Quiz — 66422a946ffbb_Exercice 1 corrigé.pdf

Question 1 sur 10 20:00

[{"id":37630,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"A. 6x - 5","option_b":"B. 3x - 5","option_c":"C. 6x² - 5","option_d":"D. 3x² - 5x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : dérivée de 3x² = 6x, dérivée de -5x = -5, dérivée de 2 = 0. Donc f'(x) = 6x - 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\": \"A. 6x - 5\", \"b\": \"B. 3x - 5\", \"c\": \"C. 6x² - 5\", \"d\": \"D. 3x² -","_debug_options_count":4},{"id":37631,"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":37632,"question":"Résolvez l'équation : 2(x - 3) = 4x + 1. Quelle est la solution ?","option_a":"A. x = -7\/2","option_b":"B. x = 7\/2","option_c":"C. x = -3","option_d":"D. x = 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Développons : 2x - 6 = 4x + 1 → 2x - 4x = 1 + 6 → -2x = 7 → x = -7\/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\": \"A. x = -7\/2\", \"b\": \"B. x = 7\/2\", \"c\": \"C. x = -3\", \"d\": \"D. x = 3","_debug_options_count":4},{"id":37633,"question":"Quelle est la limite de la fonction f(x) = (x² - 4)\/(x - 2) lorsque x tend vers 2 ?","option_a":"A. 0","option_b":"B. 4","option_c":"C. Indéterminée","option_d":"D. -4","option_e":"","option_f":"","bonne_reponse":"b","explication":"Factorisons le numérateur : (x-2)(x+2)\/(x-2) = x+2 pour x ≠ 2. Donc la limite lorsque x→2 est 2+2 = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 4\", \"c\": \"C. Indéterminée\", \"d\": \"D. -4\"}}","_debug_options_count":4},{"id":37634,"question":"Dans un triangle ABC, si AB = 5 cm, BC = 7 cm et AC = 8 cm, alors le triangle est :","option_a":"A. Rectangle en A","option_b":"B. Rectangle en B","option_c":"C. Rectangle en C","option_d":"D. Non rectangle","option_e":"","option_f":"","bonne_reponse":"d","explication":"Vérifions avec le théorème de Pythagore : 5² + 7² = 25 + 49 = 74 ≠ 8² = 64. Le triangle n'est pas rectangle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"A. Rectangle en A\", \"b\": \"B. Rectangle en B\", \"c\": \"C. Rectangle ","_debug_options_count":4},{"id":37635,"question":"La fonction f(x) = x³ est-elle paire, impaire ou ni l'une ni l'autre ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction est impaire si f(-x) = -f(x). Ici, f(-x) = (-x)³ = -x³ = -f(x). Donc la fonction est impaire.","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":37636,"question":"Quelle est la solution de l'inéquation : 3x - 7 \u003E 2x + 5 ?","option_a":"A. x \u003E 12","option_b":"B. x \u003C 12","option_c":"C. x \u003E -12","option_d":"D. x \u003C -12","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 2x \u003E 5 + 7 → x \u003E 12. L'inéquation est vérifiée pour tous les x supérieurs à 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\": \"A. x \u003E 12\", \"b\": \"B. x \u003C 12\", \"c\": \"C. x \u003E -12\", \"d\": \"D. x \u003C -12","_debug_options_count":4},{"id":37637,"question":"Le vecteur u(3; -2) a pour norme :","option_a":"A. 1","option_b":"B. √13","option_c":"C. 5","option_d":"D. √5","option_e":"","option_f":"","bonne_reponse":"b","explication":"La norme d'un vecteur (x; y) est √(x² + y²) = √(9 + 4) = √13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 1\", \"b\": \"B. √13\", \"c\": \"C. 5\", \"d\": \"D. √5\"}}","_debug_options_count":4},{"id":37638,"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 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":37639,"question":"Quelle est l'équation de la droite passant par les points A(1; 2) et B(3; 6) ?","option_a":"A. y = 2x","option_b":"B. y = 2x + 1","option_c":"C. y = x + 1","option_d":"D. y = 3x - 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur est (6-2)\/(3-1) = 2. L'équation est y = 2x (car elle passe par l'origine).","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. y = 2x\", \"b\": \"B. y = 2x + 1\", \"c\": \"C. y = x + 1\", \"d\": \"D. y","_debug_options_count":4}]