Quiz — annexe S2 principale.pdf

Question 1 sur 10 20:00

[{"id":25404,"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 = 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 5 = 7 ⇒ 3x = 12 ⇒ x = 4. Cette équation est du premier degré, résolue en isolant x.","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 = 6\"}}","_debug_options_count":4},{"id":25405,"question":"La fonction f(x) = 2x + 3 est-elle une fonction linéaire ?","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. Ici, f(x) = 2x + 3 est affine, car elle contient un terme constant.","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":25406,"question":"Quel est le coefficient directeur de la droite d'équation y = -4x + 1 ?","option_a":"1","option_b":"-4","option_c":"4","option_d":"0","option_e":"","option_f":"","bonne_reponse":"b","explication":"Dans une équation de droite y = ax + b, a est le coefficient directeur. Ici, a = -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\": \"1\", \"b\": \"-4\", \"c\": \"4\", \"d\": \"0\"}}","_debug_options_count":4},{"id":25407,"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 stipule 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":25408,"question":"Résoudre l'inéquation 2x + 1 \u003E 5.","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":"a","explication":"2x + 1 \u003E 5 ⇒ 2x \u003E 4 ⇒ x \u003E 2. L'inégalité change de sens si on multiplie ou divise par un nombre négatif.","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 \u003E 2\", \"b\": \"x \u003C 2\", \"c\": \"x \u003E 3\", \"d\": \"x \u003C 3\"}}","_debug_options_count":4},{"id":25409,"question":"Quelle est l'image de 2 par la fonction f(x) = x² - 3x + 2 ?","option_a":"0","option_b":"2","option_c":"-2","option_d":"4","option_e":"","option_f":"","bonne_reponse":"b","explication":"f(2) = 2² - 3×2 + 2 = 4 - 6 + 2 = 0. L'image de 2 est donc 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"2\", \"c\": \"-2\", \"d\": \"4\"}}","_debug_options_count":4},{"id":25410,"question":"Dans un triangle ABC, si AB = 5 cm, BC = 12 cm et AC = 13 cm, est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"13² = 169 et 5² + 12² = 25 + 144 = 169. D'après le théorème de Pythagore, le triangle est rectangle en B.","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":25411,"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 : a² - b² = (a - b)(a + b). Ici, a = x et b = 3.","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":25412,"question":"La droite d'équation y = 5x - 2 passe-t-elle par le point (1, 3) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour x = 1, y = 5×1 - 2 = 3. Le point (1, 3) appartient bien à la 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":25413,"question":"Quel est le résultat de l'expression (3x² - 2x + 1) - (x² + 4x - 3) ?","option_a":"2x² - 6x + 4","option_b":"2x² - 6x - 2","option_c":"4x² + 2x - 2","option_d":"3x² - 6x + 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"On soustrait les termes semblables : (3x² - x²) + (-2x - 4x) + (1 + 3) = 2x² - 6x + 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\": \"2x² - 6x + 4\", \"b\": \"2x² - 6x - 2\", \"c\": \"4x² + 2x - 2\", \"d\": ","_debug_options_count":4}]