Quiz — cor ex3 S6 jalleli.pdf

Question 1 sur 10 20:00

[{"id":21639,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0,5 ou x = 2","option_c":"x = -1 ou x = 2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Résolvez l'équation en utilisant le discriminant Δ = b² - 4ac. Ici, Δ = 25 - 16 = 9, donc x = (5 ± 3)\/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 = 1 ou x = 2\", \"b\": \"x = 0,5 ou x = 2\", \"c\": \"x = -1 ou x = 2\",","_debug_options_count":4},{"id":21640,"question":"La fonction f(x) = x² - 4x + 3 est-elle croissante sur l'intervalle [2 ; +∞[ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 2x - 4 est positive pour x ≥ 2, donc la fonction est croissante sur cet intervalle.","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":21641,"question":"Quel est le coefficient directeur de la droite d'équation y = -3x + 5 ?","option_a":"5","option_b":"-3","option_c":"3","option_d":"-5","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur est le nombre devant x dans l'équation réduite d'une droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"5\", \"b\": \"-3\", \"c\": \"3\", \"d\": \"-5\"}}","_debug_options_count":4},{"id":21642,"question":"L'inéquation x² - 3x - 4 ≤ 0 a pour solution :","option_a":"x ∈ [-1 ; 4]","option_b":"x ∈ ]-∞ ; -1] ∪ [4 ; +∞[","option_c":"x ∈ [-4 ; 1]","option_d":"x ∈ ℝ","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvez l'inéquation en trouvant les racines de x² - 3x - 4 = 0, puis déterminez le signe du polynôme.","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 ∈ [-1 ; 4]\", \"b\": \"x ∈ ]-∞ ; -1] ∪ [4 ; +∞[\", \"c\": \"x","_debug_options_count":4},{"id":21643,"question":"Le théorème de Pythagore s'applique-t-il dans un triangle rectangle ?","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.","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":21644,"question":"Quelle est l'image de 2 par la fonction f(x) = 3x + 1 ?","option_a":"4","option_b":"7","option_c":"5","option_d":"-5","option_e":"","option_f":"","bonne_reponse":"b","explication":"Remplacez x par 2 dans l'expression de la fonction : f(2) = 3*2 + 1 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"4\", \"b\": \"7\", \"c\": \"5\", \"d\": \"-5\"}}","_debug_options_count":4},{"id":21645,"question":"La droite d'équation y = 2x - 1 passe-t-elle par le point A(1 ; 1) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Vérifiez si les coordonnées de A satisfont l'équation : 1 = 2*1 - 1 → 1 = 1 (faux, car 1 ≠ 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":21646,"question":"Quel est le sommet de la parabole d'équation y = x² - 4x + 3 ?","option_a":"(2 ; -1)","option_b":"(0 ; 3)","option_c":"(-2 ; 15)","option_d":"(1 ; 0)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le sommet d'une parabole y = ax² + bx + c a pour abscisse x = -b\/(2a). Ici, x = 4\/2 = 2, et y = 4 - 8 + 3 = -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\": \"(2 ; -1)\", \"b\": \"(0 ; 3)\", \"c\": \"(-2 ; 15)\", \"d\": \"(1 ; 0)\"}}","_debug_options_count":4},{"id":21647,"question":"L'équation 3x - 5 = 2x + 1 a pour solution :","option_a":"x = 4","option_b":"x = 6","option_c":"x = -4","option_d":"x = -6","option_e":"","option_f":"","bonne_reponse":"b","explication":"Isoler x : 3x - 2x = 1 + 5 → x = 6.","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 = 4\", \"b\": \"x = 6\", \"c\": \"x = -4\", \"d\": \"x = -6\"}}","_debug_options_count":4},{"id":21648,"question":"La fonction f(x) = (x + 1)\/(x - 2) est-elle définie pour x = 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction n'est pas définie pour x = 2 car le dénominateur s'annule (division par zéro).","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}]