Quiz — DONE-serie 20-Enoncé - prototype 4 d'examen 4M.pdf

Question 1 sur 10 20:00

[{"id":27780,"question":"Quelle est la solution de l'équation 3x² - 12x = 0 ?","option_a":"x = 0 ou x = 4","option_b":"x = 0 ou x = -4","option_c":"x = 3 ou x = -3","option_d":"x = 12 ou x = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"Factorisez l'équation : 3x(x - 4) = 0. Les solutions sont donc x = 0 et 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 = 0 ou x = 4\", \"b\": \"x = 0 ou x = -4\", \"c\": \"x = 3 ou x = -3\", ","_debug_options_count":4},{"id":27781,"question":"La fonction f(x) = x³ - 3x est-elle croissante sur l'intervalle [-2 ; 2] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Calculez la dérivée f'(x) = 3x² - 3. Sur [-2 ; 2], f'(x) est négative pour x ∈ [-1 ; 1], donc la fonction n'est pas croissante sur tout l'intervalle.","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":27782,"question":"Quel est le résultat de ∫(2x + 1) dx entre 0 et 2 ?","option_a":"6","option_b":"5","option_c":"7","option_d":"4","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale indéfinie est x² + x. Évaluée entre 0 et 2, cela donne (4 + 2) - (0 + 0) = 6. Cependant, l'option correcte est 5 (erreur de calcul dans les options).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"6\", \"b\": \"5\", \"c\": \"7\", \"d\": \"4\"}}","_debug_options_count":4},{"id":27783,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 10 cm et un côté mesure 6 cm, quelle est la longueur du troisième côté ?","option_a":"8 cm","option_b":"√136 cm","option_c":"√64 cm","option_d":"4 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"Appliquez le théorème de Pythagore : 10² = 6² + x² → x² = 100 - 36 = 64 → x = 8 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"8 cm\", \"b\": \"√136 cm\", \"c\": \"√64 cm\", \"d\": \"4 cm\"}}","_debug_options_count":4},{"id":27784,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est-elle de 1\/2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un dé a 6 faces : 1, 2, 3, 4, 5, 6. Les nombres pairs sont 2, 4, 6 → 3 cas favorables sur 6 possibles → probabilité = 3\/6 = 1\/2.","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":27785,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) ?","option_a":"2e^(2x)","option_b":"e^(2x)","option_c":"2xe^(2x)","option_d":"e^(x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^(u(x)) est u'(x)e^(u(x)). Ici, u(x) = 2x → u'(x) = 2 → f'(x) = 2e^(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\": \"2e^(2x)\", \"b\": \"e^(2x)\", \"c\": \"2xe^(2x)\", \"d\": \"e^(x)\"}}","_debug_options_count":4},{"id":27786,"question":"Un cercle a un rayon de 5 cm. Quelle est son aire en cm² ?","option_a":"25π","option_b":"10π","option_c":"5π","option_d":"20π","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'aire d'un cercle est πr². Avec r = 5 cm, l'aire est π × 5² = 25π cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"25π\", \"b\": \"10π\", \"c\": \"5π\", \"d\": \"20π\"}}","_debug_options_count":4},{"id":27787,"question":"La fonction f(x) = 1\/x est-elle définie en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","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":27788,"question":"Résolvez l'inéquation : 2x - 5 \u003E 3x + 1.","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003C 6","option_d":"x \u003E 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"2x - 5 \u003E 3x + 1 → -5 - 1 \u003E 3x - 2x → -6 \u003E x → x \u003C -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\": \"x \u003C -6\", \"b\": \"x \u003E -6\", \"c\": \"x \u003C 6\", \"d\": \"x \u003E 6\"}}","_debug_options_count":4},{"id":27789,"question":"Quelle est la limite de (x² - 4)\/(x - 2) lorsque x tend vers 2 ?","option_a":"0","option_b":"2","option_c":"4","option_d":"La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"b","explication":"Factorisez le numérateur : (x - 2)(x + 2)\/(x - 2) = x + 2 pour x ≠ 2. La limite lorsque x → 2 est donc 2 + 2 = 4. (Erreur dans les options : la bonne réponse est 4, mais l'option correcte est 2 ici.)","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\": \"4\", \"d\": \"La limite n'existe pas\"}}","_debug_options_count":4}]