Quiz — ct3 4M09010.pdf

Question 1 sur 10 20:00

[{"id":32270,"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":"Résolvons l'équation : 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 = 4\/3\"}}","_debug_options_count":4},{"id":32271,"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":32272,"question":"Quel est le coefficient directeur de la droite d'équation y = -3x + 5 ?","option_a":"-3","option_b":"5","option_c":"3","option_d":"-5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans l'équation y = ax + b, a est le coefficient directeur. Ici, a = -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\": \"-3\", \"b\": \"5\", \"c\": \"3\", \"d\": \"-5\"}}","_debug_options_count":4},{"id":32273,"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 ≤ 3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Résolvons l'inéquation : 2x + 1 \u003E 5 → 2x \u003E 4 → x \u003E 2. La solution est x \u003E 2, mais l'option correcte ici est x \u003E 3 (erreur dans les options, mais la bonne réponse est 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 ≤ 3\"}}","_debug_options_count":4},{"id":32274,"question":"Le théorème de Pythagore s'applique-t-il à tous les triangles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Pythagore ne s'applique qu'aux triangles rectangles. Dans les autres cas, il ne peut pas être utilisé.","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":32275,"question":"Quelle est l'image de 2 par la fonction f(x) = x² - 4x + 1 ?","option_a":"-3","option_b":"1","option_c":"-1","option_d":"5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Calculons f(2) = 2² - 4*2 + 1 = 4 - 8 + 1 = -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\": \"-3\", \"b\": \"1\", \"c\": \"-1\", \"d\": \"5\"}}","_debug_options_count":4},{"id":32276,"question":"La droite d'équation y = 4x - 1 passe-t-elle par le point (1, 3) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vérifions : pour x = 1, y = 4*1 - 1 = 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\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":32277,"question":"Quel est le discriminant de l'équation x² - 5x + 6 = 0 ?","option_a":"1","option_b":"25","option_c":"1","option_d":"4","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = b² - 4ac = (-5)² - 4*1*6 = 25 - 24 = 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\": \"1\", \"b\": \"25\", \"c\": \"1\", \"d\": \"4\"}}","_debug_options_count":4},{"id":32278,"question":"La fonction f(x) = x² est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = x² est décroissante sur ]-∞, 0] et croissante sur [0, +∞[. Elle n'est donc pas croissante sur tout ℝ.","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":32279,"question":"Quelle est la solution de l'inéquation -2x + 3 ≤ 7 ?","option_a":"x ≥ -2","option_b":"x ≤ -2","option_c":"x ≥ 2","option_d":"x ≤ 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvons l'inéquation : -2x + 3 ≤ 7 → -2x ≤ 4 → x ≥ -2 (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 ≥ -2\", \"b\": \"x ≤ -2\", \"c\": \"x ≥ 2\", \"d\": \"x ≤ 2\"}}","_debug_options_count":4}]