Quiz — corrigé_s12.pdf

Question 1 sur 10 20:00

[{"id":19329,"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 = 10\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 10, on ajoute d'abord 5 aux 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 = 10\/3\"}}","_debug_options_count":4},{"id":19330,"question":"La fonction f(x) = 2x² - 3x + 1 est une fonction linéaire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction linéaire est de la forme f(x) = ax + b. Ici, le terme x² montre qu'il s'agit d'une fonction du second degré.","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":19331,"question":"Quel est le discriminant de l'équation x² - 4x + 4 = 0 ?","option_a":"Δ = 0","option_b":"Δ = 4","option_c":"Δ = -4","option_d":"Δ = 16","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant Δ = b² - 4ac = (-4)² - 4(1)(4) = 16 - 16 = 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\": \"Δ = 0\", \"b\": \"Δ = 4\", \"c\": \"Δ = -4\", \"d\": \"Δ = 16\"}}","_debug_options_count":4},{"id":19332,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est le théorème de Pythagore : c² = a² + b², où c est l'hypoténuse.","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":19333,"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 se calcule terme par terme : (5x³)' = 15x², (-2x²)' = -4x, (x)' = 1, (-7)' = 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":19334,"question":"La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'un événement impossible est 0, tandis que celle d'un événement certain est 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":19335,"question":"Quelle est la solution de l'inéquation 2x + 3 \u003E 7 ?","option_a":"x \u003E 2","option_b":"x \u003E -2","option_c":"x \u003C 2","option_d":"x \u003C -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"On soustrait 3 des deux côtés (2x \u003E 4), puis on divise par 2 (x \u003E 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\": \"x \u003E 2\", \"b\": \"x \u003E -2\", \"c\": \"x \u003C 2\", \"d\": \"x \u003C -2\"}}","_debug_options_count":4},{"id":19336,"question":"Le centre de gravité d'un triangle est le point d'intersection des médianes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le centre de gravité est bien le point d'intersection des médianes, et il divise chaque médiane dans un rapport de 2:1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":19337,"question":"Quelle est la formule de l'aire d'un cercle de rayon r ?","option_a":"A = πr²","option_b":"A = 2πr","option_c":"A = πr","option_d":"A = 4πr²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'aire d'un cercle est donnée par la formule A = πr², où r est le rayon.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A = πr²\", \"b\": \"A = 2πr\", \"c\": \"A = πr\", \"d\": \"A = 4πr²\"}}","_debug_options_count":4},{"id":19338,"question":"La médiane d'un triangle est une droite qui passe par un sommet et le milieu du côté opposé.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, une médiane relie un sommet au milieu du côté opposé.","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}]