Quiz — devoir-de-synthèse-n°2--2012-2013(mosrati-chawki).pdf

Question 1 sur 10 20:00

[{"id":5196,"question":"Quelle est la forme canonique d'une fonction trinôme du second degré f(x) = ax² + bx + c ?","option_a":"f(x) = a(x - α)² + β","option_b":"f(x) = a(x + α)² + β","option_c":"f(x) = a(x - α) + β","option_d":"f(x) = a(x + α)² - β","option_e":"","option_f":"","bonne_reponse":"a","explication":"La forme canonique d'une fonction trinôme est f(x) = a(x - α)² + β, où α et β sont les coordonnées du sommet de la parabole.","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) = a(x - α)² + β\", \"b\": \"f(x) = a(x + α)² + β\", \"c\": \"f","_debug_options_count":4},{"id":5197,"question":"L'équation x² - 5x + 6 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant Δ = (-5)² - 4*1*6 = 25 - 24 = 1 \u003E 0, donc l'équation admet deux solutions réelles distinctes.","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":5198,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 2x + 5 ?","option_a":"f'(x) = 6x - 2","option_b":"f'(x) = 3x - 2","option_c":"f'(x) = 6x² - 2x","option_d":"f'(x) = 3x² - 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par 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\": \"f'(x) = 6x - 2\", \"b\": \"f'(x) = 3x - 2\", \"c\": \"f'(x) = 6x² - 2x\",","_debug_options_count":4},{"id":5199,"question":"Dans une pyramide à base carrée, si l'arête latérale mesure 5 cm et la hauteur 4 cm, quelle est la longueur de l'arête de la base ?","option_a":"3 cm","option_b":"4 cm","option_c":"√7 cm","option_d":"√41 cm","option_e":"","option_f":"","bonne_reponse":"b","explication":"En utilisant le théorème de Pythagore dans la section triangulaire, on trouve que la moitié de l'arête de la base est √(5² - 4²) = 3 cm, donc l'arête complète mesure 4 cm.","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 cm\", \"b\": \"4 cm\", \"c\": \"√7 cm\", \"d\": \"√41 cm\"}}","_debug_options_count":4},{"id":5200,"question":"La fonction f(x) = x³ est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² est toujours positive (sauf en x=0 où elle est nulle), donc la fonction est strictement croissante.","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":5201,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 1","option_b":"x \u003E 4","option_c":"x \u003C 4","option_d":"x \u003E -1","option_e":"","option_f":"","bonne_reponse":"b","explication":"En résolvant l'inéquation : 2x \u003E 8 → x \u003E 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\": \"x \u003E 1\", \"b\": \"x \u003E 4\", \"c\": \"x \u003C 4\", \"d\": \"x \u003E -1\"}}","_debug_options_count":4},{"id":5202,"question":"Un dé équilibré est lancé deux fois. Quelle est la probabilité d'obtenir deux fois le chiffre 6 ?","option_a":"1\/6","option_b":"1\/12","option_c":"1\/36","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"c","explication":"La probabilité d'obtenir un 6 est 1\/6. Pour deux lancers indépendants, la probabilité est (1\/6) * (1\/6) = 1\/36.","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\/6\", \"b\": \"1\/12\", \"c\": \"1\/36\", \"d\": \"1\/2\"}}","_debug_options_count":4},{"id":5203,"question":"La section d'un cube par un plan parallèle à une face est toujours un carré.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un plan parallèle à une face d'un cube coupe les arêtes selon des segments de même longueur, formant ainsi un carré.","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":5204,"question":"Quelle est l'expression développée de (x + 3)(x - 2) ?","option_a":"x² + x - 6","option_b":"x² - x - 6","option_c":"x² + x + 6","option_d":"x² - 6x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En développant : x² - 2x + 3x - 6 = x² + x - 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\": \"x² + x - 6\", \"b\": \"x² - x - 6\", \"c\": \"x² + x + 6\", \"d\": \"x² -","_debug_options_count":4},{"id":5205,"question":"La fonction f(x) = 1\/x est définie pour tout x réel.","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}]