Quiz — devoir-de-synthèse-n°3--2014-2015(mr-meddeb-tarek).pdf

Question 1 sur 10 20:00

[{"id":39070,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A. 6x + 2","option_b":"B. 3x + 2","option_c":"C. 6x² + 2x","option_d":"D. 6x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation terme à terme : f'(x) = 6x + 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. 6x + 2\", \"b\": \"B. 3x + 2\", \"c\": \"C. 6x² + 2x\", \"d\": \"D. 6x - ","_debug_options_count":4},{"id":39071,"question":"L'équation x² - 4x + 4 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0, donc l'équation admet une solution double (x = 2).","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":39072,"question":"Quelle est la médiane d'une série statistique dont les valeurs sont : 12, 15, 18, 20, 22, 25 ?","option_a":"A. 16","option_b":"B. 18","option_c":"C. 19","option_d":"D. 20","option_e":"","option_f":"","bonne_reponse":"c","explication":"La médiane est la moyenne des deux valeurs centrales (18 et 20), soit (18+20)\/2 = 19.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 16\", \"b\": \"B. 18\", \"c\": \"C. 19\", \"d\": \"D. 20\"}}","_debug_options_count":4},{"id":39073,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à :","option_a":"A. La somme des carrés des deux autres côtés","option_b":"B. Le produit des deux autres côtés","option_c":"C. La différence des carrés des deux autres côtés","option_d":"D. La moitié du produit des deux autres côtés","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est le théorème de Pythagore : c² = a² + b².","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. La somme des carrés des deux autres côtés\", \"b\": \"B. Le pro","_debug_options_count":4},{"id":39074,"question":"La fonction f(x) = 1\/x est-elle 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":39075,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 7 ?","option_a":"A. x \u003E 5","option_b":"B. x \u003C 5","option_c":"C. x \u003E 2","option_d":"D. x \u003C 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"2x - 3 \u003E 7 ⇒ 2x \u003E 10 ⇒ x \u003E 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. x \u003E 5\", \"b\": \"B. x \u003C 5\", \"c\": \"C. x \u003E 2\", \"d\": \"D. x \u003C 2\"}}","_debug_options_count":4},{"id":39076,"question":"Dans une classe de 30 élèves, 40% sont des filles. Combien y a-t-il de garçons ?","option_a":"A. 12","option_b":"B. 18","option_c":"C. 20","option_d":"D. 24","option_e":"","option_f":"","bonne_reponse":"b","explication":"40% de 30 = 12 filles, donc 30 - 12 = 18 garçons.","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. 12\", \"b\": \"B. 18\", \"c\": \"C. 20\", \"d\": \"D. 24\"}}","_debug_options_count":4},{"id":39077,"question":"La fonction f(x) = x³ est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = -x³ ≠ x³, donc elle 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":39078,"question":"Quelle est la valeur de l'expression (2 + 3)² - (2² + 3²) ?","option_a":"A. 0","option_b":"B. 12","option_c":"C. 25","option_d":"D. 10","option_e":"","option_f":"","bonne_reponse":"c","explication":"(2 + 3)² = 25 et (2² + 3²) = 4 + 9 = 13, donc 25 - 13 = 12. La bonne réponse est 12 (option B).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 12\", \"c\": \"C. 25\", \"d\": \"D. 10\"}}","_debug_options_count":4},{"id":39079,"question":"L'aire d'un cercle de rayon r est donnée par la formule :","option_a":"A. πr","option_b":"B. 2πr","option_c":"C. πr²","option_d":"D. 4πr²","option_e":"","option_f":"","bonne_reponse":"c","explication":"La formule de l'aire d'un cercle est A = πr².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. πr\", \"b\": \"B. 2πr\", \"c\": \"C. πr²\", \"d\": \"D. 4πr²\"}}","_debug_options_count":4}]