Quiz — P-PB09-40-CM.pdf

Question 1 sur 10 20:00

[{"id":134212,"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":134213,"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":134214,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 4 ?","option_a":"f'(x) = 2x + 3","option_b":"f'(x) = x + 3","option_c":"f'(x) = 2x - 4","option_d":"f'(x) = 3x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -4 est 0. Donc f'(x) = 2x + 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\": \"f'(x) = 2x + 3\", \"b\": \"f'(x) = x + 3\", \"c\": \"f'(x) = 2x - 4\", \"d\"","_debug_options_count":4},{"id":134215,"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},{"id":134216,"question":"Quelle est la solution de l'inéquation 2x + 7 \u003E 3x - 1 ?","option_a":"x \u003C 8","option_b":"x \u003E 8","option_c":"x \u003C -8","option_d":"x \u003E -8","option_e":"","option_f":"","bonne_reponse":"a","explication":"On soustrait 2x des deux côtés : 7 \u003E x - 1, puis on ajoute 1 : 8 \u003E x, soit x \u003C 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\": \"x \u003C 8\", \"b\": \"x \u003E 8\", \"c\": \"x \u003C -8\", \"d\": \"x \u003E -8\"}}","_debug_options_count":4},{"id":134217,"question":"La fonction f(x) = 1\/x est définie pour 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":134218,"question":"Quelle est la probabilité de tirer un as dans un jeu de 32 cartes ?","option_a":"1\/8","option_b":"1\/32","option_c":"4\/32","option_d":"1\/4","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un jeu de 32 cartes contient 4 as. La probabilité est donc 4\/32 = 1\/8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\/8\", \"b\": \"1\/32\", \"c\": \"4\/32\", \"d\": \"1\/4\"}}","_debug_options_count":4},{"id":134219,"question":"Le produit de deux nombres négatifs est toujours positif.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par exemple, (-2) × (-3) = 6, qui est positif. La règle est donc vraie.","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":134220,"question":"Quelle est la limite de la fonction f(x) = (3x² - 2x + 1) \/ (x² + 1) quand x tend vers l'infini ?","option_a":"3","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par x², on obtient (3 - 2\/x + 1\/x²) \/ (1 + 1\/x²). Quand x tend vers l'infini, les termes en 1\/x tendent vers 0, donc la limite est 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"3\", \"b\": \"1\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":134221,"question":"Dans un cercle de rayon 5 cm, quelle est la longueur d'un arc de 60° ?","option_a":"5π\/3 cm","option_b":"5π cm","option_c":"10π\/3 cm","option_d":"π\/3 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"La longueur d'un arc est donnée par (θ\/360) × 2πr. Ici, (60\/360) × 2π × 5 = (1\/6) × 10π = 5π\/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\": \"5π\/3 cm\", \"b\": \"5π cm\", \"c\": \"10π\/3 cm\", \"d\": \"π\/3 cm\"}}","_debug_options_count":4}]