Quiz — ds2_ex3.doc

Question 1 sur 10 20:00

[{"id":14699,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0,5 ou x = 2","option_c":"x = -1 ou x = 2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"b","explication":"On utilise la formule des racines du second degré : x = [5 ± √(25 - 16)] \/ 4 = [5 ± 3]\/4. Les solutions sont donc 2 et 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\": \"x = 1 ou x = 2\", \"b\": \"x = 0,5 ou x = 2\", \"c\": \"x = -1 ou x = 2\",","_debug_options_count":4},{"id":14700,"question":"L'inéquation 3x - 7 ≤ 2x + 5 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant 3x - 7 ≤ 2x + 5, on obtient x ≤ 12. La solution est donc 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":14701,"question":"Soit f(x) = x² - 4x + 3. Quelle est l'image de 2 par f ?","option_a":"-1","option_b":"0","option_c":"1","option_d":"3","option_e":"","option_f":"","bonne_reponse":"b","explication":"f(2) = 2² - 4*2 + 3 = 4 - 8 + 3 = -1. L'image de 2 est donc -1.","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\": \"0\", \"c\": \"1\", \"d\": \"3\"}}","_debug_options_count":4},{"id":14702,"question":"La fonction f(x) = 1\/x est définie pour :","option_a":"x ∈ ℝ","option_b":"x ∈ ℝ*","option_c":"x ∈ ℝ+","option_d":"x ∈ ℤ","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/x est définie pour tout x réel non nul, soit x ∈ 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\": \"x ∈ ℝ\", \"b\": \"x ∈ ℝ*\", \"c\": \"x ∈ ℝ+\", \"d\": \"x ∈ ℤ","_debug_options_count":4},{"id":14703,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est le théorème de Pythagore : dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","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":14704,"question":"Quelle est la dérivée de 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 de 3x³ est 9x², celle de -2x² est -4x, celle de x est 1, et celle de -5 est 0. Donc f'(x) = 9x² - 4x + 1.","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":14705,"question":"L'équation d'une droite parallèle à l'axe des abscisses est de la forme :","option_a":"y = ax + b","option_b":"x = a","option_c":"y = b","option_d":"y = ax","option_e":"","option_f":"","bonne_reponse":"c","explication":"Une droite parallèle à l'axe des abscisses a une équation de la forme y = b, où b est une constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"y = ax + b\", \"b\": \"x = a\", \"c\": \"y = b\", \"d\": \"y = ax\"}}","_debug_options_count":4},{"id":14706,"question":"Le volume d'une pyramide à base carrée de côté 3 cm et de hauteur 4 cm est :","option_a":"12 cm³","option_b":"36 cm³","option_c":"16 cm³","option_d":"24 cm³","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le volume d'une pyramide est donné par V = (1\/3) * base * hauteur. Ici, base = 3² = 9 cm², donc V = (1\/3)*9*4 = 12 cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"12 cm³\", \"b\": \"36 cm³\", \"c\": \"16 cm³\", \"d\": \"24 cm³\"}}","_debug_options_count":4},{"id":14707,"question":"La fonction f(x) = √x est définie pour :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = √x est définie pour x ≥ 0, car la racine carrée d'un nombre négatif n'est pas un nombre 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":14708,"question":"Quelle est la limite de f(x) = (2x² + 3x - 1)\/(x² - 1) quand x tend vers l'infini ?","option_a":"0","option_b":"2","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) = (2 + 3\/x - 1\/x²)\/(1 - 1\/x²). Quand x → ∞, les termes en 1\/x tendent vers 0, 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\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"2\", \"c\": \"1\", \"d\": \"∞\"}}","_debug_options_count":4}]