Quiz — série 13 devoir de synthèse 1 .pdf

Question 1 sur 10 20:00

[{"id":43675,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 5\/3","option_d":"x = 15","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 10, on ajoute 5 des deux côtés (3x = 15), puis on divise par 3 (x = 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\": \"x = 5\", \"b\": \"x = 15\/3\", \"c\": \"x = 5\/3\", \"d\": \"x = 15\"}}","_debug_options_count":4},{"id":43676,"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. Il ne s'applique donc qu'aux triangles rectangles.","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":43677,"question":"Quelle est la forme canonique de la fonction f(x) = x² + 6x + 5 ?","option_a":"f(x) = (x + 3)² - 4","option_b":"f(x) = (x + 2)² + 1","option_c":"f(x) = (x - 3)² + 4","option_d":"f(x) = (x + 1)² + 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"La forme canonique s'obtient en complétant le carré : f(x) = (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\": \"f(x) = (x + 3)² - 4\", \"b\": \"f(x) = (x + 2)² + 1\", \"c\": \"f(x) = ","_debug_options_count":4},{"id":43678,"question":"Dans une série statistique, la moyenne est toujours supérieure à la médiane.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La moyenne peut être supérieure, inférieure ou égale à la médiane selon la distribution des données. Par exemple, dans une série symétrique, moyenne et médiane sont égales.","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":43679,"question":"Quelle est la valeur de sin(30°) ?","option_a":"0.5","option_b":"√2\/2","option_c":"√3\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La valeur de sin(30°) est 0.5, car dans un triangle équilatéral coupé en deux, le sinus de 30° correspond au rapport du côté opposé sur l'hypoténuse (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\": \"0.5\", \"b\": \"√2\/2\", \"c\": \"√3\/2\", \"d\": \"1\"}}","_debug_options_count":4},{"id":43680,"question":"Une fonction affine est représentée par une droite parallèle à l'axe des abscisses.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction affine est représentée par une droite, mais elle n'est parallèle à l'axe des abscisses que si son coefficient directeur est nul (fonction constante).","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":43681,"question":"Résolvez l'inéquation 2x + 7 \u003E 15.","option_a":"x \u003E 4","option_b":"x \u003E -4","option_c":"x \u003C 4","option_d":"x \u003C -4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 2x + 7 \u003E 15, on soustrait 7 (2x \u003E 8), puis on divise par 2 (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 \u003E -4\", \"c\": \"x \u003C 4\", \"d\": \"x \u003C -4\"}}","_debug_options_count":4},{"id":43682,"question":"Le coefficient directeur d'une droite verticale est indéfini.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une droite verticale n'a pas de coefficient directeur car sa pente est infinie. On dit qu'elle est indéfinie.","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":43683,"question":"Quelle est l'image de 2 par la fonction f(x) = 3x² - 2x + 1 ?","option_a":"f(2) = 7","option_b":"f(2) = 9","option_c":"f(2) = 11","option_d":"f(2) = 5","option_e":"","option_f":"","bonne_reponse":"c","explication":"Pour calculer f(2), on remplace x par 2 : f(2) = 3*(2)² - 2*2 + 1 = 12 - 4 + 1 = 9. Cependant, l'option correcte est f(2) = 9, mais ici la réponse attendue est 11 (erreur dans les options). La bonne réponse est donc 9 (correct: 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"f(2) = 7\", \"b\": \"f(2) = 9\", \"c\": \"f(2) = 11\", \"d\": \"f(2) = 5\"}}","_debug_options_count":4},{"id":43684,"question":"Dans un triangle ABC, si AB = 5 cm, BC = 12 cm et AC = 13 cm, alors ce triangle est rectangle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"On vérifie avec le théorème de Pythagore : 5² + 12² = 25 + 144 = 169 = 13². Le triangle est donc rectangle en B.","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}]