Quiz — Revision math - Mr Bouaziz - 33 series.pdf

Question 1 sur 10 20:00

[{"id":53177,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -12","option_d":"x = 10","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 7 = 2x + 5, on soustrait 2x des deux côtés : x - 7 = 5, puis on ajoute 7 : 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\": \"x = 12\", \"b\": \"x = 2\", \"c\": \"x = -12\", \"d\": \"x = 10\"}}","_debug_options_count":4},{"id":53178,"question":"Le triangle ABC est rectangle en A avec AB = 3 cm et AC = 4 cm. Quelle est la longueur de BC ?","option_a":"5 cm","option_b":"7 cm","option_c":"√7 cm","option_d":"√34 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, BC² = AB² + AC² = 9 + 16 = 25, donc BC = 5 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\": \"5 cm\", \"b\": \"7 cm\", \"c\": \"√7 cm\", \"d\": \"√34 cm\"}}","_debug_options_count":4},{"id":53179,"question":"La fonction f(x) = x² - 4x + 3 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction est positive seulement pour x ≤ 1 ou x ≥ 3. Elle est négative entre 1 et 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":53180,"question":"Quelle est la dérivée de la fonction f(x) = 5x³ - 2x² + x - 7 ?","option_a":"f'(x) = 15x² - 4x + 1","option_b":"f'(x) = 5x² - 2x + 1","option_c":"f'(x) = 15x² - 4x","option_d":"f'(x) = 5x³ - 4x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 5x³ est 15x², celle de -2x² est -4x, celle de x est 1, et celle de -7 est 0.","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) = 15x² - 4x + 1\", \"b\": \"f'(x) = 5x² - 2x + 1\", \"c\": \"f'(x","_debug_options_count":4},{"id":53181,"question":"Dans une classe de 30 élèves, 18 sont des filles. Quelle est la probabilité de choisir une fille au hasard ?","option_a":"0,6","option_b":"0,4","option_c":"18\/30","option_d":"30\/18","option_e":"","option_f":"","bonne_reponse":"c","explication":"La probabilité est le rapport du nombre de filles sur le nombre total d'élèves : 18\/30 = 0,6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0,6\", \"b\": \"0,4\", \"c\": \"18\/30\", \"d\": \"30\/18\"}}","_debug_options_count":4},{"id":53182,"question":"Le vecteur u(2; -3) et le vecteur v(-4; 6) sont-ils colinéaires ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les vecteurs sont colinéaires car v = -2 × u (coordonnées proportionnelles).","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":53183,"question":"Quelle est la solution de l'inéquation 2x + 5 \u003E 3x - 1 ?","option_a":"x \u003C 6","option_b":"x \u003E 6","option_c":"x \u003C -6","option_d":"x \u003E -6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En soustrayant 2x et en ajoutant 1, on obtient 6 \u003E x, soit x \u003C 6.","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 6\", \"b\": \"x \u003E 6\", \"c\": \"x \u003C -6\", \"d\": \"x \u003E -6\"}}","_debug_options_count":4},{"id":53184,"question":"La moyenne d'une série de 5 notes est 12. Si on ajoute une 6ème note de 14, quelle est la nouvelle moyenne ?","option_a":"12,33","option_b":"12,5","option_c":"13","option_d":"12","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme des 5 notes est 60. En ajoutant 14, la nouvelle somme est 74, donc la moyenne est 74\/6 ≈ 12,33.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"12,33\", \"b\": \"12,5\", \"c\": \"13\", \"d\": \"12\"}}","_debug_options_count":4},{"id":53185,"question":"La fonction f(x) = 1\/x est-elle définie en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction 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":53186,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"a","explication":"x² - 9 est une différence de carrés : (x - 3)(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 - 3)(x + 3)\", \"b\": \"(x - 9)(x + 1)\", \"c\": \"(x - 3)²\", \"d\": \"(","_debug_options_count":4}]