Quiz — Lycée Pilote Médenine - DC 2 2015.pdf

Question 1 sur 10 20:00

[{"id":14749,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12\/3","option_c":"x = 2","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 5 = 7 ⇒ 3x = 12 ⇒ x = 4. La solution est donc x = 4.","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 = 4\", \"b\": \"x = 12\/3\", \"c\": \"x = 2\", \"d\": \"x = -2\"}}","_debug_options_count":4},{"id":14750,"question":"La fonction f(x) = 2x + 3 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b. Ici, a = 2 et b = 3, donc c'est bien une fonction affine.","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":14751,"question":"Quel est le milieu du segment [AB] avec A(2; 5) et B(6; 9) ?","option_a":"(4; 7)","option_b":"(8; 14)","option_c":"(4; 14)","option_d":"(2; 2)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le milieu M a pour coordonnées ((xA + xB)\/2 ; (yA + yB)\/2) = ((2+6)\/2 ; (5+9)\/2) = (4; 7).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"(4; 7)\", \"b\": \"(8; 14)\", \"c\": \"(4; 14)\", \"d\": \"(2; 2)\"}}","_debug_options_count":4},{"id":14752,"question":"L'inéquation 2x + 1 \u003E 5 a pour solution :","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E 3","option_d":"x \u003C 3","option_e":"","option_f":"","bonne_reponse":"c","explication":"2x + 1 \u003E 5 ⇒ 2x \u003E 4 ⇒ x \u003E 2. La solution est donc x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"x \u003E 2\", \"b\": \"x \u003C 2\", \"c\": \"x \u003E 3\", \"d\": \"x \u003C 3\"}}","_debug_options_count":4},{"id":14753,"question":"La représentation graphique d'une fonction linéaire passe-t-elle toujours par l'origine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction linéaire s'écrit f(x) = ax. Elle passe donc toujours par le point (0; 0), l'origine du repère.","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":14754,"question":"Quelle est l'image de x = -1 par la fonction f(x) = x² - 3x + 2 ?","option_a":"6","option_b":"0","option_c":"-2","option_d":"2","option_e":"","option_f":"","bonne_reponse":"a","explication":"f(-1) = (-1)² - 3*(-1) + 2 = 1 + 3 + 2 = 6. L'image de x = -1 est donc 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\": \"6\", \"b\": \"0\", \"c\": \"-2\", \"d\": \"2\"}}","_debug_options_count":4},{"id":14755,"question":"L'équation de la droite passant par les points A(1; 2) et B(3; 6) est :","option_a":"y = 2x","option_b":"y = x + 1","option_c":"y = 2x + 1","option_d":"y = x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La pente m = (6-2)\/(3-1) = 2. L'équation est y = 2x + b. En utilisant A(1; 2) : 2 = 2*1 + b ⇒ b = 0. Donc y = 2x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"y = 2x\", \"b\": \"y = x + 1\", \"c\": \"y = 2x + 1\", \"d\": \"y = x + 2\"}}","_debug_options_count":4},{"id":14756,"question":"La fonction f(x) = -x² + 4x - 3 est-elle croissante sur l'intervalle [0; 2] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = -2x + 4. Sur [0; 2], f'(x) ≥ 0 ⇒ la fonction est croissante. Donc l'affirmation est vraie.","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":14757,"question":"Quelle est la distance entre les points C(1; -3) et D(4; 1) ?","option_a":"5","option_b":"√7","option_c":"√25","option_d":"√13","option_e":"","option_f":"","bonne_reponse":"c","explication":"La distance CD = √[(4-1)² + (1-(-3))²] = √[9 + 16] = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"5\", \"b\": \"√7\", \"c\": \"√25\", \"d\": \"√13\"}}","_debug_options_count":4},{"id":14758,"question":"La fonction f(x) = 3x - 7 est-elle strictement décroissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La pente de la fonction affine f(x) = 3x - 7 est 3 \u003E 0, 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\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]