Quiz — تصحيح الإختبار الأول لــ 2 عت 2014 ث أحمد قسوس.doc

Question 1 sur 10 20:00

[{"id":28970,"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 = 4\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 7, on ajoute 5 des deux côtés : 3x = 12, puis on divise par 3 : x = 4. Cette méthode est fondamentale en algèbre.","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 = 4\/3\"}}","_debug_options_count":4},{"id":28971,"question":"La fonction f(x) = 2x + 3 est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction affine f(x) = ax + b est croissante si a \u003E 0. Ici, a = 2 \u003E 0, donc la fonction est bien croissante sur ℝ.","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":28972,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"a","explication":"x² - 9 est une différence de carrés : x² - 3² = (x - 3)(x + 3). Cette identité remarquable est essentielle en algèbre.","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 - 3)(x + 3)\", \"b\": \"(x - 9)(x + 1)\", \"c\": \"(x - 3)²\", \"d\": \"(","_debug_options_count":4},{"id":28973,"question":"L'inéquation 2x + 5 ≤ 11 a pour solution x ≤ 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvons l'inéquation : 2x ≤ 6 → x ≤ 3. La solution est bien x ≤ 3, 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\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":28974,"question":"Quel est le coefficient directeur de la droite d'équation y = -4x + 7 ?","option_a":"-4","option_b":"7","option_c":"4","option_d":"-7","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans l'équation y = ax + b, a est le coefficient directeur. Ici, a = -4, donc le coefficient directeur est -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\": \"-4\", \"b\": \"7\", \"c\": \"4\", \"d\": \"-7\"}}","_debug_options_count":4},{"id":28975,"question":"La somme des angles d'un triangle est égale à 180°.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale de la géométrie plane : la somme des angles internes d'un triangle est toujours égale à 180 degrés.","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":28976,"question":"Résolvez l'inéquation : -2x + 8 \u003E 0.","option_a":"x \u003C 4","option_b":"x \u003E 4","option_c":"x ≤ 4","option_d":"x ≥ 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvons : -2x \u003E -8 → x \u003C 4 (en divisant par un nombre négatif, on change le sens de l'inégalité).","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 \u003C 4\", \"b\": \"x \u003E 4\", \"c\": \"x ≤ 4\", \"d\": \"x ≥ 4\"}}","_debug_options_count":4},{"id":28977,"question":"Quelle est l'image de 2 par la fonction f(x) = x² - 3x + 1 ?","option_a":"f(2) = -1","option_b":"f(2) = 1","option_c":"f(2) = 3","option_d":"f(2) = -3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Calculons f(2) = 2² - 3×2 + 1 = 4 - 6 + 1 = -1. Cette question teste l'application directe d'une fonction.","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(2) = -1\", \"b\": \"f(2) = 1\", \"c\": \"f(2) = 3\", \"d\": \"f(2) = -3\"}}","_debug_options_count":4},{"id":28978,"question":"Le produit de deux nombres négatifs est toujours positif.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une règle fondamentale de l'arithmétique : (-a) × (-b) = a × b \u003E 0. Cette propriété est essentielle en calcul algébrique.","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":28979,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 5 ou x = 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Factorisons : (x - 2)(x - 3) = 0 → x = 2 ou x = 3. Cette équation du second degré est un classique du programme.","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 = 2 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4}]