Quiz — ex9c-3-.pdf

Question 1 sur 10 20:00

[{"id":33470,"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 = -6","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation 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":33471,"question":"La fonction f(x) = 3x + 2 est 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, ce qui est le cas ici avec a=3 et b=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":33472,"question":"Quel est le volume d'une pyramide à base carrée de côté 4 cm et de hauteur 6 cm ?","option_a":"32 cm³","option_b":"48 cm³","option_c":"64 cm³","option_d":"96 cm³","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le volume d'une pyramide est donné par V = (1\/3) × aire de la base × hauteur. L'aire de la base est 4×4=16 cm², donc V = (1\/3)×16×6 = 32 cm³ (correction : 32 cm³, l'option correcte est 32 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\": \"32 cm³\", \"b\": \"48 cm³\", \"c\": \"64 cm³\", \"d\": \"96 cm³\"}}","_debug_options_count":4},{"id":33473,"question":"La moyenne de 5 notes : 12, 15, 10, 14, 18 est égale à 13,8.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La moyenne se calcule par (12+15+10+14+18)\/5 = 69\/5 = 13,8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":33474,"question":"Quelle est la forme canonique de l'expression x² + 6x + 5 ?","option_a":"(x+3)² - 4","option_b":"(x+2)² + 1","option_c":"(x+1)² + 4","option_d":"(x+4)² - 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La forme canonique s'obtient par (x² + 6x + 9) - 4 = (x+3)² - 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+3)² - 4\", \"b\": \"(x+2)² + 1\", \"c\": \"(x+1)² + 4\", \"d\": \"(x+4)","_debug_options_count":4},{"id":33475,"question":"Le théorème de Pythagore s'applique uniquement aux triangles rectangles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème de Pythagore énonce que 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":33476,"question":"Quelle est la limite de la suite uₙ = (2n² + 3n + 1)\/(n² + 5) quand n tend vers l'infini ?","option_a":"0","option_b":"2","option_c":"3","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par n², on obtient (2 + 3\/n + 1\/n²)\/(1 + 5\/n²) → 2\/1 = 2 quand n → ∞.","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\": \"3\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":33477,"question":"La médiatrice d'un segment est la droite qui passe par son milieu et est perpendiculaire à ce segment.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, la médiatrice d'un segment est la droite perpendiculaire à ce segment et passant par son milieu.","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":33478,"question":"Quelle est la dérivée de la fonction f(x) = 4x³ - 2x² + x - 7 ?","option_a":"12x² - 4x + 1","option_b":"12x² - 4x","option_c":"4x² - 2x + 1","option_d":"12x³ - 4x² + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée se calcule terme par terme : f'(x) = 12x² - 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\": \"12x² - 4x + 1\", \"b\": \"12x² - 4x\", \"c\": \"4x² - 2x + 1\", \"d\": \"1","_debug_options_count":4},{"id":33479,"question":"Dans une expérience aléatoire, la probabilité d'un événement est toujours comprise entre 0 et 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, une probabilité est un nombre réel compris entre 0 (événement impossible) et 1 (événement certain).","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}]