Nombre de garçons = 30 - 18 = 12. Pourcentage = (12\/30) × 100 = 40%.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"40%\", \"b\": \"60%\", \"c\": \"30%\", \"d\": \"50%\"}}","_debug_options_count":4}]